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Development of error monitoring in preschool to 12th-grade students and relations in late childhood and adolescence to social-affective processing and emotions about math

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Development of error monitoring in preschool to 12th-grade students and relations in late childhood and adolescence to social-affective processing and emotions about math

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Content DEVELOPMENT OF ERROR MONITORING IN PRESCHOOL TO 12TH-GRADE
STUDENTS AND RELATIONS IN LATE CHILDHOOD AND ADOLESCENCE TO
SOCIAL-AFFECTIVE PROCESSING AND EMOTIONS ABOUT MATH
by
Ellyn B. Pueschel
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(DEVELOPMENTAL PSYCHOLOGY)
DECEMBER 2023
Copyright 2023 Ellyn B. Pueschel

ii
Acknowledgements
I wish first to thank my advisor, Dr. Mary Helen Immordino-Yang. Her guidance and
expertise have been indispensable to my development as a researcher and scholar. The rare
combination of constructive mentorship, compassion, and empathy she provides is a privilege I
am truly grateful to have experienced.
I would also like to thank Dr. Santiago Morales for his abundant support and invaluable
mentorship during my dissertation. I am so grateful to have worked with someone so kind,
brilliant, and generous with his time and mentorship.
Additionally, I extend my heartfelt appreciation to Dr. Xiao-Fei Yang for her unwavering
support. Her infectious positivity and remarkable patience are unmatched, and much of my
abilities as a researcher are due to the technical skills she has taught and the confidence she
instilled in me.
Thank you to my committee members, Drs. Jennie Grammer, Yasemin Copur-Gencturk,
and Henrike Moll for their thoughtful support and feedback through this dissertation’s
development, implementation, and analysis. I would also like to extend a special thank you to
Dr. Moll for her mentorship in my first years as a graduate student. I am so grateful for the
opportunity she gave me to pursue my graduate career at USC.
With immense gratitude, I would like to thank the fellow students and colleagues I have
had the pleasure of working with. From the Minds in Development Lab, thank you to Alex
Raport, Vicky Ni, and Wani Qiu for being wonderful sounding boards and supporting me
throughout my research. From the BEAD Lab, thank you to Jenae Cipolla, Leona Abrahamian,
and Isaac Morales for their instrumental assistance with data collection for this dissertation. And
to my amazing colleagues at CANDLE, Dr. Christina Kundrak, Dr. Erik Jahner, Dr. Amirhossein

iii
Ghaderi, Emily Gonzalez, Gina Nadaya, Lisa Luchetta, Katrina Heine, and Mariana De Franca
Steil, I am so grateful to have the opportunity to work with and learn from you all.
I would also like to thank those who supported me during my undergraduate years at San
Diego State University (SDSU). I am grateful for my time at the Brain Development Imaging
Lab, especially for the mentorship from Drs. Inna Fishman and Joanne Jao Keehn, to whom I
undoubtedly owe my foundational skills as a researcher. Thank you also to the Initiative for
Maximizing Student Development (IMSD) program at SDSU, especially Dr. Brittnie Bloom and
Thelma Chavez, for providing the support systems that enabled me even to consider pursuing a
Ph.D.
I would also like to thank my friends and family. To my parents, your constant support,
encouragement, and belief in me have made all of the difference as I have embarked on this
journey. Thank you to my brothers, Brett, Andy, and Matt, and my sister, Josie. I would also like
to thank my extended family, Rob, Katharine, and Jack, for always cheering me on. And most
importantly, thank you to my fiancé, Ben, for being by my side through it all. No one else has
seen the ups and downs of it all quite like you, and your confidence in me and optimism have
been instrumental in my success.
And finally, as someone who cannot work in silence, I would be remiss if I did not thank
my fictional friends who kept me company along the way. Thank you to Shawn Spencer and
Burton Guster for the daily dose of ridiculousness and laughter that made long days and nights of
writing more bearable. Truly, I do not know if I would have made it through without you.
It has been a privilege to have so many people in my corner. Thank you all from the
bottom of my heart.

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Table of Contents
Acknowledgements ...................................................................................................................... ii
List of Tables ................................................................................................................................ v
List of Figures .............................................................................................................................. vi
Abstract ...................................................................................................................................... vii
General Introduction ................................................................................................................... 1
Paper 1: The development of post-error responses from preschool through high school
Abstract .......................................................................................................................................... 8
Introduction .................................................................................................................................... 9
Methods ........................................................................................................................................ 15
Results .......................................................................................................................................... 24
Discussion .................................................................................................................................... 30
Paper 2: Error monitoring as a mechanism by which math anxiety affects math
performance
Abstract ........................................................................................................................................ 37
Introduction .................................................................................................................................. 38
Methods ........................................................................................................................................ 44
Results .......................................................................................................................................... 55
Discussion .................................................................................................................................... 64
Paper 3: Relations among the meaning secondary students make of a true social story and
their patterns of error monitoring and emotions in a math task
Abstract ........................................................................................................................................ 70
Introduction .................................................................................................................................. 71
Methods ........................................................................................................................................ 76
Results .......................................................................................................................................... 86
Discussion .................................................................................................................................... 91
General Discussion ..................................................................................................................... 96
References ................................................................................................................................. 101
Supplemental Information....................................................................................................... 116

v
List of Tables
Table 1-1. Example PES and PEA calculation in the Flanker Task ..............…….…................ 22
Table 1-2. Descriptive statistics by grade level …………………………………………........... 25
Table 1-3. Correlation coefficients of relationships between PEA, PES, IQ, and gender
broken down by grade level………………………..............................………………….……... 26
Table 2-1. Items in the math anxiety and positive feelings about math questionnaires .............. 49
Table 2-2. Example PES and PEA calculation in the math task ................................................. 53
Table 2-3. Correlation coefficients of relationships between measures and demographic
variables ....................................................................................................................................... 56
Table 2-4. Means, standard deviations, and one-way ANOVA by grade level of math
anxiety, positive feelings about math, and generalized anxiety scores ........................................ 57
Table 3-1. Description and examples of meaning-making conceptual categories ...................... 79
Table 3-2. Example PES and PEA calculation in the math task ................................................. 83
Table 3-3. Items in the math anxiety and positive feelings about math questionnaires .............. 85
Table 3-4. Meaning-making and emotion about math scores relations to demographic
variables........................................................................................................................................ 87

vi
List of Figures
Figure 1-1. Visual representation of the Flanker Task ......................................................... 18
Figure 1-2. Example trials during the Flanker Task ............................................................. 21
Figure 1-3. Average PEA and PES by grade level ..................................................................... 28
Figure 1-4. Illustration of the moderation of grade level on the relationship between
PES and PEA ............................................................................................................................... 30
Figure 2-1. Visual representation of the math task .............................................................. 48
Figure 2-2. Example trials during the math task .................................................................. 52
Figure 2-3. Average PES and PEA by grade level ..................................................................... 58
Figure 2-4. Illustration of the moderating effect of grade level on the relationship
between math anxiety and PEA ................................................................................................... 60
Figure 2-5. Visual representation of three-way interaction between math anxiety,
positive feelings about math, and PES ......................................................................................... 63
Figure 3-1. Visual representation of the math task .............................................................. 81
Figure 3-2. Example trials during the math task .................................................................. 83
Figure 3-3. Schematic depicting relations between meaning-making and emotions about
math............................................................................................................................................... 89
Figure 3-4. Visual representation of how concrete meaning-making moderates the
relationship between PES and PEA ............................................................................................. 91

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Abstract
Error monitoring (EM) is the cognitive, affective process by which individuals notice and react
to errors. EM is known to be instrumental in academic learning, however, it remains unclear how
EM develops during the school-aged years and how EM may differ in academic contexts and
relate to social-emotional functioning. In this dissertation, I employ a cross-sectional study
design to investigate developmental patterns of EM in preschool through high school and
examine relationships between EM in math, emotions about math, and broader dispositions of
social processing in older children and adolescents. Participants were 396 students in preschool
through 12th grade. Participants completed a combination of developmentally appropriate study
activities, including EM tasks and questionnaires. I show that EM patterns differ across the
school-aged years and that children engage in EM as early as preschool (Paper 1). Further
investigating how patterns of EM develop in an academic context, I demonstrate that socialaffective experiences during math moderate the effectiveness of children and adolescents’ EM
during a math task (Paper 2). Bridging adolescents’ dispositions of social processing and socialaffective experiences and EM in math, I show that adolescents who engage in more transcendent,
reflective thinking also enjoy math more, and conversely, adolescents who engage in more
concrete, reactive thinking, experience more math anxiety and demonstrate less adaptive patterns
of EM (Paper 3). These findings suggest EM as a potential mechanism connecting socialemotional functioning and learning. This dissertation speaks to the need to educate the "whole
child" in schools.

1
General Introduction
There is a growing awareness in the interdisciplinary education field that academic
learning is rooted in neurological systems that undergo a range of developmental processes,
shaped by cultural experiences, and experienced through social interaction (Immordino-Yang &
Damasio, 2007; Immordino-Yang et al., 2019; Nasir et al., 2021). These insights underscore the
need to support children’s academic learning and social and emotional development in a
coordinated way, a movement referred to as “whole child” education by applied researchers and
educators (Immordino-Yang et al., 2019; Noddings et al., 2005). However, the affective and
cognitive mechanisms that shape academic learning are understudied. A better understanding of
these mechanisms, including their social aspects, can help attune education practices to better
holistically support students’ learning and development. This raises the question: How do
affective and cognitive learning mechanisms manifest in shared patterns across academic and
social contexts?
To begin to address this question, this dissertation focused on error monitoring, the
neuropsychological process by which individuals notice and react to their mistakes. Specifically,
this dissertation examined the behavioral correlates of error monitoring, namely how individuals
slow and improve performance after errors. Examining only these behavioral responses is
sometimes referred to as performance monitoring, as neuroscientific data is needed to confirm
the presence of the neural markers associated with error detection. However, this dissertation
refers to the examination of behavioral error responses as error monitoring.
Error Monitoring is a Cognitive, Affective Process Important for Academic Learning
Engaging with mistakes effectively facilitates academic learning and can promote a
deeper conceptual understanding of complex subjects, such as in math learning (Kapur, 2008,

2
2014). Accordingly, neuroscientific evidence has shown error monitoring capacities to be linked
to academic achievement, for example, in reading and math (Kim et al., 2016), and mindsets
such as growth mindset (Moser et al., 2011) and intellectual humility (Danovitch et al., 2019), as
well as to cooperative learning (Castellar et al., 2011; Koban et al., 2010).
The neural mechanisms of error monitoring also implicate it as an affective process.
Neuropsychological research shows that the anterior cingulate cortex (ACC) is a brain region
involved in emotion processing in social situations and anxiety (Etkin et al., 2011; Somerville et
al., 2016), also known to be involved in error monitoring (Botvinick et al., 2004; Bush et al.,
2000). Through its neural correlates rooted in the ACC, error monitoring has been associated
with negative affect (Hajcak et al., 2004; Hajcak & Foti, 2008; Hill et al., 2016; Luu et al., 2000;
Spunt et al., 2012), and anxiety disorders in adults (Hajcak et al., 2003a; Moser et al., 2013) and
children and adolescents (Carrasco et al., 2013; Kujawa et al., 2016; Lo et al., 2017; Meyer,
2017; Meyer et al., 2016; Weinberg et al., 2015). This confluence suggests the possibility that
error monitoring may be one mechanism that ties academic learning to social and emotional
processing more broadly.
Math Learning as a Particularly Salient Context to Examine Error Monitoring
One academic domain in which the study of error monitoring is particularly relevant is
math learning. In math learning, individuals must navigate complex problem spaces and often
face errors. Moreover, math learning in school is known to be related to life outside of the
classroom. For example, math achievement has been linked to career choices (Ahmed &
Mudrey, 2019) and even financial literacy skills (Skagerlund et al., 2018). Given its importance,
the insights gained from studying error monitoring in this context could have implications even
beyond academic learning.

3
In addition to its complexity and importance for broader learning, math learning is
relevant to the study of error monitoring because it is also well-known to be connected to affect.
For example, many people experience math anxiety (Luttenberger et al., 2018) and math
achievement has even been related to positive affect (Villavicencio & Bernardo, 2016).
Error monitoring and math learning are also similar as they are both known to be
influenced by social contexts. Error responses differ when being observed by peers (Barker et al.,
2018), working as a team (Castellar et al., 2011), and are influenced by cultural (Rapp et al.,
2021) and pedagogical contexts (Denervaud, Knebel, et al., 2020). While math ability is known
to be affected by social situations, such as being under high pressure (Beilock, 2008), and
impacted by broader social contexts, such as harmful gender (e.g., Cvencek et al., 2021;
Robinson-Cimpian et al., 2014) and racial (McKown & Strambler, 2009) biases.
Given this evidence linking both the process of error monitoring and the academic
outcome of math learning to social-affective experiences, perhaps one of the core mechanisms by
which social-affective experiences influence math is error monitoring.
Social-Emotional Dispositions and their Potential Relations to Math Achievement and
Math Anxiety
Recent work has shown that adolescents’ dispositions of mind are not divorced from their
learning. Transcendent thinking, a reflective process that involves “stepping back” and
connecting current happenings to the broader social context, has been related to adolescents’
working memory, long-term memory, creative flexibility, and self-directed executive
functioning. While concrete thinking, a context-dependent, reactive disposition, has been related
to adolescents’ satisfaction with social relationships (Gotlieb et al., 2022a). However, how these
dispositions of mind may emerge in specific academic contexts such as math learning has yet to
be explored. There could be parallels in which these dispositions of mind play out in the patterns

4
of reflective engagement with errors and in terms of propensity towards the enjoyment and
appreciation of math or vulnerability to math anxiety.
Overview of Papers
This dissertation is comprised of three studies written in the form of separate papers for
which I am the lead author. Each paper, when prepared for publication, will be co-authored with
Drs. Xiao-Fei Yang, Santiago Morales, and Mary Helen Immordino-Yang.
Paper 1: The Development of Post-Error Responses from Preschool through High School
Although error monitoring is instrumentally involved in academic learning, its behavioral
responses are most often studied in adults who are beyond formal schooling. There remains a
need to understand better how behavioral responses to errors develop during the school years.
Two behavioral error responses, post-error slowing and post-error accuracy, are thought to be
adaptively related, such that slowing down after errors facilitates accuracy in following trials
(Botvinick et al., 2001). Therefore, this dissertation first investigates how post-error slowing and
post-error accuracy develop from preschool to 12th grade. It was hypothesized that younger
children who tended to slow more after errors, and that older children and adolescents, whose
capacities for error monitoring are more developed, who tended to slow less after errors, would
also tend to be more accurate after errors. Paper 1 revealed that young children demonstrated the
hypothesized patterns. However, that was not the case in older children and adolescents. This
investigation suggests a need to better understand older children and adolescents’ error
monitoring and its relevance to academic learning.
Paper 2: Error Monitoring as a Mechanism by Which Math Anxiety Affects Math
Performance
Research investigations of the relations between error monitoring and academic
achievement most often associate academic performance with error monitoring during standard

5
cognitive tasks that are different from the kinds of activities students do in school to practice
their learning (e.g., Danovitch et al., 2019). Therefore, Paper 2 investigates how children and
adolescents monitor and respond to errors during a math task. Further, while error monitoring
has been associated with general anxiety (Hajcak et al., 2003a), how error monitoring may be
related to math anxiety is understudied. Thus, Paper 2 also investigates whether error monitoring
is a process by which math anxiety affects learning. Findings from Paper 2 revealed that children
and adolescents do exhibit typical behavioral error responses during a math task and that these
responses differed from the same children and adolescents’ patterns in a standard error
monitoring task in Paper 1. This investigation also revealed that error monitoring in a math task
was related to emotions about math. Math anxiety was associated with worse, and positive
feelings about math was associated with better, performance on the math task. The findings also
suggested that children and adolescents with higher levels of math anxiety are not engaging in
adaptive control when slowing after their errors. Paper 2 underscores the need to examine error
monitoring in relevant contexts and suggests that error monitoring may be one mechanism by
which emotions about math are related to math achievement.
Paper 3: Relations Among the Meaning Secondary Students Make of a True Social Story
and Their Patterns of Error Monitoring and Emotions in a Math Task
The third investigation of this dissertation examines whether behavioral responses to
errors during math are potentially connected to math-specific social-emotional functioning and
broader, domain-general social-emotional functioning. Specifically, Paper 3 examined whether
broader dispositions of thinking, namely meaning-making, paralleled social-affective
experiences of learning and error monitoring in math. Paper 3 revealed that adolescents who
engaged in more reflective thinking also reported having more positive feelings about math,
which, in turn, were related to more adaptive patterns of error monitoring. Conversely, a

6
disposition towards reactivity was associated with math anxiety and less adaptive error
monitoring.
Together, these papers give a view of the development of error responses, the context
specificity of error monitoring, and the shared dispositions across the social and academic
domains.
Methodology and Design
This dissertation comprises a cross-sectional study of 396 students in preschool through
12th grade. In a research investigation advised by Drs. Immordino-Yang and Morales, my
colleagues and I collected data in Southern and Central California schools serving primary lowincome youth of color to examine the behavioral correlates of error monitoring across
development, in the context of math learning, and relations to context-specific and broader
social-emotional functioning. We utilized an innovative, school-based mixed-methods design,
including a standard error monitoring task (Flanker Task) and questionnaires about emotions in
math learning. We also developed a novel math task to study behavioral responses during math
in children and adolescents in a way that has not yet been explored. Additionally, this
dissertation integrated a social-emotional meaning-making measure, the qualitative nature of
which provides insights into adolescents’ naturally emerging dispositions of thinking. Depending
on developmental appropriateness, participants could complete some or all of the tasks and
measures. A breakdown of the number of participants who completed each task and measure can
be seen in the Supplemental Information (see page 124).
Depending on age and task completion, participants could be included in one, two, or all
three papers. Paper 1 included participants of any age who completed the Flanker Task. Paper 2
included participants in 3rd grade and older who completed the math task and the emotions about

7
math measures. Paper 3 included participants in 6th grade and older who completed the same
tasks as in Paper 2 in addition to the social-emotional meaning-making task. To illustrate an
example, a preschooler could only be included in Paper 1, while an 8th grader who completed all
of the tasks could be included in Papers 1, 2, and 3.
Significance of Dissertation
The results of this dissertation hold the promise of informing a more comprehensive
understanding of how children and adolescents monitor and respond to errors across the entirety
of formal schooling. The studies proposed in this dissertation are among the first to examine how
students engage with errors in tasks similar to the learning activities they complete in school. By
examining error monitoring in combination with emotions about learning and in examining how
dispositional ways of thinking about the social world may parallel in academic contexts, this
dissertation holds the promise of providing rich insights that afford new understandings of the
shared mechanisms of emotions and learning. In the larger scope of education research, these
findings also hold promise of contributing to the movement of “whole child” education, that is,
reforming educational practices that recognize, in part, the interconnectedness of children’s
social-emotional development and their academic learning. While “whole child” educational
practices are not directly examined in these studies, applied researchers and educators could
build upon insights to examine new ways to support children’s social-emotional functioning and
learning in a coordinated way. For example, examining whether educational practices that aim to
mitigate math anxiety also increase children’s ability to learn from errors, or in turn, whether
better supporting children’s ability to learn from their errors results in decreased math anxiety.

8
Paper 1: The Development of Post-Error Responses from Preschool through High School
Abstract
Two distinct behavioral responses to errors have been established over several decades of
research. However, to date, there has been limited research on the development of these
behavioral responses to errors through childhood and adolescence. Understanding the
development of error monitoring during the school-aged years is of interest because this process
is instrumentally involved in academic learning and has been linked to psychopathology. We
examined post-error slowing and post-error accuracy in 365 participants ages 3 to 18 (M = 11.63,
SD = 3.23) recruited from public schools in low-SES communities. We utilized a child-friendly
version of the Flanker Task and visited schools to test participants in their classrooms. We found
that secondary students were more accurate than pre-and primary-school students. We found an
effect of age on the relationship between post-error slowing and accuracy, such that slowing was
more reliably associated with accuracy in younger children. However, adolescents were more
likely to slow after errors. The findings contribute to knowledge of behavioral responses to errors
in childhood and adolescence in a school context.
Keywords: error monitoring; post-error slowing; cognitive development; preschool; childhood;
adolescence

9
The Development of Post-Error Responses from Preschool through High School
From birth, humans are prone to mistakes—ranging from an infant grasping for a toy just
out of reach to his mother bumping his head while loading him into the car. While these mistakes
can elicit negative emotions (Hajcak et al., 2004), learning how to manage them is important for
functioning in the world. We manage mistakes by engaging in error monitoring, the process by
which individuals detect and respond to inaccurate responses. Substantial research stemming
from cognitive psychology about error monitoring has provided insight into the attentional
control, memory processing, and cognitive flexibility recruited in this process (Taylor et al.,
2007). However, most studies have focused on adults and employed neuroscientific methods
(e.g., Wessel, 2012). There remains a need for further research examining the behavioral
correlates of error monitoring and their development. This is especially prudent for the schoolaged years, as productively engaging with mistakes has been shown to help students develop a
deeper conceptual understanding of their learning (Kapur, 2008). Gaining a better understanding
of behavioral responses to errors may contribute to a more holistic understanding of child
development and, moreover, provide useful insights for ways to leverage the understanding of
error monitoring to support academic learning. Therefore, the present study examined the
behavioral correlates of error monitoring from preschool through high school.
1.1 Behavioral Responses to Errors
Decades of research stemming from cognitive psychology have identified two distinct
behavioral phenomena that occur in response to errors. One of these phenomena is post-error
slowing (PES; Rabbitt, 1966; Ullsperger et al., 2014), broadly measured as the difference in
reaction times between post-error and post-correct responses. While the occurrence of PES is
well established, a clear consensus on its underlying cause is lacking, and instead, there are

10
several competing theories (Dutilh, Vandekerckhove, et al., 2012). The most popular account
suggests that PES is a mechanism of cognitive control that facilitates more cautious behavior
after errors by increasing the time to think and adjust to avoid another error (Botvinick et al.,
2001), which is potentially substantiated by studies that show a link between PES and improved
task performance (e.g., de Mooij et al., 2022; Denervaud, Knebel, et al., 2020). Conversely, it
has also been put forth that PES is driven by attentional mechanisms in response to the
distraction of an error (e.g., Houtman et al., 2012; Houtman & Notebaert, 2013) and that this
may be especially true for infrequent errors (Notebaert et al., 2009). Another proposition is that
PES reflects motor inhibition rather than a conscious response to an error (Kühn et al., 2004).
Studies that show no relationship between PES and task accuracy may support these two theories
(Danielmeier & Ullsperger, 2011).
The lack of understanding of PES may also be confounded by the various ways it is
calculated. The traditional method is to subtract the mean reaction time (RT) pre-error from the
mean RT post-error. This approach can be altered by setting parameters for a trial to be included
in the PES calculation. For example, Denervaud, Knebel, et al. (2020) calculated PES by only
including trials with RT>250 ms and within two standard deviations of the mean RT. Other
variations include calculating PES for congruent and incongruent trials separately (Li et al.,
2023). However, some cautions have been raised about these types of traditional approaches.
One is that motivation may affect PES throughout the task (Dutilh, Van Ravenzwaaij, et al.,
2012). For example, participants may err more and take longer to respond on the latter end of a
task due to decreased motivation. In a recent study, de Mooij et al. (2022) approached this
problem by calculating PES in three different ways that considered the impact of fatigue, general
response speed, and the magnitude of the RT difference and found no significant difference in

11
the main results between the varied measures of PES. Even so, the disconnect between these
theories and the determination of PES puts forward a need for more research examining this
behavioral phenomenon.
The additional behavioral phenomenon in error responses is post-error accuracy (PEA),
sometimes measured as trial-by-trial adjustments that result in changes in accuracy immediately
after making an error (Danielmeier & Ullsperger, 2011) or average accuracy after errors.
Compared to PES, the understanding of PEA is clearer, although there are some discrepancies in
the literature (Danielmeier & Ullsperger, 2011). For instance, some research has suggested that
PEA occurs after only conscious awareness of errors (Klein et al., 2007), while other work,
through the use of neuroscience methods, has demonstrated that PEA can be observed after both
conscious and unconscious detection of errors (e.g., Marco- Pallareś et al., 2008).
1.2 The Development of PES
Similar to the lack of consensus about what underlies PES, its onset and development is
also unclear (see Smulders et al., 2016 for review). In a study examining self-regulatory
processes, Jones et al. (2003) employed a Simon Says task to examine children’s responses to
errors and found evidence of PES in children as young as 39 months. Several studies have shown
that PES linearly increases with age. Hogan et al. (2005) measured error monitoring during a
Flanker Task and found that PES increased with age in participants 12 to 22. Using a similar
approach, Overbye et al. (2019) reported that PES increased within age in their sample of
children and adolescents aged 8 to 19. Further, a study by Santesso & Segalowitz (2008) using
Flanker and Go/NoGo tasks found that 18-year-old males demonstrated more PES than 15-yearold males.

12
However, not all studies have found positive or linear trends in PES. Smulders et al.
(2016) investigated the development of PES in participants aged 5 to 25 and showed a decrease
in PES when responding to a standard two-choice task. In comparison, Denervaud et al. (2021)
reported no differences in PES between children aged 8-12 and adult participants during a
Go/NoGo task. In contrast, de Mooij et al. (2022), in examining error monitoring in an online
learning environment in participants aged 5 to 13, found that PES increased from 6 to 9 years of
age and then decreased from ages 9 to 13. Similarly, Denervaud, Knebel, et al. (2020) found, in a
Flanker Task, that PES increased from ages 4 to 11 and decreased from ages 11 to 15.
Interestingly, Denevevaud, Knebel, et al. (2020) also uncovered a non-linear relationship
between PES and PEA, such that younger children who tended to slow more after errors also
tended to be more accurate after errors and that the reverse was true for older children and
adolescents. Notably, the tasks used in these studies are varied. Potentially clearer developmental
trends could be established with further standardization of tasks or longitudinal studies using the
same task across development.
1.3 Relevant Evidence from Developmental Neuroscience
Though the present study explores the behavioral correlates of error monitoring, much of
what is known about the development of error monitoring in children stems from explorations of
the neural correlates of error responses using EEG methods and warrants review.
Similar to how two behavioral phenomena have been well established, numerous EEG
studies have identified two neural indices of error monitoring: the error-related negativity (ERN)
and the error positivity (Pe) event-related potential (ERP) signals. The ERN is characterized by a
negative deflection signal that peaks approximately 50 to 100 ms after an error (Falkenstein et
al., 1991; Gehring et al., 1993). The Pe is characterized by a signal peak between 200 and 500

13
ms after errors (Falkenstein et al., 1991; Herrmann et al., 2004). It has been posited that the ERN
and the Pe represent different facets of error monitoring. There is increasing evidence that the Pe
is associated with the conscious awareness of errors, such that a larger signal occurs during a
conscious error, as opposed to a nonconscious one (Endrass et al., 2005, 2007; Hajcak et al.,
2003a; Nieuwenhuis et al., 2001; O’Connell et al., 2007). In comparison, the ERN has been
shown not to change dependent on the consciousness of the error (Hoonakker et al., 2016). The
ERN has been shown to be present in children as early as preschool-aged (Brooker et al., 2011;
Brooker & Buss, 2014; Grammer et al., 2014; Morales et al., 2022), and there is much consensus
that the ERN increases with age from early childhood to adolescence (Davies et al., 2010;
Overbye et al., 2019; Tamnes et al., 2013). On the other hand, there is less agreement amongst
the literature on the development of the Pe from childhood, through adolescence, to adulthood.
One developmental investigation found the Pe to increase from the preschool-aged years through
childhood (Grammer et al., 2014), and several other studies have shown that the Pe remains
constant from ages 7 through 25 (Davies et al., 2004; Davies et al., 2010; Overbye et al., 2019;
Santesso et al., 2006; Wiersema et al., 2007). However, somewhat conflicting research has
shown that Pe decreases from adolescence to adulthood (Ladouceur et al., 2007).
Understanding how these neural mechanisms develop is useful when considering
behavioral hypotheses and investigations. For example, the presence of ERN in preschool-aged
children gives reason to further explore and expand on the limited understanding of behavioral
error responses in early childhood. It is also interesting to consider the similarly heterogeneous
findings about the development of Pe and PES (which have also been shown to be related to one
another, e.g., Hajcak et al., 2003b). An increased understanding of either mechanism may inform
the other.

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1.4 Support for the Importance of Error Monitoring in Academic Learning
Compelling evidence has shown children’s error monitoring to be related to their
academic learning and mindsets. For instance, intellectual humility, the ability to understand the
limits of one’s own knowledge capacity, has been associated with error monitoring. One study
showed the ERN to be associated with an ability for self-assessment and an increased Pe (the
amplitude posited to be associated with conscious awareness of an error) to be associated with a
child’s willingness to delegate their questions to an expert (Danovitch et al., 2019). Regarding
academic mindsets, children who embrace growth mindsets, such that they believe their
intelligence is malleable (Dweck, 2008), have been shown to attend to their mistakes more, as
evidenced by a larger Pe and greater PEA (Moser et al., 2011; Schroder et al., 2017). Error
monitoring also appears to play an important role in math and reading achievement. For
example, a disruption in error monitoring capacities has been associated with reading and math
disabilities, as evidenced by a smaller Pe (Burgio-Murphy et al., 2007). Conversely, early strong
reading and math abilities have been associated with increased error monitoring capacities later
in childhood, characterized by a larger Pe (Kim et al., 2016). A noticeable lack of investigations
on academic learning and behavioral error responses suggests a real need for further research in
this area.
1.5 The Present Study
The present study examined the development of behavioral responses to errors from
preschool through high school. We administered a child-friendly Flanker Task to classrooms of
children and adolescents aged 3-18 from public schools in low-SES communities in Southern
and Central California. We hypothesized that a) PEA would increase with age; b) PES would
increase with age but plateau in early adolescence; and c) young children who tended to slow

15
more after errors (i.e., exhibited higher PES), and adolescents who tended to slow less after
errors (i.e., exhibited lower PES), would also tend to be more accurate after errors (i.e.,
demonstrated higher PEA), a shift that is thought to reflect more efficient patterns of error
monitoring as youth age (Denervaud, Knebel, et al., 2020).
2. Methods
2.1 Participants
Participants were 365 children and adolescents between the ages of 3 and 18 (M = 11.63,
SD = 3.23), and were 167 males and 166 females (10 participants identified as non-binary or
selected “other” and 22 were missing gender data). Per a combination of parent and student selfreport, 40 participants identified as Black or African American, 26 Asian, 6 Native American or
Alaskan Native, 7 Native Hawaiian or other Pacific Islander, 101 White, and 128 selected
“other.” One hundred and sixty-one participants identified as Latinx/Hispanic. Due to missing
responses, racial and ethnic identity data was unavailable from 57 and 48 participants,
respectively.
The study was approved by the University of Southern California Institutional Review
Board (UP-22-00308). Consent procedures varied across schools based on their protocols and
preferences. For all preschools and one school serving TK-12th grade, parents received written
consent forms via RedCap (a HIPPA-compliant online data collection platform). The six other
participating schools used opt-out consent, which required anonymous data collection. In the
case of opt-out consent, parents received detailed information sheets outlining the purpose of the
study and its activities. The information sheet also explicitly stated that it was assumed their
child would participate unless the parents returned the form and indicated their decision to opt
their child out by checking the designated box.

16
While opt-out consent allowed for a larger, more diverse sample, it limited the
demographic information we could obtain from participants since it relied solely on student’s
self-report. Not all students knew of specific demographic details, resulting in missing data and
potential inaccuracies. Due to this, we did not include race or socioeconomic status as variables
in analyses. However, we identified school-wide data based on publicly available resources to
represent the racial and socioeconomic diversity of the sample at least descriptively. The median
household income per school zip code ranged from $22,420 to $88,415, averaging $52,660
(United States ZIP Codes, n.d.). The percentage of children eligible for free or reduced-price
lunch across the schools ranged from 31% to 76%, averaging 59.5%, and the range of students
who identify as Black, Indigenous, and other People of Color (BIPOC) across the schools was
71% to 92%, with an average of 82.5% (U.S. News & World Report, n.d.; these estimates
excluded the preschools due to lack of publicly available data). A summary of how many
participants were included from each school can be found in the Supplemental Information (see
page 124).
2.2 Procedure
The study took place while participants were in school. Researchers visited participants’
classrooms for approximately 1.5 - 2 hours. As part of a larger investigation on error monitoring
and social-emotional functioning in academic learning, participants completed a combination of
developmentally appropriate testing activities that could include error monitoring tasks, an IQ
measure, questionnaires, a qualitative survey, and a short video.
2.3 Measures
2.3.1 The Flanker Task

17
To assess error monitoring, participants completed a child-friendly adaptation of the
Flanker Task (Eriksen & Eriksen, 1974). The task was presented via E-Prime software (E-Prime
Go; Psychology Software Tools, 2020) on provided Microsoft Surface 3 tablets (10.52" x 7.36" x
0.34"). A visual representation of the task is presented in Figure 1. In this task, a row of five fish
appears in the center of the screen. Participants are instructed to “help feed the hungry fish” by
pressing either the right or left white arrow sticker on the tablet that corresponds to the direction
in which the middle fish is pointing. The task includes congruent and incongruent trials. In the
congruent trials, the fish surrounding the middle one point in the same direction as the middle
fish, while in the incongruent trials, the surrounding fish point in the opposite direction of the
middle fish.
The task began with a practice block of 10 trials. In the practice block, participants
received trial-by-trial feedback on their performance through a smiling (correct) or frowning
(incorrect) emoji displayed on the screen immediately after their response. Each trial was
preceded by a fixation screen displayed for a time between 500-900 ms. Participants had to be at
least 60% accurate on a practice block to advance to the task blocks. Participants could attempt
as many practice blocks as possible to meet the accuracy threshold. After the practice block(s),
the task consisted of up to 8 blocks, each with 40 trials, for a total of 320 trials. There was a
blank screen of 140 ms between the fixation and the stimulus. Following best practices for
examining error monitoring with children (Brooker et al., 2020; Gavin & Davies, 2008; Lin et
al., 2022; Stieben et al., 2007), we utilized an iterative procedure that changed the stimuli
presentation rate and response time window. In this procedure, we established an initial stimulus
duration of 1500 ms and adapted it based on children’s accuracy every five trials. If children had
100% accuracy during those 5 trials, the stimulus duration was reduced by 50 ms. If children’s

18
accuracy was 60% or below, the stimulus duration increased by 50 ms. Finally, if the accuracy
was 80% (i.e., one error in five trials), the stimulus duration remained the same. Participants did
not receive feedback on the accuracy of their responses; however, a cartoon sloth appeared on
the screen if they were too slow based on the adaptive response window. Participants were told
before starting the task that the presence of the sloth indicated that they should try to respond
faster. Participants were given breaks to wiggle or rest between each block. Preschoolers and
kindergarteners completed the task with direct supervision from an experimenter, either one-onone or in small groups of two to three. In testing sessions with all other participants, the task was
completed by an entire classroom (approximately 15-30 students) simultaneously with one to
three experimenters and their teacher present.
Figure 1
Visual Representation of the Flanker Task
Note. Participants were instructed to complete the task using their index fingers on both hands.
The red and green buttons were not used for this task; they were for a separate game.

19
2.3.2 The Raven’s Standard Progressive Matrices
We measured IQ to be included as a covariate in analyses. Participants completed an
abbreviated, age-appropriate version of the Raven’s Standard Progressive Matrices (Raven,
1998). This test comprises a series of designs with a piece missing, and respondents are asked to
identify the piece required to complete the design from six to eight options shown beneath.
For elementary, middle, and high school participants, a 15-item Raven’s Standard
Progressive Matrices test (Langener et al., 2022) was administered via E-Prime (E-Prime Go;
Psychology Software Tools, 2020). This version included tests for two age groups: 9-12 and 13-
16 years. Participants outside these age ranges completed whichever test was closest to their age.
We opted to administer these shortened versions because they have been shown to be strongly
correlated with scores on the standard 60-item versions (r = 0.89 for 9-12 years and r = 0.93 for
13-16 years; Langener et al., 2022). Participant scores were calculated as the percentage of
correct responses out of the 15 items. The raw accuracy scores were then standardized within
their respective age groups through z-scoring to reduce the correlation with age.
Preschool and kindergarten participants completed the Raven’s 2 Digital Short Form
assessment. This method was selected for the younger participants because it is sensitive to
participants' performance and brief. After completion, the test automatically generated standard
and percentile rankings for each participant. We further standardized the rankings through zscoring within this age group.
2.4 Analysis Overview
2.4.1 Defining Variables
Grade Level. Participants were grouped into four grade levels for analyses:
Preschool/Kindergarten, Elementary, Middle, and High School. This grouping was similar to that

20
in Denervaud, Knebel, et al. (2020), which aimed to reflect transitional periods in schooling. It
also allowed for more participants to be included in analyses of developmental effects because
participants could be grouped based on what school they were tested in (e.g., an Elementary vs.
Middle School) if they were missing age data. Thus, the grade levels were grouped as follows:
the Preschool/Kindergarten level comprised children attending preschools and/or under 7 years
old (N = 31 participants). The Elementary School grade level included children in 3rd and 4th
grade or and/or between the ages of 7 and 10 (N = 125 participants). The Middle School grade
level consisted of participants in 6th-8th grade and/or 11 to 14 years old (N = 148 participants),
and the High School grade level included participants in 10th-12th grade and/or 15+ years old (N
= 54 participants). Seven participants were missing the necessary data to be grouped into a grade
level.
Post-Error Accuracy (PEA) and Post-Error Slowing (PES). PEA was calculated as
the percentage of accurate trials that followed errors. This calculation included missed responses
after errors counted as incorrect; however, as in previous studies involving RT-based tasks with
children (Bowers et al., 2021; Morales et al., 2016), we excluded responses in which participants
responded too quickly (<150ms) from the accuracy calculation.
PES was calculated as the average RT post-error minus average RT pre-error. This
calculation only included correct trials and excluded responses faster than 150ms. Higher PES
scores indicate more slowing after errors. By calculating PES in this way, rather than calculating
average RT post-error minus RT post-correct, we aimed to account for differences in attention
and motivation across the task. For example, suppose a participant is paying attention and highly
motivated at the beginning of the task. In that case, they may be answering many trials correctly,
but as their motivation decreases, they begin making more errors. By calculating average RT pre-

21
and post-error, we aim to capture correct responses as close as possible to errors, possibly
mitigating the effect of attention on the calculation while still capturing differences in pre- and
post-error behavior.
The nature of PES and PEA calculations is such that not all trials are included in the
calculations, nor are the same trials used in each calculation. Figure 2 shows an example set of
20 trials, and Table 1 shows how PES and PEA would be calculated from these trials.
Figure 2.
Example Trials During the Flanker Task
Note. Trial 8 would be excluded from analyses because the reaction time was less than 150 ms.

22
Table 1.
Example PES and PEA Calculation in the Flanker Task
Note. Trial 8 is excluded from the calculations because the RT was less than 150 ms.
It is important to note that measuring the relationship between PES and PEA using these
calculations is not a within-person analysis showing that making an error led to more or less
slowing. Rather, these calculations reflect children and adolescents’ tendencies to generally be
more cautious or more accurate after errors, as in previous studies of error monitoring in children
and adolescents (e.g., Denervaud, Knebel, et al., 2020).
2.4.2 Statistical Overview
All data preparation and statistical analyses were performed using RStudio (version 4.3.0;
R Core team, 2023).
Descriptive Statistics. Pearson correlation tests were run to assess relationships between
each of the predictor and outcome variables. We calculated descriptive statistics on the average
number of trials, number of errors with response, and number of missed trials. We also assessed
whether the typical flanker interference effects were present using one-sample t-tests to
determine if the mean differences in reaction time and accuracy between incongruent and

23
congruent trials significantly differed from zero. Additionally, we calculated the average PEA
and PES and the percentage of participants who exhibited PES (as opposed to no difference in
slowing pre- and post-error, or pre-error slowing).
PES, PEA, and their Relationship across Development. A series of Analysis of
Variance (ANOVA) tests and linear regression models were run to investigate the relationships
between grade level, PES, and PEA. First, in two separate ANOVAs, it was tested whether PEA
and PES differed between grade levels. To probe significant effects of grade level, we conducted
separate linear regression models, with Grade Level dummy coded and the
Preschool/Kindergarten grade level as the reference. Next, to test whether there was a
developmental trend in the relationship between PES and PEA, we ran a two-way ANOVA to
determine whether grade level moderated the relationship between PES and PEA. To probe the
significant moderating effect of grade level, we conducted separate linear regression models,
with Grade Level dummy coded and the Preschool/Kindergarten grade level as the reference. In
addition, to examine the effects within each grade level, we ran separate linear regression models
for each of the four grade-level groups testing the relationship between PES and PEA. All
analyses were controlled for gender, and IQ was added as a control in a second step. If the results
did not differ after IQ was controlled for, only the model with IQ included is reported. If the
results differed, we report the model with and without IQ as a control. Regression tables showing
the differences in each model can be found in the Supplemental Information (see page 126-128).
Removing Outliers. We removed outliers by trimming the data. We used a percentile
approach and determined the upper and lower 5% of the distribution of the total number of errors
with response participants made (a visualization of this distribution can be seen in the
Supplemental Information on page 126). Based on this, we restricted the analyses to only

24
participants who made more than 4 and fewer than 70 errors. Under these parameters, three
participants were removed from the Preschool/Kindergarten group, 20 from the Elementary, 11
from the Middle, and 10 from the High School group. We found that results were similar when
including all data (i.e., not removing outliers); therefore, we only report the analyses with
outliers removed.
3. Results
3.1 Descriptive Statistics
Participants completed an average of 257 trials (range = 33-320, SD = 73.59), made an
average of 25 errors with a response (range = 0-150, SD = 22.13), and did not respond to an
average of 13 trials (range = 0-146, SD = 20.87). Our modified task version exhibited the typical
flanker interference effects. Specifically, reaction times were significantly longer on incongruent
trials than congruent trials, t(364) = 15.49, p < .001. Furthermore, accuracy rates were
significantly lower on incongruent trials than congruent trials, t(364) = 12.74, p < .001.
Additionally, we found that the percentage of participants who exhibited post-error slowing, as
opposed to no difference pre- and post-error, or slowing before errors, was higher in the
secondary school participants than the pre- and primary-school participants, as seen in Table 2
(the distribution of PES by grade level can also be seen in the Supplemental Information, see
page 125).
We examined correlations among each of the predictor and outcome variables. The
resulting coefficients and their significance can be seen in Table 3. Of note, it was found that
across all participants, IQ scores were positively related to PEA (p < .001). However, when
assessed individually within grade levels, results revealed that there was a positive relationship
between PEA and IQ within only the Elementary (p < .001) and Middle School (p = .01) grade

25
levels. There was no relationship within the Preschool/Kindergarten (p = .33) and High School
grade levels (p = .23). Additionally, it was found that female participants demonstrated higher IQ
scores than male participants within only the Elementary School grade level (p = .01).
Table 2.
Descriptive Statistics by Grade Level
Note. The error responses were calculated after removing outliers.

26
Table 3.
Correlation Coefficients of Relationships between PEA, PES, IQ, and Gender Broken Down by
Grade Level
Note. These correlations do not control for any variables. *p < .05, ***p < .001
3.2 The Development of PEA and PES
We found that PEA differed significantly between grade levels, F(3, 227) = 22.03, p <
.001, ηp2 = 0.22. IQ also predicted PEA, F(1, 227) = 21.87, p < .001, ηp2 = 0.09. In accordance

27
with our hypothesis that PEA would increase with grade level, the Elementary, b = 10.37, t(227)
= 3.49, p = .001, Middle, b = 18.43, t(227) = 6.79, p < .001, and High School, b = 20.98, t(227) =
6.66, p < .001 grade levels all showed significantly higher PEA than the Preschool/Kindergarten
grade level.
We found that PES did not differ between grade levels, F(3, 227) = 1.37, p = .25, ηp2 =
0.02. Against our hypothesis that PES would increase until early adolescence and then plateau,
neither the Elementary, b = -.04, t(227) = -.002, p = .99, Middle, b = 21.46, t(227) = 1.16, p =
.25, or High School, b = 23.60, t(227) = 1.10, p = .27 grade levels significantly differed in their
PES from the Preschool/Kindergarten grade level. In fact, in further evidence against our
hypothesis, an exploratory analysis comparing the PES of the pre-and primary-school (the
Preschool/Kindergarten and Elementary School grade levels) and the secondary school (the
Middle and High School grade levels) participants revealed that secondary school participants
showed higher PES than pre- and primary-school participants, b = 21.98, t(229) = 2.03, p = .04.
The average PEA and PES by grade level are depicted in Figure 3.

28
Figure 3.
Average PEA and PES by Grade Level
Note. Averages were calculated after removing outliers and do not account for control variables.
Error bars represent one standard error from the mean.
3.3 The Development of the Relationship between PES and PEA
Grade level was found to moderate the relationship between PES and PEA, F(3, 223) =
4.94, p = .002, ηp2 = .06. The moderating effect of grade level was such that relationship
between PES and PEA was significantly weaker in the Elementary, b = -8.99, t(223) = -3.36, p =
.001, and Middle School, b = -6.27, t(223) = -2.21, p = .03, grade levels as compared to the
Preschool/Kindergarten grade level, b = 6.14, t(223) = 2.68, p = .01. While the relationship
between PES and PEA High School grade level, b = 1.15, t(223) = .25, p = .80 did not differ
significantly from the Preschool/Kindergarten grade level.
To probe this moderation and examine whether the differences among grade level were
aligned with our hypothesis that higher PES would be associated with higher PEA in the younger
participants and lower PES would be associated with higher PEA in the older participants, we
examined the relationship between PES and PEA separately within each grade level. In partial

29
support of our prediction, we found a significant positive relationship between PES and PEA
within the Preschool/Kindergarten grade level, b = .07, t(24) = 2.60, p = .02, ηp2 = .22. However,
against our prediction, the pattern of results within the High School grade level was similar to the
Preschool/Kindergarten grade level, such that there was a non-significant positive trend between
PES and PEA, b = .06, t(39) = 1.87, p = .07, ηp2
= .08. Additionally, no significant relationships
were found in the Elementary, b = -.01, t(91) = -.71, p = .48, ηp2
= .01 or Middle School, b = -
.01, t(123) = -.70, p = .48, ηp2 = .003, grade levels. These relationships within grade levels are
illustrated in Figure 4.
Notably, we found that the relationships between PES and PEA within the grade levels
changed after adding IQ as a control variable in the models. We found that there was no longer a
significant relationship between PES and PEA in the Preschool/Kindergarten grade level, b =
.04, t(17) = 1.28, p = .22, ηp2 = .10. Conversely, the relationship between PES and PEA became
significant in the Elementary, b = -.03, t(50) = -2.19, p = .03, ηp2 = .09, and High School, b =
.07, t(31) = 2.48, p = .02, ηp2 = .16, grade levels. The relationship remained non-significant in
the Middle School grade level, b = -.004, t(117) = -.23, p = .82, ηp2 = .0004.

30
Figure 4.
Illustration of The Moderation of Grade Level on the Relationship between PES and PEA
Note. This graph illustrates the marginal effect of PES on PEA within each grade level while
controlling for gender and excluding outliers.
4. Discussion
Two behavioral indices of error monitoring, PES and PEA, have been well-established in
adults (Ullsperger et al., 2014; Danielmeier & Ullsperger, 2011); however, the literature on the
development of these behaviors in childhood and adolescence is heterogenous (Smulders et al.,
2016). Similarly, how PES and PEA are related across development is not well understood.
Given that error monitoring is linked to academic achievement (Kim et al., 2016), there is a need
to better understand error responses during the school-aged years. To address this gap, we
examined behavioral responses to errors in preschool through high school students.

31
Per our hypothesis, we found that children and adolescents tended to be more accurate
after errors as grade level increased. However, we found opposing evidence for our hypothesis
that children and adolescents’ tendency to slow after errors would decrease and then plateau,
such that there was no significant difference in PES between the grade levels. Further, an
exploratory analysis revealed that the pre-and primary-school (the Preschool/Kindergarten and
Elementary School grade levels) participants slowed significantly less after errors than the
secondary school (the Middle and High School grade levels) participants.
It is not entirely clear how to interpret this trend. Our hypothesis was based on the notion
that a decrease in PES may reflect more efficient patterns of error monitoring that develop with
age, and, potentially, a shift to more proactive, than reactive control (de Mooij et al., 2022;
Denervaud, Knebel, et al. 2020). While the main analyses did not support this prediction,
perhaps this idea was partially supported by the descriptive statistics showing that the percentage
of participants who exhibited PES, instead of speeding up or not changing speed after errors,
increased with grade level. Potentially, this finding reflects that as youth age, they more reliably
engage in error monitoring.
An examination of the literature suggests another possible interpretation of the findings,
such that developmental trends of PES may be related to task differences. Our finding that PES
was higher in older students is aligned with other studies that used similar Flanker Tasks (Hogan
et al., 2005; Overbye et al., 2019), while the studies that used more challenging tasks (e.g., a
math task) found the trend that we expected of PES (de Mooij et al., 2022; Denervaud, Knebel,
et al. 2020; Smulders et al., 2016). Potentially, with a more challenging task, we would have
observed the predicted developmental trend of PES.

32
We also found that grade level moderated the relationship between PES and PEA.
However, in contrast with our hypothesis and the findings of Denervaud, Knebel, et al. (2020), a
probing of the moderation revealed that there was a significant positive relationship between
PES and PEA within the Preschool/Kindergarten grade level and a non-significant trend towards
a positive relationship in the High School grade level. We are unsure how we should interpret
this moderation. While the Preschool/Kindergarten finding aligns with what we expected, such
that younger children who tended to slow down more after errors also tended to be more accurate
after errors, we expected the inverse pattern of the High School participants.
One possible reason we see the unexpected relationship among the High School
participants may be how we removed outliers. Of the Preschool/Kindergarten group, all outlier
participants were removed for making too many errors; conversely, in the High School group,
most outlier participants were removed for making too few errors. In this approach, we may have
overinflated the youngest group’s accuracy and underestimated the oldest group’s. We may also
only see this trend between these two groups due to their considerably smaller sample sizes than
the Elementary and Middle School groups, potentially making the effect of removing outliers
more apparent.
Although support for our hypotheses was mixed, the present study’s findings contribute
to the growing developmental literature on the behavioral correlates of error monitoring. The
most notable contribution is evidence that young children show behavioral responses to errors. In
alignment with Jones et al.’s (2003) report of PES in children as young as 39 months and
Smulders et al.’s (2016) findings of PES at age 5, the present study shows evidence for error
responses as early as 3 years of age. Additionally, the present study shows that while not a
measure of trial-by-trial performance adjustments, the Preschool/Kindergarten participants who

33
tended to slow more after errors also tended to be more accurate after errors, suggesting the
possibility that they are adjusting their performance based on their errors. This is in contrast to a
previous suggestion by Smulders et al. (2016) that while young children can detect their errors,
they are less able to implement performance adjustments.
The present study also suggests potential relations between IQ and error monitoring. In
the Preschool/Kindergarten participants, we found that adding IQ as a control variable resulted in
a non-significant relationship between PES and PEA. For the Elementary grade level, the reverse
was true, such that a negative relationship between PES and PEA became significant when
controlling for IQ, and the positive relationship within the High School grade level became
significant. There is little precedent for this finding in the literature. Of the studies that do report
examining potential differences in IQ, they are often from the Autism and ADHD literature,
using IQ as a matching variable, and these studies show no relationship between IQ and
behavioral responses or neural correlates of error monitoring (Schachar et al., 2004; Vlamings et
al., 2008). Although, one study that examined intellectual humility and error monitoring found a
positive relationship between the ERN (a measure of error detection) and verbal IQ (Danovitch
et al., 2019).
It is also possible that our measure was not properly capturing IQ. Since we examined IQ
as a covariate rather than investigating it as a main variable of interest, we used abbreviated
versions that could be completed in roughly 10 minutes. We also differed the versions by age to
account for developmental differences, which may have led to inconsistent measures of IQ. Most
notably, due to uneven task completion, controlling for IQ significantly decreased the sample
size within each group, which may have also driven these differences. Even considering the

34
limitations of our measure of IQ, perhaps our results suggest an avenue for further research
exploring the relationships between IQ and error monitoring.
A strength of this study was the collection of data while participants were in school
instead of in a lab environment. Using this method, we examined how children and adolescents
reacted to errors in a learning environment and among their peers and teachers. Error monitoring
has been shown to be context-dependent (e.g., Castellar et al., 2011), so potentially, this
approach led to better insight into error monitoring in the context of academic learning. Another
strength of this study was the diverse sample. Although we were unable to examine the specific
effects of racial and socioeconomic differences, our sample is representative of the majorityminority student populations in United States classrooms (Maxwell, 2014) and addresses a
current call in the literature to include more representative youth in psychological studies
(Buchanan et al., 2021; Roberts & Mortenson, 2022). A further strength of the study is that, in
addition to being diverse, our sample included a wide age range of participants. As pointed out
previously, there is a lack of developmental research on behavioral responses to errors, and a
wide age range extending across early childhood to adolescence fills in some of this gap.
Additionally, using only one task across participants of all ages may have helped mitigate the
existing confound of task differences in the current developmental literature.
The current study’s findings and interpretations should be considered regarding several
limitations. First is the missing demographic data. By being unable to control demographic
variables, we may be missing insights into racial or socioeconomic differences in the data.
Secondly, the grade level groups that participants were divided into were uneven. The
Preschool/Kindergarten and High School grade levels had approximately half as many
participants as the Elementary and Middle School grade levels. Given this, our observed

35
differences between the groups should be interpreted cautiously. Additionally, the task may have
needed to be more challenging for the oldest participants. Although we attempted to address this
issue by adapting the task to their speed, the version used may have still been too "childfriendly" for adolescent participants. A traditional Flanker Task that utilizes arrows (e.g., < < > <
<) instead of fish might have been more appropriate. A further methodological limitation was
that testing 20-30 participants at a time (excluding younger children who were tested in small
groups) resulted in less control over the task. Compared to a traditional lab setting, it was more
challenging to ensure that participants were staying on task. For example, some participants took
extended breaks between blocks, resulting in fewer trials due to time constraints. In contrast,
other participants were found to have navigated off the task entirely, using the tablet for nonstudy-related tasks. It is possible that this impact on trials completed affected the results, as
previous studies have shown that identifying a robust developmental trend in PES requires a
substantial number of trials (e.g., Smulders et al., 2016).
The findings of this study and its limitations suggest a few avenues for future research.
Most importantly, forthcoming investigations will have to include longitudinal explorations of
the development of error monitoring, as this was a limitation of the present study and, to our
knowledge, has not been addressed by any other study. Additionally, to better understand the
role of error monitoring in academic learning, future studies should not only test participants in a
school context but use domain-specific tasks more relevant to their learning in subjects such as
math (e.g., de Mooij et al., 2022).
In conclusion, the present study contributes to the growing understanding of the
development of the behavioral indices of error monitoring during the school-aged years. The
findings of this study show tantalizing preliminary evidence that young children engage in

36
adaptive patterns of error monitoring, such that those who tended to slow more also tended to be
more accurate after errors. This study also contributes, although somewhat puzzling, information
on the development of these behavioral error responses through childhood and adolescence.
Taken together, these findings emphasize the need for continued exploration of error monitoring
and its importance for learning during the school-aged years.

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Paper 2: Error Monitoring as a Mechanism by Which Math Anxiety Affects Math
Performance
Abstract
Error monitoring (EM) is the process by which individuals track their performance and fix
errors, such as when doing math problems. EM shares neural correlates with emotion processing,
specifically with the anterior cingulate cortex, a physiologically regulatory brain region. EM has
also been implicated in anxiety. However, most studies of EM have neglected the effects of
context and domain, such that they use domain-general tasks (e.g., a Flanker task). Given this,
here we ask how math anxiety and positive feelings about math among 314 3rd-12th grade
students (Mage = 12.47, SD = 2.55) may relate to behavioral patterns of EM during a novel math
task. Specifically, we examine post-error slowing (PES) and post-error accuracy (PEA). We
found that overall, PES was positively related to PEA during the task and that this relationship
was weaker for students with higher math anxiety. Positive feelings about math were associated
with increased performance, while anxiety was associated with lower performance. When
examining the function of PES, we also found a three-way interaction between math anxiety,
positive feelings about math, and PES to predict PEA: such that slowing was most related to
PEA for students with low math anxiety and low positive feelings about math. Implications for
the relationship between emotions about math and math performance are discussed.
Keywords: error monitoring; post-error slowing; math learning; cognitive development; math
anxiety; positive feelings about math; childhood; adolescence

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Error Monitoring as a Mechanism by Which Math Anxiety Affects Math Performance
Math anxiety is an adverse response to math and mathematical situations (Ashcraft &
Ridley, 2005) and is a pervasive problem across development. Math anxiety occurs in young
children (Ramirez et al., 2013), is widely prevalent in adolescence (Luttenberger et al., 2018;
OECD, 2013), and even persists into adulthood (Blazer, 2011). Individuals with math anxiety
experience tension and anxiety that interferes with solving math problems in academic settings
and manipulating numbers even in everyday life situations (Richardson & Suinn, 1972). In
addition to the psychological effects of tension, apprehension, nervousness, and worry, math
anxiety can induce physiological responses such as increased heart rate, clammy hands, upset
stomach, and lightheadedness (see Luttenberger et al., 2018 for review). Moreover,
neuroscientific evidence has revealed that math-anxious individuals show increased activation in
brain regions associated with pain and emotions before and after engaging in math (e.g., Lyons
& Beilock, 2012).
It has been well-established that math anxiety negatively affects math achievement from
early childhood through adulthood (Barroso et al., 2021; Namkung et al., 2019; Suárez-Pellicioni
et al., 2016; Zhang et al., 2019). However, what underlies this relationship is not fully
understood. In one direction, it could be that students who do poorly in math are more anxious
about their performance. In accordance with this, it has been shown that high math-anxious
individuals have difficulty with basic numerical processing, such as counting and assessing
numerical distance (Maloney et al., 2010, 2011), and a deficit in these skills may contribute to
poor math performance. In the other direction, math anxiety may negatively interfere with the
cognitive processes recruited in math learning. For example, working memory, the process of
regulating and controlling information needed to complete complex cognitive tasks (Miyake &

39
Shah, 1999), is known to be important for math learning (see Friso-van den Bos et al., 2013;
Raghubar et al., 2010 for review). Numerous studies have shown math anxiety to be related to
reduced working memory capacity during math tasks (e.g., Ashcraft & Kirk, 2001; Ashcraft &
Krause, 2007; Passolunghi et al., 2016). It has also been demonstrated that low math-anxious
students exhibit more fluency than high math-anxious students, such that they can more
efficiently, correctly, and effortlessly complete mathematical tasks (Cates & Rhymer, 2003).
However, even though these mechanisms for learning math are influenced by math anxiety, there
has been little investigation into how math anxiety may impact other cognitive processing
instrumental in academic learning.
1.1 Error Monitoring as a Candidate Mechanism Linking Math Anxiety and Math
Performance
Error monitoring is the neuropsychological process by which individuals track their
performance and respond to errors, such as when doing math problems. This process is known to
be affective, as the neural correlates of error monitoring are partially rooted in the anterior
cingulate cortex (ACC; Botvinick et al., 2004), a brain region associated with emotional
processing (Bush et al., 2000). Error monitoring is also context dependent. For example, error
responses differ when being observed by peers (Barker et al., 2018), working as a team (Castellar
et al., 2011), or dependent on cultural context (Rapp et al., 2021). Given what is known about
math anxiety as an affective, context-dependent process, perhaps error monitoring may be one of
the cognitive processes that math anxiety disrupts.
Another indicator that math anxiety may disrupt error monitoring is that research has
shown that math-anxious individuals are aversive to mistakes. For example, young children
report the fear of making mistakes and the difficulty of mathematical tasks as reasons for their

40
math anxiety (Petronzi et al., 2019; Szczygieł & Pieronkiewicz, 2022). Math-anxious individuals
also exhibit increased activity in neural responses related to threat avoidance, even to brief
exposure to math problems (Pizzie & Kraemer, 2017), which may indicate a tendency to avoid
engaging with mistakes.
Additionally, studies have shown that math-anxious individuals may not fully engage
with math problems, affecting their ability to learn from mistakes. For example, math-anxious
students have been shown to speed through math problems during experimental tasks (Pizzie et
al., 2020) and math exams (Núñez-Peña & Bono, 2021), potentially reflecting a desire to “just
get it over with,” which does not leave adequate time to engage with and learn from mistakes.
Moreover, neuroscientific research has shown that math-anxious individuals exhibit reduced
neural activity associated with arithmetic processing during math problems (Pizzie et al., 2020),
possibly reflecting disengagement, also a cognitive state during which learning from mistakes
could be more challenging.
Taken together, this evidence suggests that managing mistakes may be especially difficult
for individuals with math anxiety. Examining error monitoring in relation to math anxiety, a link
that has been underexplored, may help to understand an additional cognitive process recruited in
math learning that math anxiety hinders.
1.2 Behavioral Responses Exhibited During Error Monitoring
Two well-established behavioral responses to errors are post-error accuracy (PEA) and
post-error slowing (PES). PEA is the phenomenon that individuals are more accurate in
responses following errors (Danielmeier & Ullsperger, 2011), and PES occurs when individuals
slow down more after an error than they do after a correct response (Rabbitt, 1966; Ullsperger et
al., 2014). PES has been widely documented; however, the function of PES has been debated

41
(Dutilh, Vandekerckhove, et al., 2012). One of the most prominent theories is that PES is a
cognitive control mechanism that facilitates more cautious behavior to improve performance
post-error (Botvinick et al., 2001). We interpret numerous studies identifying a positive
relationship between PES and PEA to support this account (e.g., de Mooij et al., 2022;
Denervaud, Knebel, et al., 2020).
Conversely, it has been suggested that PES reflects a distraction from the task due to
increased attention to the error, which may lead to worse performance post-error (Notebaert et
al., 2009). There are a few studies that show support for this theory as well (e.g., Houtman &
Notebaert, 2013). This disconnect suggests a need for further investigations of the psychological
underpinnings of PES.
Potentially, differences in PES may reflect the social-emotional processing involved in
learning, such as math anxiety. For example, for high math anxious students, PES may reflect a
freeze response to an error rather than cautious behavior. A study by Núñez-Peña et al. (2017)
may partially support this hypothesis, such that they found that high-math-anxious young adults
were slower and less accurate after errors than low-math-anxious adults. However, further
investigations are needed, especially in children and adolescents.
1.3 Evidence for a Relationship between Error Monitoring and Math Anxiety
Further evidence that error monitoring and math anxiety are related is the known link
between the neural correlates of error monitoring and other anxiety disorders. The primary neural
correlate that has been identified as a link between anxiety and error monitoring is the error
negativity signal (ERN), a negative deflection signal that peaks approximately 50 to 100 ms after
an error (Falkenstein et al., 1991; Gehring et al., 1993) and is thought to be partially generated in
the ACC. Several studies have identified an enhanced ERN in individuals with a range of anxiety

42
disorders, such as generalized anxiety and social anxiety (Kujawa et al., 2016; Moser et al.,
2013; Weinberg et al., 2010, 2015; Xiao et al., 2011), a pattern that has been shown to emerge in
childhood (see Meyer, 2017 for review). Moreover, an enhanced ERN in early childhood has
also been shown to predict social anxiety in later childhood and adolescence (Buzzel et al., 2017;
Filippi et al., 2020; Lahat et al., 2014). In adults one known study identified an increased ERN in
high math-anxious individuals (Suárez-Pellicioni et al., 2013).
1.4 The Importance of Examining Math Anxiety in Coordination with Positive Feelings
about Math
Not all emotions in math learning are negative. Many students enjoy math, and liking
math has been shown to predict the careers students choose, especially in STEM (Ahmed &
Mudrey, 2019). However, the study of positive emotions about math learning is less common
than that of math anxiety. Of what is known, positive feelings about math have been shown to
predict math achievement above and beyond math anxiety (Villavicencio & Bernardo, 2016).
Additionally, positive mood, in general, has been shown to affect working memory (Storbeck &
Maswood, 2016), a cognitive process also known to be influenced by math anxiety (e.g.,
Ashcraft & Kirk, 2001). Error monitoring could also be a mechanism by which positive emotions
about math affect math performance. Students who enjoy math may be less averse to errors and
more comfortable working through their mistakes. Gaining a better understanding of how
positive feelings about math contribute to students’ learning could contribute to knowledge on
how to foster positive emotions about math among students better.
1.5 The Need to Study Error Monitoring in Domain-Specific Tasks
Previous research that has identified links between error monitoring and academic
performance has predominantly relied on correlational analyses between performance on

43
standard conflict monitoring tasks and separate measures of academic achievement (e.g., BurgioMurphy et al., 2007; Danovitch et al., 2019; Kim et al., 2016). In these conflict tasks, such as the
Flanker Task (Eriksen & Eriksen, 1974) and Go/noGo tasks (Nosek & Banaji, 2005), stimuli
range from arrows (e.g., < < > < <), fish, or other animals (Grammer et al., 2014) and are
unrelated to tasks children might engage in at school, such as reading or math. Thus, a real need
remains to understand how individuals respond to errors in domain-specific tasks, particularly
given the research showing this process to be context-dependent. A study by Suárez-Pellicioni et
al. (2013) underscores this need. In comparing participants with high and low math anxiety, they
found no differences during a classical Stroop task in which participants saw stimuli such as
“red” written in blue letters and had to respond to the color the word spelled rather than the color
of the letters. However, differences were observed between the two groups during a numerical
Stroop task, in which participants saw stimuli such as a “2” in large font and a “9” in small font
and had to respond to which number was higher in numerical magnitude, ignoring the physical
size.
A few additional studies with young adults have started to address this domain-specific
gap in the context of math learning. PES has been observed during a variety of math tasks,
including multiplication (Desmet et al., 2012), division (Lavro et al., 2018), and addition
(Núñez-Peña et al., 2017). Two studies have conducted similar explorations with children. In a
non-laboratory task, de Mooij et al. (2022) examined error responses in an existing online
learning platform. They found a non-linear trend of PES in children aged 5 to 13 during addition,
division, and other math-related games, such that PES increased until age 9 and then declined.
Denervaurd, Fornari, et al. (2020) employed a multiplication task with children 8-12 years old
and found neural evidence of error monitoring during this math task. Notably, all but one of

44
these studies (for exception, see Lavro et al., 2018) included feedback in the task procedure, such
that immediately after the response, participants were made aware of the accuracy of their
response, which leaves open questions about whether PES may be observed when participants
have to monitor their errors, as opposed to feedback monitoring.
1.6 The Present Study
The present study examined the relationship between error monitoring during math and
emotions about math in 3rd to 12th-grade students. Employing a novel math task, we assessed
students’ PES and PEA and administered self-report measures of math anxiety and positive
feelings about math. This study had two aims: to examine 1) the development of PEA, PES, and
their relationship in the context of math, and 2) whether emotions about math affected PES and
PEA or moderated the relationship between PES and PEA. We hypothesized that PEA would
increase with age, PES would decrease, and there would be a positive relationship between PES
and PEA. We also hypothesized that high math anxiety would negatively affect the relationship
between PES and PEA and that positive feelings about math would strengthen the relationship
between PES and PEA.
2. Methods
2.1 Participants
Participants were 314 children and adolescents between the ages of 7 and 18 (M = 12.47,
SD = 2.55), and were 142 males and 137 females (12 participants identified as non-binary or
selected “other” and 23 were missing gender data). Per a combination of parent and student selfreport, 40 participants identified as Black or African American, 21 Asian, 6 Native American or
Alaskan Native, 3 Native Hawaiian or other Pacific Islander, 85 White, and 110 selected “other.”

45
One hundred and thirty-six participants identified as Latinx/Hispanic. Due to missing responses,
racial and ethnic identity data is unavailable from 49 and 47 participants.
The study was approved by the University of Southern California Institutional Review
Board (UP-22-00308). Consent procedures varied across schools based on their protocols and
preferences. For one school serving TK-12th grade, parents received written consent forms via
RedCap (a HIPPA-compliant online data collection platform). The six other participating schools
used opt-out consent, which required anonymous data collection. In the case of opt-out consent,
parents received detailed information sheets outlining the purpose of the study and its activities.
The information sheet also explicitly stated that it was assumed their child would participate
unless the parents returned the form and indicated their decision to opt their child out by
checking the designated box.
While opt-out consent allowed for a larger, more diverse sample, it limited the
demographic information we could obtain from participants since it relied solely on student’s
self-report. Not all students knew of specific demographic details, resulting in missing data and
potential inaccuracies. Due to this, we did not include race or socioeconomic status as variables
in analyses. However, we identified school-wide data based on publicly available resources to at
least descriptively represent the racial and socioeconomic diversity of the sample. The median
household income per school zip code ranged from $48,514 to $88,415, averaging $51,282
(United States ZIP Codes, n.d.). The percentage of children eligible for free or reduced-price
lunch across the schools ranged from 31% to 76%, averaging 59.5%. Additionally, the range of
students who identify as Black, Indigenous, and other People of Color (BIPOC) across the
schools was 71% to 92%, with an average of 82.5% (U.S. News & World Report, n.d.). A

46
summary of how many participants were included from each school can be found in the
Supplemental Information (see page 124).
2.2 Procedure
The study took place while participants were in school. Researchers visited participants’
classrooms for approximately 1.5 - 2 hours. As part of a larger investigation on error monitoring
and social-emotional functioning in academic learning, participants completed a combination of
developmentally appropriate testing activities that could include error monitoring tasks, an IQ
measure, questionnaires, a qualitative survey, and a short video.
2.3 Measures
2.3.1 Math Task
To examine responses to errors in the context of math, we developed a novel math task
adapted from Desmet et al. (2012) and Denervered, Fornari et al. (2020). The task was presented
via E-Prime software (E-Prime Go; Psychology Software Tools, 2020) on provided Microsoft
Surface 3 tablets (10.52" x 7.36" x 0.34"). A visual representation of the task is presented in
Figure 1. In this task, participants were asked to determine the correctness of single-digit
multiplication solutions by pressing either a red sticker (indicating "incorrect") or a green sticker
(indicating "correct") on the tablet. The stickers were placed over the "2" and "9" keys on the
tablet and counterbalanced between subjects. Half of the trials presented problems with correct
solutions (e.g., 2 × 3 = 6), while the other half presented problems with incorrect solutions. For
the incorrect solutions, following Desmet et al. (2012), we manipulated the distance from the
correct solution so that the multiplication network was one step away from the correct solution.
The selected problems ranged from 2 × 3 to 8 × 9, excluding same-number problems (e.g., 2 × 2
= 4). This resulted in a total of 28 problems. For each of these 28 problems, we included four

47
different incorrect outcomes: (a + 1) × b, (a - 1) × b, a × (b + 1), and a × (b - 1). Each problem
occurred in both the "larger × smaller" and "smaller × larger" order (e.g., 6 × 4 = 24 and 4 × 6 =
24). Correct responses were repeated to ensure an equal number of incorrect and correct trials.
The task began with a practice block of 10 trials. In the practice block, participants
received trial-by-trial feedback on their performance through a smiling (correct) or frowning
(incorrect) emoji displayed on the screen immediately after their response. The practice block did
not include any problems from the primary task; instead, it consisted of multiples of 1 and 10.
Each trial was preceded by a fixation screen displayed for a time between 500-900 ms.
Participants had to be at least 60% accurate on a practice block to advance to the task blocks.
Participants could attempt as many practice blocks as possible to meet the accuracy threshold.
After the practice block(s), the task consisted of up to 448 trials in blocks of 35 trials. Following
best practices for examining error monitoring with children (Brooker et al., 2020; Gavin &
Davies, 2008; Lin et al., 2022; Stieben et al., 2007), we utilized an iterative procedure that
changed the stimuli presentation rate and response time window. In this procedure, we
established an initial stimulus duration and adapted it based on their accuracy every five trials.
The initial stimulus duration was 4500 ms for the Elementary School students, 2500 ms for the
Middle School students, and 1500 ms for the High School students. If children had 100%
accuracy during those 5 trials, the stimulus duration was reduced by 50 ms. If children’s
accuracy was 60% or below, the stimulus duration increased by 50 ms. Finally, if the accuracy
was 80% (i.e., one error in five trials), the stimulus duration remained the same. Participants did
not receive feedback on the accuracy of their responses; however, a cartoon sloth appeared on
the screen if they were too slow based on the adaptive response window. Participants were told
before starting the task that the presence of the sloth indicated that they should try to respond

48
faster. Participants were given breaks to wiggle or rest between each block. The task was
completed by an entire classroom (approximately 15-30 students) simultaneously with one to
three experimenters and their teacher present.
Figure 1.
Visual Representation of the Math Task
Note. As depicted, participants were instructed to use their index fingers on both hands to
complete the task. The white arrows on the keyboard were not used for the math task; they were
for a separate game.
2.3.2 Emotions About Math
Math Anxiety. Participants completed the modified Abbreviated Math Anxiety Scale
(mAMAS; Carey et al., 2017) to assess math anxiety. The scale, initially developed for British
participants, was adapted for this study to American English (e.g., “maths class” changed to
“math class”). The adapted items of the mAMAS are listed in Table 1. This scale was selected
amongst other math anxiety scales because of its validity and reliability for measuring math
anxiety among children and adolescents. Using a single scale instead of multiple age-specific
scales, we aimed to facilitate comparisons of math anxiety across all participants. Scores ranged
from 9-45 (M = 23.60, SD = 8.61). The distribution of the scores (overall and broken down by

49
grade level) can be found in the Supplemental Information (see page 129). The reliability of the
adapted mAMAS, determined using Cronbach’s alpha, was good for this sample (α = .86).
Positive Feelings about Math. We constructed a Positive Feelings about Math
Questionnaire adapted from Martin & Rimm-Kaufman (2015) to examine participants’ positive
social and emotional engagement with math. The items from the questionnaire can be found in
Table 1. Item 6 (“I feel bored in math class”) was reverse-coded. Scores ranged from 9-36 (M =
21.43, SD = 5.84). The distribution of the scores (overall and broken down by grade level) can be
found in the Supplemental Information (see page 130). Reliability, determined using Cronbach’s
alpha, was good in the present sample (α = .83).
Table 1.
Items in the Math Anxiety and Positive Feelings about Math Questionnaires
2.3.3 Covariates
Generalized Anxiety Measure. We used the Spence Children’s Anxiety Scale (SCAS;
Spence et al., 2003) to assess generalized anxiety. This scale consists of 38 items that measure

50
separation anxiety, social anxiety, generalized anxiety, panic/agoraphobia, obsessive-compulsive
disorder, and fears of physical injury. The SCAS is a self-report measure in which participants
are asked to indicate the frequency with which each statement applies to them on a 4-point Likert
scale, ranging from "Never" to "Always." Some examples are "I feel suddenly as if I cannot
breathe when there is no reason for this" and "I worry what other people think of me."
The SCAS provides individual scores for each anxiety dimension and a total anxiety
score. Higher scores indicate higher levels of anxiety. The reliability of the SCAS was
determined using Cronbach’s alpha. The full-scale reliability was strong (α = .93) for this
sample. The reliability of the generalized anxiety subscale used for analysis was moderate for
this sample (α = .79). The distribution of the generalized anxiety subscale scores (overall and
broken down by grade level) can be found in the Supplemental Information (see page 131).
Raven’s Progressive Matrices. We measured IQ to be included as a covariate in
analyses. Participants completed an abbreviated, age-appropriate version of the Raven’s Standard
Progressive Matrices (Raven, 1998). This test comprises a series of designs with a piece missing,
and respondents are asked to identify the piece required to complete the design from a number of
six to eight options shown beneath.
A 15-item Raven’s Standard Progressive Matrices test (Langener et al., 2022) was
administered via E-Prime (E-Prime Go; Psychology Software Tools, 2020). This version
included tests for two age groups: 9-12 and 13-16. Participants outside these age ranges
completed whichever test was closest to their age. We opted to administer these shortened
versions because they strongly correlate with scores on the standard 60-item versions (r = 0.89
for 9-12 years and r = 0.93 for 13-16 years; Langener et al., 2022). Participant scores were
calculated as the percentage of correct responses out of the 15 items. The raw accuracy scores

51
were then standardized within their respective age groups through z-scoring to reduce the
correlation with age.
2.4 Analysis Overview
2.4.1 Defining Variables
Grade Level. Participants were grouped into three grade levels for analyses: Elementary,
Middle, and High School. This allowed for more participants to be included in analyses of
developmental effects because participants could be grouped based on what school they were
tested in (e.g., an Elementary vs. Middle School) if they were missing age data. Thus, the grade
levels were grouped as follows: the Elementary School grade level included children in 3rd and
4th grade and/or between the ages of 7 and 10 (N = 108 participants). The Middle School grade
level consisted of participants in 6th-8th grade and/or 11 to 14 years old (N = 144 participants),
and the High School grade level included participants in 10th-12th grade and/or 15+ years old (N
= 57 participants). Five participants could not be placed into a group due to missing age and
school information and were excluded from further analyses.
Post-Error Accuracy (PEA) and Post-Error Slowing (PES). PEA was calculated as
the percentage of accurate trials that followed errors. This calculation included missed responses
after errors counted as incorrect; however, as in previous studies involving RT-based tasks with
children (Bowers et al., 2021; Morales et al., 2016), we excluded responses in which participants
responded too quickly (<150ms) from the accuracy calculation.
PES was calculated as the average RT post-error minus average RT pre-error. This
calculation only included correct trials and excluded responses faster than 150ms. Higher PES
scores indicate more slowing after errors. By calculating PES in this way, rather than calculating
average RT post-error minus RT post-correct, we aimed to account for differences in attention

52
and motivation across the task. For example, suppose a participant is paying attention and highly
motivated at the beginning of the task. In that case, they may be answering many trials correctly,
but as their motivation decreases, they begin making more errors. By calculating average RT preand post-error, we aim to capture correct responses as close as possible to errors, possibly
mitigating the effect of attention on the calculation while still capturing differences in pre- and
post-error behavior.
The nature of PES and PEA calculations is such that not all trials are included in the
calculations, nor are the same trials used in each calculation. Figure 2 shows an example set of
20 trials, and Table 2 shows how PES and PEA would be calculated from these trials.
Figure 2.
Example Trials During the Math Task

53
Table 2.
Example PES and PEA Calculation in the Math Task
It is important to note that measuring the relationship between PES and PEA using these
calculations is not a within-person analysis showing that making an error led to more or less
slowing. Rather, these calculations reflect children and adolescents’ tendencies to generally be
more cautious or more accurate after errors, as in previous studies of error monitoring in children
and adolescents (e.g., Denervaud, Knebel, et al., 2020).
2.4.2 Statistical Overview
All data preparation and statistical analyses were performed using RStudio (version 4.3.0;
R Core team, 2023).
Descriptive Statistics. We report descriptive data on the trials completed, answered
incorrectly, and missed. We also assessed whether this novel math task exhibited the same
interference effects observed in standard Flanker tasks. In the case of the math task, we expected
that incorrect solutions (e.g., 2x3 = 7) would interfere with performance similarly to incongruent
trials in a standard Flanker task. One-sample t-tests were run to determine if the mean differences
in reaction time and accuracy between correct and incorrect solution trials significantly differed

54
from zero. Additionally, Pearson correlations were run to determine any association between
math anxiety, positive feelings about math, and the covariate variables.
Aim 1: Error Monitoring in the Math Task. To investigate the relationships between
grade level, PES, PEA, and their development, we first conducted two separate ANOVAs testing
whether PES and PEA differed by grade level. We conducted separate linear regression models
to probe the significant effects of grade level, with Grade Level dummy coded and the
Elementary School grade level as the reference. Next, a linear regression model was run with
PEA as the dependent variable and PES as the predictor. Lastly, we ran an ANOVA to determine
whether grade level moderated the relationship between PES and PEA. All of these analyses
were controlled for gender. Additionally, each test was run a second time controlling for IQ. If
IQ had no effect, only the second model was reported, and if it did have an effect, both tests were
reported. Tables showing the differences in the coefficients with and without covariates can be
seen in the Supplemental Information (see pages 133-135).
Aim 2: The Relationship Between Emotions about Math and Error Responses in the
Math Task. To examine if emotions about math related to error responses, we ran four separate
linear regression models in combinations of positive feelings about math and math anxiety as
predictors and PES and PEA as the dependent variables. In a second step, we tested the unique
effects of emotions about math by including both measures in the model, one for PES and one
for PEA. Next, we ran four separate ANOVAs to examine whether grade level moderated these
relationships. We conducted separate linear regression models to probe the significant effects of
grade level, with Grade Level dummy coded and the Elementary School grade level as the
reference. Further, individual linear regression models were run within each grade level. Then,
we examined whether math anxiety and positive feelings about math moderated PES in a three-

55
way interaction. We ran a linear regression model of the interaction term between the three
variables with PEA as the dependent variable. We conducted a follow-up test to assess how the
slopes of the interaction differed. Each of these analyses was controlled for gender and then
repeated, controlling for generalized anxiety and IQ. If the covariates were significant, both
analyses were reported; if they were non-significant, only the second model was reported. Tables
showing the differences in the coefficients with and without covariates can be seen in the
Supplemental Information (see pages 133-135).
Sensitivity Analyses. To assess the robustness of our findings, we conducted additional
analyses. First, we ran each analysis as a multilevel model with participants nested within
schools. We found a similar pattern of results—namely, no changes in significance from the
results reported below. Similarly, we ran analyses with participants nested within grade levels
and found no changes in significance from the results reported below. Additionally, we
examined these relationships with only generalized anxiety to establish further the unique effect
of math anxiety in this math task. We found no significant relationship with generalized anxiety
alone.
3. Results
3.1 Descriptive Statistics
Participants completed an average of 316 trials (range = 105-448, SD = 83.75), made an
average of 72 (range = 6-211, SD = 41.26) errors with response, and did not respond to an
average of 22 (range = 0-156, SD = 21.14) trials.
Participants performed worse when responding to incorrect trials (e.g., 2x3 = 7) than
correct trials (e.g., 2x3 = 6). Specifically, reaction times were significantly longer on incorrect

56
trials than on correct trials, t(313) = 13.87, p < .001. Furthermore, accuracy rates were
significantly lower on incongruent trials than congruent trials, t(313) = 4.26, p < .001.
Math anxiety was negatively correlated with positive feelings about math, r (264) = -.22,
p < .001. Female participants reported significantly higher scores of math anxiety than male
participants, r (263) = .18, p < .001. Math anxiety was negatively correlated with IQ, r (228) = -
.20, p < .001, positively correlated with generalized anxiety, r(242) = .44, p < .001. Positive
feelings about math were positively correlated with IQ, r (231) = .18, p < .001, and unrelated to
generalized anxiety, r(237) = -.06, p = .33, and gender, r (260) = .05, p = .44. These correlation
coefficients, additional relationships between demographic variables, and their significance can
be seen in Table 3.
Table 3.
Correlation Coefficients of Relationships between Measures and Demographic Variables
Note. ***p < .001. Gender was coded as Male = 1 and Female = 2.
Regarding grade level differences among the variables, it was found that math anxiety,
F(2, 275) = .79, p = .45, and generalized anxiety, F(2, 248) = .90, p = .41 scores did not differ by
grade level. However, positive feelings about math scores did significantly differ by grade level,
F(2, 273) = 20.89, p < .001. This difference was such that Middle, b = -4.21, t(273) = -5.65, p <

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.001, and High School, b = -5.20, t(273) = -5.45, p < .001, participants reported less positive
feelings about math than Elementary School participants. These relationships can be seen in
Table 4.
Table 4.
Means, Standard Deviations, and One-Way ANOVA by Grade Level of Math Anxiety, Positive
Feelings about Math, and Generalized Anxiety Scores
Note. Df = degrees of freedom. Df changes between ANOVAs due to uneven completion of
measures by participants.
3.2 The Development of PES, PEA, and their Relationship in the Math Task
We found that PEA differed significantly between the grade levels, F(2, 220) = 8.39, p <
.001, ηp2 = 0.07. IQ also predicted PEA, F(1, 220) = 17.62, p < .001, ηp2 = 0.07. In line with our
hypothesis that PEA would increase with grade level, we found that participants in the Middle, b
= 8.72, t(220) = 3.93, p < .001, and High School, b = 7.99, t(220) = 2.87, p = .005 grade levels
showed significantly higher PEA than the Elementary grade level. Conversely, against our
hypothesis that PES would decrease with grade level, we found that PES did not significantly
differ between the grade levels, F(2, 220) = .40, p = .67, ηp2 = 0.004.

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Per our hypothesis, we found a positive relationship between PES and PEA, b = .02,
t(219) = 2.80, p = .01, ηp2 = .03. This relationship was such that participants who tended to slow
more after errors also tended to be more accurate after errors. We found that this relationship was
not moderated by grade level, F(2, 217) = 2.25, p = .11, ηp2 = 0.02. The average PES and PEA
by grade level can be seen in Figure 3.
Figure 3.
Average PES and PEA by Grade Level
Note. Error bars represent one standard error from the mean. These graphs do not account for any
control variables.
3.3 The Effect of Emotions about Math on PEA, PES, and Their Relationship
3.3.1 Emotions about Math and PEA
Math Anxiety. Math anxiety was found to be negatively related to PEA, b = -.31, t(258)
= -2.91, p = .004, ηp2 = .03, such that the participants with higher math anxiety scores tended to
be less accurate after errors. However, after adding IQ and generalized anxiety as covariates to

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the model, math anxiety was no longer related to PEA, b = -.13, t(189) = -.95, p = .34, ηp2 =
.005.
Grade level was found to moderate the relationship between math anxiety and PEA, F(2,
256) = 5.41, p = .005, ηp2 = .04. The moderation was such that the relationship between math
anxiety and PEA was weaker in the Middle, b = 4.92, t(256) = 2.30, p = .02 and High School
participants, b = 8.97, t(256) = 3.23, p = .001, than the Elementary School participants, b = -7.05,
t(256) = -3.92, p < .001. However, as in the models investigating the relationship between math
anxiety and PEA, the moderation was no longer significant after controlling for generalized
anxiety and IQ, F(2, 187) = 2.17, p = .12, ηp2 =.02.
To further investigate the moderating effect of grade level on the relationship between
math anxiety and PEA, we examined this relationship separately within each grade level. We
found that within the Elementary School grade level, participants with higher math anxiety
scores also tended to be less accurate after errors, b = -.81, t(81) = -3.81, p < .001, ηp2 = .15. A
similar, non-significant trend was found within the Middle School participants, b = -.27, t(124) =
-1.90, p = .06, ηp2 = .03, and there was no significant relationship between math anxiety and
PEA within the High School participants, b = .29, t(49) = 1.34, p = .18, ηp2 = .04. These
relationships are depicted in Figure 4. To further examine the robustness of the significant
finding within the Elementary School grade level, we added IQ and generalized anxiety to the
model, and found that the significant relationship between math anxiety and PEA remained, b = -
.81, t(81) = -2.18, p = .04, ηp2 = .12.

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Figure 4.
Illustration of the Moderating Effect of Grade Level on the Relationship between Math Anxiety
and PEA
Note. This illustration shows the marginal effect of math anxiety within each grade level while
controlling for gender, IQ, and generalized anxiety.
Positive Feelings about Math. We found that participants who reported more positive
feelings about math also tended to be more accurate after errors, b = .67, t(210) = 3.87, p < .001,
ηp2 = .07, and that this relationship did not significantly differ between the grade levels, F(2,
253) = 1.07, p = .34, ηp2 =.01.
Unique Effects of Emotions about Math. In a model that included both math anxiety
and positive feelings about math as predictors of PEA, we found that positive feelings about
math were positively related to PEA, b = .67, t(242) = 4.07, p < .001, ηp2 = .06, and that there
was a non-significant negative trend between math anxiety and PEA, b = -.19, t(242) = -1.73, p =
.08, ηp2 = .01. After controlling for covariates, positive feelings about math was still significantly

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positively related to PEA, b = .58, t(182) = 2.81, p = .04, however the non-significant trend
between math anxiety and PEA was no longer present, b = -.04, t(182) = -.32, p = .74, ηp2 = .001.
3.3.2 Emotions about Math and PES
Results showed that math anxiety was unrelated to PES, b = -.12, t(258) = -.11, p = .91,
ηp2 < .001, and this relationship did not differ between the grade levels, F(2, 256) = .77, p = .47,
ηp2 =.006. We also found a non-significant positive trend between positive feelings about math
and PES, b = 2.81, t(255) = 1.69, p = .09, ηp2 = .01. This relationship did not differ between
grade levels, F(2, 253) = .06, p = .94, ηp2 < .001.
In a model that included both math anxiety and positive feelings about math as predictors
of PES, we found a significant positive relationship between positive feelings about math and
PES, b = 3.64, t(242) = 2.11, p = .04, ηp2 = .02, such that participants who reported more positive
feelings about math also tended to slow down more after errors. There was no relationship
between math anxiety and PES in this model. In a second model with covariates added, we found
a non-significant (p = .05) positive trend between positive feelings about math and PES, b =
3.70, t(182) = 1.97, p = .05, ηp2 = .02. Additionally, in this model, we found a significant
negative relationship between generalized anxiety and PES, b = -5.47, t(182) = -2.09, p = .04,
ηp2 = .02, such that participants who reported higher generalized anxiety also tended to slow less
after their errors.
3.3.3 The Moderating Effect of Emotions about Math on the Relationship Between PES and
PEA
Math Anxiety. We found that math anxiety moderated the effect of PES on PEA, b = -
2.49, t(256) = -2.49, p = .01, ηp2 = .02. Per our prediction, the moderation was such that
participants with lower levels of math anxiety demonstrated a stronger positive relationship

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between PES and PEA. However, after controlling for covariates, the moderation was no longer
significant, b = -1.51, t(187) = -1.31, p = .19, ηp2 = .009. We also found no differences in this
moderation between the grade levels, F(2, 250) = 1.85, p = .16, ηp2 =.01.
Positive Feelings about Math. We found that positive feelings about math moderated
the effect of PES on PEA, b = -1.92, t(253) = -2.25, p = .03, ηp2 = .02. In contrast to our
prediction that more positive feelings about math would be related to a stronger positive
relationship between PES and PEA, the moderation was such that participants with lower
positive feelings about math demonstrated a stronger relationship between PES and PEA.
However, after controlling for covariates, the moderation was no longer significant, b = -1.20,
t(208) = -1.19, p = .23, ηp2 = .01. We also found no differences in this moderation between the
grade levels, F(2, 247) = .55, p = .58, ηp2 =.004.
The Combined Effect of Math Anxiety and Positive Feelings about Math. We found
a significant three-way interaction between math anxiety, positive feelings about math, and PES
to predict PEA, b = 3.21, t(177) = 3.25, p = .001, ηp2 = .06. To probe this interaction, we tested
simple slopes at one standard deviation above and below the average math anxiety and positive
feelings about math scores, resulting in four slopes tested: low math anxiety/low positive feelings
about math, high math anxiety/low positive feelings about math, low math anxiety/high positive
feelings about math, and high math anxiety/high positive feelings about math. We found that low
math anxiety/low positive feelings about math was the only significant slope, b = .08, p < .001.
The relationship was such that at low levels of positive feelings about math and low math
anxiety, there was a significant positive relationship between PES and PEA. At other levels of
positive feelings about math and math anxiety, the relation between PES and PEA was not

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significant. A visual representation of this three-way interaction and the significance of the
individual simple slopes can be seen in Figure 5.
While these simple slopes are based on the continuous variables of math anxiety and
positive feelings about math and are testing coefficients at set levels, rather than testing groups of
participants, a graph of the distribution of math anxiety and positive feelings about math scores
showed that we do have coverage of the participants that would fall under each of these
categories, which has been included in the Supplemental Information (see page 132).
Figure 5.
Visual Representation of Three-Way Interaction between Math Anxiety, Positive Feelings about
Math, and PES
Note. The slopes in this illustration are controlled for gender, IQ, and generalized anxiety.

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4. Discussion
Math anxiety is a widespread problem (Luttenberger et al., 2018; OECD, 2013) that has
known negative consequences for learning (Barroso et al., 2021; Namkung et al., 2019; SuárezPellicioni et al., 2016; Zhang et al., 2019). However, the ways in which math anxiety interferes
with learning processes other than working memory (Ashcraft & Kirk, 2001; Ashcraft & Krause,
2007; Passolunghi et al., 2016) are not fully understood. Children and adolescents with math
anxiety report fears of failure and making mistakes in math (Petronzi et al., 2019; Szczygieł &
Pieronkiewicz, 2022). Yet, how math anxiety influences error monitoring, a cognitive, affective
process recruited when managing mistakes, is underexplored. Here we examined error
monitoring as a potential mechanism linking math anxiety and performance. We employed a
novel task to measure participants’ PES and PEA in the context of math. Moreover, we related
their performance on this task with their levels of math anxiety and positive feelings about math.
In doing so, we aimed to examine the development of PEA, PES, and their relationship in the
context of math and whether emotions about math affected PES and PEA or moderated the
relationship between PES and PEA.
Our findings present new insights that contribute to the understanding of how children
and adolescents behaviorally respond to errors while completing a math task. Per our prediction,
participants tended to be more accurate after their errors as grade level increased. However, in
contrast with our prediction that participants would tend to slow less after their errors with grade
level, we found no significant differences between grade levels in participants’ PES. Although
descriptively, in Figure 3, it can be seen that participants in the Elementary School grade level
tended to slow more after errors than those in the Middle and High School grade levels. This
non-significant trend aligns with findings from one of the two other studies that have examined

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behavioral error responses during a math task, such that de Mooij et al. (2022) showed PES to
peak at age 9 and then decrease into early adolescence. In a further contribution to understanding
error responses during math, we found support for our hypothesis of a positive relationship
between PES and PEA, such that participants who tended to slow more after errors also tended to
be more accurate after errors. In addition to contributing to the understanding of PES during a
math task, this finding may also lend support to the theory of PES as an adaptive cognitive
control mechanism (Botvinick et al., 2001).
This study also yielded new insights into the relationship between emotions about math
and behavioral responses to errors in children and adolescents. Notably, we found that the
participants who reported higher levels of math anxiety also tended to be less accurate after
errors, and those who reported more positive feelings about math tended to be more accurate
after errors. Interestingly, when math anxiety and positive feelings about math were tested in the
same model rather than separately, we found that positive feelings about math were still
positively related to PEA. However, there was only a non-significant trend toward a negative
relationship between math anxiety and PEA. This finding is consistent with previous research
that identified math enjoyment to be more predictive of math achievement than math anxiety
(Villavicencio & Bernardo, 2016). This may suggest that future investigations should further
examine the possibility that supporting students’ positive feelings about math may be protective
against the negative impacts of math anxiety.
The findings additionally reveal insights into the link between emotions about math and
PES. Only when examining unique effects, by including math anxiety and positive feelings about
math in the same model, we found that positive feelings about math were related to an increased
tendency to slow after errors. Conversely, generalized anxiety was related to a tendency to slow

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less after errors. One potential interpretation of this finding is that students who enjoy math may
like the feeling of doing math problems or possibly feel less stress when engaging in math,
which may result in these individuals being more likely to take their time and not rush through
the task. It could also be that students who enjoy math may be more comfortable engaging with
errors, as they potentially view math as a non-stressful context. A possible interpretation of the
relationship between participants’ generalized anxiety and tendency to slow less after errors may
reflect anxious students’ general aversion to errors. These findings suggest that social-emotional
functioning may be one underlying cause of individual differences in PES.
We found mixed support for our hypothesis about the moderating effect of emotions
about math on the relationship between PES and PEA. We expected that students who were less
anxious, and had more positive feelings, about math would tend to slow more, and also tend to
be more accurate, after errors. While we found a significant, three-way interaction between math
anxiety, positive feelings about math, and PES, it was only partially in the direction we expected.
A probing of the interaction revealed that there was only a positive significant relationship
between PES and PEA at low levels of math anxiety and positive feelings about math. It is not
completely clear what this finding means, however, there are a few potential interpretations.
One possibility is that children and adolescents who fit this profile are generally
complacent about doing math and are not anxious about it, nor do they particularly like it.
However, if they take the time to slow down and be more cautious in their responses, they see an
improvement in their performance. Another possible interpretation can be identified by
examining the intercepts of Figure 5. Students with high positive feelings about math and low
math anxiety overall perform well on the task. Perhaps, if the task were more difficult for these

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students, we would have seen the hypothesized pattern. However, future investigations are
needed to examine this possibility.
This study also yielded an interesting developmental finding about the relationship
between math anxiety and PEA. This relationship became increasingly less negative in the
Middle and High school participants. This decreasing effect of math anxiety on PEA could be
due to the relative task difficulty. The Elementary School participants in our sample were in 3rd
or 4th grade; multiplication was a new math skill to them, either learned in their current school
year or the previous year. In contrast, the High School participants had the advantage of knowing
multiplication for many years. Therefore, the task’s difficulty was not balanced and was likely
more challenging for the younger participants. Potentially we would have seen similar effects of
math anxiety on PEA in the older participants if the task was more relatively difficult.
A strength of this study is that it is one of the few studies, and to our knowledge, the only
study with children, to examine error responses during math without feedback. In studies with
feedback, participants are provided the opportunity to adjust their performance based on errors
without having to detect the errors themselves. In the case of our task, there was no external
indicator to participants on the accuracy of their responses. Therefore, they had to monitor their
own errors and adjust accordingly. The findings of our study may contribute to the understanding
of children and adolescents’ abilities for error monitoring, as opposed to feedback monitoring.
One caveat of this method is that we cannot be certain that participants were aware of their own
errors. This could be addressed with a neuroscientific investigation, examining whether a neural
index such as the ERN is present when participants engage in this math task. Further, it would be
an interesting future avenue of research to examine whether behavioral patterns of error
monitoring differ when participants are given feedback or not during this math task.

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A second strength of this study is the sample. The two other known investigations of
error monitoring during math in children occurred in Dutch and Swiss samples. Therefore, this
sample provides a new perspective with United States students. Moreover, even though race and
socioeconomic factors could not be controlled for, the self-report data that could be obtained and
the publicly available information about school-wide demographic data revealed that this sample
is representative of, and may be more generalizable to, the majority-minority population of
students in the United States (Maxwell, 2014).
The findings of this study should be interpreted in light of several limitations. One
limitation of this task was the disproportionate difficulty level by grade level. Future
investigations would benefit from better calibrating math problems to students’ abilities. Another
limitation was a lack of a measure of math achievement, a known correlate to math anxiety.
Additionally, our data lacked the proper information to account for racial and socioeconomic
variability. Given the known associations between harmful race biases and math learning (e.g.,
Copur-Gencturk et al., 2020), this will be important to examine in future investigations.
The findings of this study, and its limitations, generate many avenues for future research.
First, it would be interesting to examine whether participants’ responses vary based on the type
of solution they are responding to. A basic comparison would be examining responses to correct
and incorrect solutions. However, a more complex approach could include examining whether
the type of incorrect solution (e.g., the varying distances from the correct responses) affected
error monitoring. Relatedly, it would be curious to examine whether behavioral error responses
differ based on the varying difficulty of the multiplication problems (e.g., 9x8 is more difficult to
solve than 2x3). This is especially interesting, considering individuals are known to recruit
different strategies depending on difficulty (Siegler, 1988). Additionally, examining teachers’

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error monitoring in accordance with their math anxiety could reveal new insights, as studies have
shown that teachers’ math anxiety negatively affects their students’ math achievement (Beilock
et al., 2010; Ramirez et al., 2018).
In conclusion, this study is one of the first to examine behavioral error responses during
math across childhood and adolescence. The presence of PES and PEA during this task suggests
that it can be used as a new tool for researchers to understand error monitoring during math
better. Additionally, to our knowledge, this is the first study to examine how behavioral error
responses during a math task may be related to students’ math anxiety and positive feelings
about math. The findings suggest that error monitoring may be one learning process by which
math anxiety affects math achievement and has the potential to inform future research about
educational practices that support students’ learning and social-emotional functioning in a
coordinated way.

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Paper 3: Relations Among the Meaning Secondary Students Make of a True Social Story
and Their Patterns of Error Monitoring and Emotions in a Math Task
Abstract
Extensive research from education and psychology highlights connections between emotions and
academic learning, but the mechanisms by which these interact are understudied.
Neuropsychological research shows that the anterior cingulate cortex is involved in emotion
processing in social situations, in anxiety, and in error monitoring, for example, during a math
task. This confluence suggests the possibility that error monitoring may be one mechanism that
ties academic learning to social and emotional processing more broadly. In a range of schools
serving primarily low-income youth of color, we measured 222 adolescents’ (Mage = 13.90, SD =
1.81) responses to errors in a math task and collected their written responses to a compelling
mini documentary about a teenager. Students also reported their levels of math anxiety and
positive feelings about math. We found that adolescents who demonstrated more transcendent,
reflective thinking about the documentary also reported more positive feelings about math,
which were in turn related to slowing after errors, an adaptive pattern. Conversely, students who
exhibited higher levels of concrete, reactive thinking about the documentary also reported higher
levels of math anxiety and showed a weaker relationship between post-error slowing and
accuracy. These findings reveal a connection between the processing of social information and
self-monitoring in an academic task. Implications for education and social-emotional learning are
discussed.
Keywords: social emotions; adolescence; transcendent thinking; concrete thinking; math
anxiety; meaning-making

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Relations Among the Meaning Secondary Students Make of a True Social Story and Their
Patterns of Error Monitoring and Emotions in a Math Task
Meaning-making is the social-emotional and cognitive process by which we construct
narratives about the social world by making sense of the experiences, emotions, and motives of
others while extracting personal relevance, values, and belief systems (Singer, 2004). This
process is relevant to students’ learning as they relate their school experiences to their identity
and feelings of belonging (e.g., Craggs & Kelly, 2018; Faircloth, 2009; Korpershoek et al.,
2020). This is especially prudent in adolescence, a known period of identity development (Branje
et al., 2021). Recent interdisciplinary theories about education underscore the need to understand
the bidirectional relationship between children and adolescents’ social-emotional experiences
and their academic learning (Nasir et al., 2021). However, how broader social-emotional and
cognitive processes such as meaning-making are related to academic learning is understudied.
Potentially, ways of meaning-making in the social world reflect dispositions of mind that may be
carried across processing domains, such as in academic learning. Here we investigate whether
adolescents’ social-emotional meaning-making in reaction to a social story relates to their socialaffective experiences and learning processes in an academic context.
1.1 Concrete and Transcendent Meaning-Making
In childhood, there is a propensity for concrete meaning-making, characterized by
focusing on the physical “here and now” of social situations and emotional reactivity (Gotlieb et
al., 2022a). As youth emerge into adolescence, they undergo social, emotional, and cognitive
growth that affords them more complex capacities for meaning-making, which increasingly
disposes adolescents to engage in more transcendent meaning-making, characterized by
transcending the tangible, context-specific situation to connect to the broader social world and
construct personal values (Erikson, 1968; Habermas & de Silveira, 2008; Steinberg, 2014).

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Transcendent and concrete meaning-making recruit different neural processes.
Transcendent meaning-making has been associated with greater default mode network (DMN)
activity (Gotlieb et al., 2022b). The DMN is activated during thinking that steps out of the “here
and now,” such as feelings like admiration for virtue and compassion (Immordino-Yang et al.,
2009; Yang et al., 2018), making moral inferences (Kaplan et al., 2017), and imagining
hypothetical or future scenarios (Immordino-Yang et al., 2009; Singer, 2006). Concrete
meaning-making has been associated with greater executive control network (ECN) activity
(Gotlieb et al., 2022b). The ECN has been implicated in regulating emotional reactions (Etkin et
al., 2015) and effortful thinking, acting in the “here and now” (Immordino-Yang et al., 2012).
These dispositions of meaning-making have also been linked to varied broader social and
cognitive functioning. A study by Gotlieb et al. (2022a) showed that the more adolescents made
concrete meaning about social scenarios, the more they reported positive feelings in their daily
life and satisfaction with social relationships. While the more an adolescent made transcendent
meaning, the better their working and long-term memory, creative flexibility, and self-directed
executive functioning. This was the case even controlling for IQ. Transcendent meaning-making
was also associated with an ability to make reasoning about challenges faced by the adolescents’
community. Relatedly, in a micro developmental investigation of meaning-making during an
eight-week intergenerational storytelling program, it was found that adolescents’ transcendent
meaning-making contributed to increases in life purpose and facilitated their learning from the
stories shared with them by their elder partners (Riveros et al., 2023). Even further, in a striking
longitudinal study, the benefits of transcendent meaning-making were shown to extend into early
adulthood via brain development, such that transcendent meaning-making in adolescence
predicted the ways youths’ brains developed over the next two years, which in turn, predicted

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identity development, which predicted self-liking and relationship satisfaction in young
adulthood (Gotlieb et al., 2023). These findings suggest that transcendent meaning-making is an
important developmental achievement in adolescence related to beneficial social-cognitive
functioning outcomes. However, how dispositions of meaning-making may carry over to
domain-specific academic learning, such as in math, has not been directly tested.
1.2 Math as a Salient Context to Examine Relations between Meaning-Making and
Emotions in Learning
A particularly salient context to examine links between meaning-making and learning is
math. In mathematical thinking, students must steer through particularly complex problem
spaces. This is especially the case in adolescence, as students are shifting from tangible concepts
like addition that they can add up on their fingers to more abstract concepts such as calculus that
require more complex cognition.
In addition to its complexity, math is known to be an especially affectively charged
academic context. Many students experience math anxiety, an adverse psychological and
physiological response to engaging in math problems (Ashcraft & Ridley, 2005; Richardson &
Suinn, 1972), known to negatively impact math learning (Barroso et al., 2021; Namkung et al.,
2019; Suárez-Pellicioni et al., 2016; Zhang et al., 2019). Conversely, positive feelings about and
enjoyment of math have been shown to support math achievement (Villavicencio & Bernardo,
2016). Given the significance of emotions about math for math achievement, it is important to
understand how broader social cognitive capacities, such as meaning-making, could support or
hinder affect about math.
Potentially, adolescents who are more disposed to engage in concrete meaning-making,
characterized by a focus on the “here and now” and emotional reactivity, are also more likely to

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experience math anxiety, a context-specific emotional response. In contrast, do adolescents who
tend to engage in transcendent meaning-making, a disposition to reflect and connect current
contexts within the broader social world, also experience more positive feelings about math?
Potentially the reflective nature of transcendent thinking allows adolescents to better understand
the power of math ideas beyond their classroom. However, how might these patterns of narrative
thinking relate to the more automatic cognitive processes recruited in learning that, in turn, affect
math achievement?
1.3 Error Monitoring as a Potential Link between Meaning-Making and Math
Performance
There is neuropsychological evidence to suggest that, in addition to influencing
adolescents’ emotions about math, dispositions toward meaning-making may directly relate to
error monitoring, the neuropsychological process by which individuals notice and react to their
mistakes. Error monitoring is an important process for academic learning (Danovitch et al., 2019;
Kim et al., 2016; Moser et al., 2011), and the neural correlates of error monitoring are rooted in
the anterior cingulate cortex (ACC; Botvinick et al., 2004), a brain region involved in emotional
regulation that has been implicated in the integration of social-emotional stimuli (Somerville et
al., 2016). These neural correlates have also been found to be associated with abnormal socialemotional functioning, such as generalized anxiety (e.g., Moser et al., 2013) and even math
anxiety (Suárez-Pellicioni et al., 2013). Given the affective nature of error monitoring, patterns
of error monitoring may be related to broader social-emotional functioning, such as meaningmaking.
Error monitoring is characterized by two behavioral phenomena: post-error slowing
(PES) and post-error accuracy (PEA). PES is such that individuals reliably slow down more after

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committing an error than they do after a correct response (Rabbitt, 1966; Ullsperger et al., 2014),
and PEA is such that individuals adjust their behavior after errors to be more accurate
(Danielmeier & Ullsperger, 2011). The occurrence of PES is well-established. However, its
psychological underpinnings are not well understood (Dutilh, Vandekerckhove, et al., 2012). A
predominate theory is that PES reflects cognitive control to facilitate a more cautious response
(Botvinick et al., 2001), which has been supported by studies that show a positive relationship
between PES and PEA (e.g., de Mooij et al., 2022; Denervaud, Knebel, et al., 2020; Paper 2).
Examining PES in accordance with other social-emotional functioning, such as dispositions for
concrete and transcendent meaning-making, may provide insight into what underlies PES.
Thinking transcendently requires dedicated time to step back and reflect (ImmordinoYang, 2016). Accordingly, transcendent thinking has been shown to be associated with gaze
aversion, a non-verbal indicator of a pause to distance oneself from the immediate surroundings
(Yang et al., 2018). Perhaps this disposition to slow thinking and reflection is carried into error
monitoring, such that transcendent thinking may be associated with increased PES. Conversely,
concrete thinking, a reactive disposition, may interfere with how individuals use PES to reflect
and, in turn, increase their accuracy. Research showing that math anxiety, a similar contextdependent process, weakens the relationship between PES and PEA suggests this may be the
case (Paper 2).
1.4 The Present Study
The present study examined whether adolescents’ meaning-making about a social story
related to their emotions about math and behavioral responses to errors during a math task. We
recruited adolescents aged 11-18 from urban public schools serving primarily low-income youth
of color. We employed a novel math task to measure PES and PEA and administered self-report

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measures of math anxiety and positive feelings about math. Additionally, we examined
participants’ meaning-making through qualitative coding of their responses to an inspiring video
documentary about a teenager. We hypothesized that students’ meaning-making about the social
story would be linked to their emotions about math. Specifically, a stronger disposition towards
concrete meaning-making would be associated with higher levels of math anxiety, and a stronger
disposition towards transcendent meaning-making would be associated with more positive
feelings about math. Further, we hypothesized that these dispositions would be associated with
behavioral responses to errors in the math task, such that higher levels of transcendent meaningmaking would be associated with more PES and that concrete meaning-making would negatively
moderate the relationship between PES and PEA.
2. Methods
2.1 Participants
Participants were 222 adolescents between the ages of 11 and 18 (M = 13.90, SD = 1.81),
and were 107 males and 97 females (12 participants identified as non-binary or selected “other”
and 6 were missing gender data). Per a combination of parent and student self-report, 42
participants identified as Black or African American, 16 Asian, 5 Native American or Alaskan
Native, 3 Native Hawaiian or other Pacific Islander, 76 White, and 63 selected “other.” Eightyseven participants identified as Latinx/Hispanic. Due to missing responses, racial and ethnic
identity data is unavailable from 17 and 18 participants.
The study was approved by the University of Southern California Institutional Review
Board (UP-22-00308). Consent procedures varied across schools based on their protocols and
preferences. For one school, parents received written consent forms via RedCap (a HIPPAcompliant online data collection platform). The two other participating schools used opt-out

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consent, which required anonymous data collection. In the case of opt-out consent, parents
received detailed information sheets outlining the purpose of the study and its activities. The
information sheet also explicitly stated that it was assumed their child would participate unless
the parents returned the form and indicated their decision to opt their child out by checking the
designated box.
While opt-out consent allowed for a larger, more diverse sample, it limited the
demographic information we could obtain from participants since it relied solely on students’
self-report. Not all students knew of specific demographic details, resulting in missing data and
potential inaccuracies. Due to this, we did not include race or socioeconomic status as variables
in analyses. However, we identified school-wide data based on publicly available resources to at
least descriptively represent the racial and socioeconomic diversity of the sample. The median
household income per school zip code ranged from $31,334 to $71,645, averaging $52,204
(United States ZIP Codes, n.d.). The percentage of children eligible for free or reduced-price
lunch across the schools ranged from 31% to 70%, with an average of 54%. Additionally, the
range of students who identify as Black, Indigenous, and other People of Color (BIPOC) across
the schools was 71% to 85%, with an average of 76% (U.S. News & World Report, n.d.). A
summary of how many participants were included from each school can be found in the
Supplemental Information (see page 124).
2.2 Procedures & Measures
The study took place while participants were in school. Researchers visited participants’
classrooms for approximately 1.5 - 2 hours. As part of a larger investigation on error monitoring
and social-emotional functioning in academic learning, participants completed a combination of

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developmentally appropriate testing activities that could include error monitoring tasks, an IQ
measure, questionnaires, a qualitative survey, and a short video.
2.2.1 Social-Emotional Meaning-Making Task
We utilized an established protocol to examine adolescents’ meaning-making (Gotlieb et
al., 2022a; Immordino-Yang et al., 2009) in which participants watched a 6-minute
documentary-style video clip about an inspiring story of a teenage boy growing up in Sierra
Leone (available to view at this link). After watching the video, participants were directed to an
online survey asking them to answer two open-ended questions: "How does this story make you
feel?" and "What did you learn from this story?". These questions allowed participants to
demonstrate their thinking and allowed evidence of concrete and transcendent thought to emerge
naturally (Gotlieb et al., 2022a). Participants were assured that their answers would only be used
for research purposes and not be associated with their names.
Responses to the video clip were qualitatively coded for concrete and transcendent
meaning-making, adapting the method outlined in Gotlieb et al. (2022a). The original coding
scheme consisted of six thematic categories: perspective-taking, curiosity, personally relevant
lessons, reactive emotions, emotional contagion, and advising the protagonist. Gotlieb and
colleagues’ coding scheme was developed based on responses during two-hour verbal interviews
with adolescents about their reactions to stories. In contrast, our procedure included just one
video, and participants responded online. Due to these differences, our study yielded less data to
code. Thus, we found that only four of the six themes were present. Therefore, a composite
transcendent meaning-making score was calculated by summing the conceptual category scores
for perspective-taking and personally relevant lessons. For concrete meaning-making, scores
were summed for emotional contagion and reactive emotions. Each conceptual category had

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subcategories of the types of responses included under each category. For example, “deriving a
moral” was included in the personally relevant lessons category (see Gotlieb et al., 2022a for full
list of subcategories). Example codes can be seen in Table 1.
In line with Gotlieb et al. (2022a), all coding was binary; we coded for the presence of
the category. No categories were mutually exclusive, there was no limit to the number of
categories that could be coded from a single response, and responses did not have to be coded to
any category if none was appropriate. After all of the responses were coded, a second coder,
blind to the hypotheses, coded 25% of the responses. Reliability was strong (Kappa = .91). The
first author’s coding was used for analyses. Distribution of the scores can be seen in the
Supplemental Information (see page 137).
Table 1.
Description and Examples of Meaning-Making Conceptual Categories

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2.2.2 Math Task
To examine responses to errors in the context of math, we developed a novel math task
adapted from Desmet et al. (2012) and Denervered, Fornari et al. (2020). The task was presented
via E-Prime software (E-Prime Go; Psychology Software Tools, 2020) on provided Microsoft
Surface 3 tablets (10.52" x 7.36" x 0.34"). A visual representation of the task is presented in
Figure 1. In this task, participants were asked to determine the correctness of single-digit
multiplication solutions by pressing either a red sticker (indicating "incorrect") or a green sticker
(indicating "correct") on the tablet. The stickers were placed over the "2" and "9" keys on the
tablet and counterbalanced between subjects. Half of the trials presented problems with correct
solutions (e.g., 2 × 3 = 6), while the other half presented problems with incorrect solutions. For
the incorrect solutions, following Desmet et al. (2012), we manipulated the distance from the
correct solution so that the multiplication network was one step away from the correct solution.
The selected problems ranged from 2 × 3 to 8 × 9, excluding same-number problems (e.g., 2 × 2
= 4). This resulted in a total of 28 problems. For each of these 28 problems, we included four
different incorrect outcomes: (a + 1) × b, (a - 1) × b, a × (b + 1), and a × (b - 1). Each problem
occurred in both the "larger × smaller" and "smaller × larger" order (e.g., 6 × 4 = 24 and 4 × 6 =
24). Correct responses were repeated to ensure an equal number of incorrect and correct trials.
The task began with a practice block of 10 trials. In the practice block, participants
received trial-by-trial feedback on their performance through a smiling (correct) or frowning
(incorrect) emoji displayed on the screen immediately after their response. The practice block did
not include any problems from the primary task; instead, it consisted of multiples of 1 and 10.
Each trial was preceded by a fixation screen displayed for a time between 500-900 ms.
Participants had to be at least 60% accurate on a practice block to advance to the task blocks.

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Participants could attempt as many practice blocks as possible to meet the accuracy threshold.
After the practice block(s), the task consisted of up to 448 trials in blocks of 35 trials. We
utilized an iterative procedure that changed the stimuli presentation rate and response time
window. In this procedure, we established an initial stimulus duration and adapted it based on
their accuracy every five trials. The initial stimulus duration was 2500 ms for the middle school
and 1500 ms for the high school participants. If participants had 100% accuracy during those 5
trials, the stimulus duration was reduced by 50 ms. If participants’ accuracy was 60% or below,
the stimulus duration increased by 50 ms. Finally, if the accuracy was 80% (i.e., one error in five
trials), the stimulus duration remained the same. Participants did not receive feedback on the
accuracy of their responses; however, a cartoon sloth appeared on the screen if they were too
slow based on the adaptive response window. Participants were told before starting the task that
the presence of the sloth indicated that they should try to respond faster. Participants were given
breaks to rest between each block. The task was completed by an entire classroom
(approximately 15-30 students) simultaneously with one to three experimenters and their teacher
present.
Figure 1.
Visual Representation of the Math Task

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Note. As depicted, participants were instructed to use their index fingers on both hands to
complete the task. The white arrows on the keyboard were not used for the Math Task; they were
for a separate game.
Post-Error Accuracy (PEA) and Post-Error Slowing (PES). PEA was calculated as
the percentage of accurate trials that followed errors. This calculation included missed responses
after errors counted as incorrect; however, as in previous studies involving RT-based tasks with
children (Bowers et al., 2021; Morales et al., 2016), we excluded responses in which participants
responded too quickly (<150ms) from the accuracy calculation.
PES was calculated as the average RT post-error minus average RT pre-error. This
calculation only included correct trials and excluded responses faster than 150ms. Higher PES
scores indicate more slowing after errors. By calculating PES in this way, rather than calculating
average RT post-error minus RT post-correct, we aimed to account for differences in attention
and motivation across the task. For example, suppose a participant is paying attention and highly
motivated at the beginning of the task. In that case, they may be answering many trials correctly,
but as their motivation decreases, they begin making more errors. By calculating average RT preand post-error, we aim to capture correct responses as close as possible to errors, possibly
mitigating the effect of attention on the calculation while still capturing differences in pre- and
post-error behavior.
The nature of PES and PEA calculations is such that not all trials are included in the
calculations, nor are the same trials used in each calculation. Figure 2 shows an example set of
20 trials, and Table 2 shows how PES and PEA would be calculated from these trials.

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Figure 2.
Example Trials During the Math Task
Table 2.
Example PES and PEA Calculation in the Math Task
It is important to note that measuring the relationship between PES and PEA using these
calculations is not a within-person analysis showing that making an error led to more or less
slowing. Rather, these calculations reflect children and adolescents’ tendencies to generally be

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more cautious or more accurate after errors, as in previous studies of error monitoring in children
and adolescents (e.g., Denervaud, Knebel, et al., 2020).
2.2.3 Emotions about Math
Math Anxiety. Participants completed the modified Abbreviated Math Anxiety Scale
(mAMAS; Carey et al., 2017) to assess math anxiety. The scale, initially developed for British
participants, was adapted for this study to American English (e.g., “maths class” changed to
“math class”). The adapted items of the mAMAS are listed in Table 3. This scale was selected
amongst other math anxiety scales because of its validity and reliability for measuring math
anxiety among children and adolescents. Scores ranged from 9-45 (M = 23.60, SD = 8.61; see
Supplemental Information page 136 for distribution of scores). The reliability of the adapted
mAMAS for the present sample, determined using Cronbach’s alpha, was strong (α = .90).
Positive Feelings about Math. We constructed a Positive Feelings about Math
Questionnaire adapted from Martin & Rimm-Kaufman (2015) to examine participants’ positive
social and emotional engagement with math. The items from the questionnaire can be found in
Table 3. Item 6 (“I feel bored in math class”) was reverse-coded. Scores ranged from 9-36 (M =
21.43, SD = 5.84; see page 135 for distribution of scores). Reliability for the present sample,
determined using Cronbach’s alpha, was good (α = .84).

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Table 3.
Items in the Math Anxiety and Positive Feelings about Math Questionnaires
2.2.4 Covariates
Generalized Anxiety. We used the Spence Children’s Anxiety Scale (SCAS; Spence et
al., 2003) to assess generalized anxiety. This scale consists of 38 items that measure separation
anxiety, social anxiety, generalized anxiety, panic/agoraphobia, obsessive-compulsive disorder,
and fears of physical injury. The SCAS is a self-report measure in which participants are asked
to indicate the frequency with which each statement applies to them on a 4-point Likert scale,
ranging from "Never" to "Always." Some examples are "I feel suddenly as if I cannot breathe
when there is no reason for this" and "I worry what other people think of me."
The SCAS provides individual scores for each anxiety dimension and a total anxiety
score. Higher scores indicate higher levels of anxiety (see Supplemental Information page 136
for distribution of scores). The reliability of the SCAS was determined using Cronbach’s alpha.
The full-scale reliability was strong (α = .94). The reliability of the generalized anxiety subscale
used for analysis was moderate (α = .80).

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Raven’s Progressive Matrices. We measured IQ to be included as a covariate in
analyses. Participants completed an abbreviated version of the Raven’s Standard Progressive
Matrices (Raven, 1998). This test comprises a series of designs with a piece missing, and
respondents are asked to identify the piece required to complete the design from six to eight
options shown beneath.
A 15-item Raven’s Standard Progressive Matrices test (Langener et al., 2022) was
administered via E-Prime (E-Prime Go; Psychology Software Tools, 2020). Participant scores
were calculated as the percentage of correct responses out of the 15 items.
2.2.5 Statistical Overview
All data preparation and statistical analyses were performed using RStudio (version 4.3.0;
R Core team, 2023).
3. Results
3.1 Descriptive Statistics
Pearson correlation tests were run to examine relationships between meaning-making,
emotions about math, and the covariates. We found that concrete and transcendent meaningmaking scores were negatively correlated, r(171) = -.31, p < .001. As seen in Table 4, neither
concrete nor transcendent meaning-making scores were related to age, IQ, or generalized anxiety
(ps > .30). Female participants had higher concrete meaning-making scores than male
participants (p = .02). There were no gender differences between the transcendent meaningmaking scores (p = .77).
Additionally, we found that math anxiety and positive feelings about math scores were
negatively correlated, r(200) = -.29, p < .001. Math anxiety was higher in younger participants
(p = .04), female participants had higher math anxiety scores than male participants (p < .001),

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and math anxiety scores were positively correlated with generalized anxiety scores (p < .001).
Positive feelings about math scores were positively correlated with IQ (p < .001).
Table 4.
Meaning-Making and Emotion about Math Scores Relations to Demographic Variables
Note. *p < .05, ***p < .001
3.2 Meaning-Making and Emotions about Math
Per our hypothesis, results from two separate linear regression models showed that
adolescents who demonstrated more concrete meaning-making also reported higher math
anxiety, b = 3.61, t(126) = 2.83, p = .01, ηp2 = .06, and conversely, adolescents who
demonstrated more transcendent meaning-making reported lower levels of math anxiety, b = -
3.24, t(126) = -2.57, p = .01, ηp2 = .05. Figure 3 illustrates these relationships. When examining
the unique effects of meaning-making on math anxiety, by accounting for the variance of each
type of meaning-making in the same linear regression model, concrete meaning-making scores

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remained as a significant predictor of math anxiety, b = 2.90, t(125) = 2.20, p = .03, ηp2 = .04,
however, there was only a non-significant trend of the relationship between transcendent
meaning-making and math anxiety, b = -1.91, t(125) = -2.43, p = .06, ηp2 = .03. Each of these
analyses controlled for age, gender, IQ, and generalized anxiety. A table showing the regression
coefficients for each predictor in these models can be found in the Supplemental Information
(see page 137).
Also, in support of our hypothesis, results from two separate linear regression models
showed that adolescents who demonstrated more transcendent meaning-making also reported
more positive feelings about math, b = 2.36, t(129) = 2.63, p = .01, ηp2 = .05. There was no
relationship between concrete meaning-making and positive feelings about math, b = -1.01,
t(129) = -1.09, p = .28, ηp2 = .01. When examining the unique effects of meaning-making on
positive feelings about math, by accounting for the variance of each type of meaning-making in
the same linear regression model, we found that transcendent meaning-making remained a
significant predictor of positive feelings about math, b = 2.26, t(128) = 2.41, p = .02, ηp2 = .04.
Each of these analyses controlled for age, gender, and IQ. A table showing the regression
coefficients for each predictor in these models can be found in the Supplemental Information
(see page 137).

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Figure 3.
Schematic Depicting Relations Between Meaning-Making and Emotions about Math
Note. Each line represents either a linear model or a Pearson correlation. Control variables in
linear regression models can be seen under the corresponding line. Abbreviations: LM = linear
model and GA = generalized anxiety. *p < .01, *** p < .001
3.3 Meaning-Making and Error Monitoring in the Math Task
3.3.1 Meaning-Making and Post-Error Slowing
In partial support of our hypothesis, results from a linear regression model showed that
there was a non-significant trend toward a positive relationship between transcendent meaningmaking and PES, b = 32.50, t(125) = 1.63, p = .10, ηp2 = .02. IQ also predicted PES, b = 19.57,
t(125) = 2.12, p = .04, ηp2 = .03. Concrete meaning-making was unrelated to PES, b = 17.22,
t(125) = .86, p = .39, ηp2 = .01. This model also controlled for gender and age, which were nonsignificant.

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In a second linear regression model, positive feelings about math, math anxiety, and
generalized anxiety were added as predictors. In this case, positive feelings about math was the
only predictor of PES, such that participants with more positive feelings about math exhibited
more PES, b = 4.10, t(114) = 2.03, p = .045, ηp2 = .03.
Given this finding, we conducted an exploratory mediation analysis to examine whether
positive feelings about math may mediate the relationship between transcendent meaningmaking and PES. A mediation model was run using the “process” package in R (Hayes, 2013),
that included transcendent meaning-making as the predictor, positive feelings about math as the
mediator, and PES as the outcome variable, controlling for age and gender. The indirect effect
was 13.62 with standard error 7.99, 95% CI [2.81, 28.25], confirming a significant mediation of
positive feelings about math on the relationship between transcendent meaning-making and PES.
3.3.2 The Moderating Effect of Meaning-Making on the Relationship Between PES and PEA
Overall, the relationship between PES and PEA, b = .01, t(179) = 1.09, p = .28, ηp2 = .01
was non-significant. However, we found that concrete meaning-making moderated the
relationship between PES and PEA, b = -3.56, t(112) = -3.01, p = .003, ηp2 = .07. The direction
of the moderation was such that participants who demonstrated more concrete meaning-making
also showed a weaker relationship between PES and PEA. This model was controlled for all
demographic variables, positive feelings about math, and transcendent meaning-making.
To probe this interaction, we tested simple slopes at one standard deviation above and
below the average concrete meaning-making score, resulting in two slopes tested: low concrete
meaning-making and high concrete meaning-making. We found a significant positive
relationship for the low concrete meaning-making slope, b = .08, p < .001. The relationship was

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such that there was a significant positive relationship between PES and PEA at low levels of
concrete meaning-making. A visual representation of the moderation can be seen in Figure 4.
Figure 4.
Visual Representation of How Concrete Meaning-Making Moderates the Relationship Between
PES and PEA
Note. The slopes in this illustration are controlled for age, gender, IQ, math anxiety, transcendent
meaning-making and positive feelings about math.
4. Discussion
Recent interdisciplinary theories of education have brought attention to the need to study
how adolescents’ academic learning in school is coordinated with their social-emotional
development (Nasir et al., 2021). Meaning-making is a social-emotional and cognitive process
by which we construct narratives about the social world (Singer, 2004). This process is relevant
for learning (Craggs & Kelly, 2018), and capacities for meaning-making grow in adolescence

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(Erikson, 1968; Habermas & de Silveira, 2008; Steinberg, 2014). Here, we examined how
adolescents’ dispositions for meaning-making about a social story related to their emotions about
math and error monitoring during a math task. We employed a novel math task to examine
behavioral error responses, asked participants to report their levels of math anxiety and positive
feelings about math, and examined their meaning-making in response to a social story.
We found, as predicted, that adolescents who demonstrated more transcendent meaningmaking in response to the story also reported more positive feelings about math. Notably, this
finding was significant even accounting for IQ. This finding suggests that a disposition towards
transcendent meaning-making within a broader social context may carry over into an academic
context. Potentially, the proclivity to reflect and make broader connections facilitates students’
appreciation for the satisfaction of understanding math and the enjoyment of engaging with
mathematical ideas. Supporting this interpretation, transcendent meaning-making was associated
with lower levels of math anxiety, potentially because the slow, more reflective stance
implicated in transcendent meaning-making helps adolescents overcome the immediate, contextdependent emotional reactivity profiles associated with anxiety. This interpretation aligns with
previous research showing how reflective practices, such as writing about feelings before taking
an exam, help to mitigate test anxiety (Ramirez & Beilock, 2011). Here, we show that
adolescents may harness this disposition for reflectiveness in a way that is protective against
anxiety in a different domain.
In the opposite direction, concrete meaning-making, a negative correlate of transcendent
meaning-making in the present task, was associated with a tendency to math anxiety, above and
beyond the protective influence of transcendent meaning-making. Concrete meaning-making is
context-dependent and reactive to emotions pertaining to the current situation rather than to

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broader values and lessons. Math anxiety is a similarly context-dependent anxiety invoked
specifically in the context of doing math. While concrete meaning-making has previously been
related to positive social relationships and acceptance of diversity (Gotlieb et al., 2022a), this
study reveals that such a disposition to concrete processing may also be a liability in an academic
learning context.
Though our hypothesis that transcendent meaning-making would relate directly to PES
was not supported, we found that positive feelings about math did positively predict PES.
Further, a follow up analysis revealed a significant mediating effect of positive feelings about
math on the relationship between transcendent meaning-making and PES. Given this finding, it
may be that a transcendent disposition of thinking is most proximally translated into the ways of
understanding math, which in turn, influences how one responds to errors. Adolescents who
think more transcendently may reflect more on the importance and interest of math and derive
more positive feelings about it, making them less inclined to rush through important
opportunities for learning. Research has shown that students with math anxiety, a negative
correlate of positive feelings about math, speed through exams, which hinders their accuracy
(Núñez-Peña & Bono, 2021). Future investigations will need to explore further the relationships
between transcendent thinking, positive feelings about math, and the mechanisms and processing
individuals undergo when they engage with errors.
Importantly, we found that at low levels of concrete meaning-making, a tendency to slow
more after errors was associated with a tendency to be more accurate after errors. This finding
may suggest that when adolescents with greater proclivities for concrete thinking slow after
errors, they are not using that time to improve their performance effectively. Notably, this
finding remained significant even accounting for math anxiety, which has also been shown to

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moderate relations between post-error slowing and accuracy (Paper 2). These findings suggest
that theories of post-error slowing should consider social-emotional dispositions as a possible
underlying psychological mechanism.
A strength of this study was the open-ended nature of the meaning-making task. This
allowed participants to demonstrate their thinking and allowed concrete and transcendent
meaning-making patterns to emerge naturally (Gotlieb et al., 2022a). Relatedly, this study’s
findings suggest that these thinking patterns can be identified in fairly brief responses. The
original protocol that this task was developed from includes hours-long interviews and the
viewing of many social stories. While extremely generative, this method can be more difficult to
implement with a large number of participants. This study shows that abbreviated versions of
this protocol can also provide insights into adolescents’ patterns of meaning-making.
The current study presented a few limitations. While the brevity of the social-emotional
meaning-making task facilitated assessing capacities for meaning-making during classroom-wide
data collection, it may have limited the complexity of students’ responses. Due to the survey
format of the questions, as opposed to the interview structure from which this task was
developed, we could not prompt students to elaborate on their responses, resulting in many
responses that were only a sentence or two. Even so, we found that these responses revealed
dispositions of meaning-making. An additional limitation was the inability to control for
demographic variables such as race and socioeconomic status due to missing or potentially
inaccurate data. Future investigations should aim to better control for these factors, particularly
in contexts such as math, in which harmful racial biases are known to affect learning (CopurGencturk et al., 2020).

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The findings of this study may have implications for students beyond their math
classrooms. Research has shown that high school students who enjoy science, a math-adjacent
subject, are more likely to want to pursue a career in STEM (Ahmed & Mudrey, 2019). This was
found to be the case even accounting for STEM career awareness and socioeconomic status.
Potentially, supporting students’ transcendent meaning-making may increase their enjoyment of
math, affecting the careers they pursue as adults. This would align with results from the
longitudinal study that showed transcendent meaning-making to predict positive outcomes in
young adulthood (Gotlieb et al., 2023). Future studies should continue to explore how these
patterns of thinking may carry into adulthood, as well as other academic contexts.
Taken together, the findings of this study demonstrate the possibility that patterns of
meaning-making about the broader social world may be paralleled in academic contexts.
Moreover, these parallels may affect students’ emotions and academic learning. This study also
contributes to the understanding of error monitoring as an affective process, suggesting that
emotions may be one mechanism underlying its behavioral indices.

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General Discussion
Advances in interdisciplinary education research have brought increasing awareness to
the fact that students’ social-emotional functioning and academic learning bidirectionally affect
one another (Immordino-Yang & Damasio, 2007; Immordino-Yang et al., 2019; Nasir et al.,
2021). However, for researchers and educators to build upon these insights, there is a need to
understand better how emotions and learning in the classroom are interconnected. What shared
neuropsychological mechanisms link academic learning and emotions? To begin to address this
question, this dissertation examined error monitoring as a potential mechanism through its
behavioral correlates.
This dissertation is comprised of three papers that aimed to 1) examine the development
of error responses across the school-aged years; 2) examine whether these responses could be
identified in a math task, similar to the learning opportunities children and adolescents engage
with in school; 3) investigate whether emotions about math are related to patterns of error
responses during a math task; and 4) examine whether domain-general social-emotional
functioning is related to adolescents’ error responses during a math task.
The findings from Paper 1 contribute to the growing literature on the development of
error responses from preschool through high school. Most notably, the findings demonstrate
preliminary evidence that young children show capacities for adaptive patterns of error detection
and self-correction. Paper 2 made two significant contributions. First, the findings demonstrated
that error responses were present in a task similar to those children complete during school.
Second, the findings demonstrated that error monitoring may be one learning process by which
math anxiety affects math achievement and that positive feelings about math may also affect
math achievement. Paper 3 furthered the understanding of the possible links between error

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monitoring and social-emotional functioning by examining the connection between error
responses in math and math-specific social-emotional functioning and whether error responses in
math were connected to meaning-making, a domain-general social-emotional process. The
findings of Paper 3 demonstrated that adolescents’ dispositions of thinking about the broader
social world may carry over into patterns of affective experiences and error monitoring in math.
Taken together, the findings from these papers emphasize error monitoring as an instrumental
process in academic learning and suggest the possibility that this process is one mechanism by
which domain-specific and broader social-emotional functioning are linked to academic learning.
In addition to the individual contribution of these studies, a comparison of Papers 1 and 2
underscores the importance of studying error monitoring in context-specific tasks. The different
patterns of error monitoring observed between Paper 1, which used the Flanker Task, and Paper
2, which used a math task, suggest that children’s error responses were context-dependent. To
investigate this further, several exploratory analyses were conducted comparing the error
responses of participants who completed both tasks. First, it was tested whether patterns of PES
differed between the two tasks. A t-test revealed that participants slowed down more after errors
in the math task than they did in the Flanker Task (p = .01). Second, we examined whether the
patterns between math anxiety and PES and PEA in the math task were also present with math
anxiety and PES and PEA in the Flanker Task. Results showed that math anxiety was unrelated
to PES in the Flanker Task (p = .23) and did not interact with PES to predict PEA in the Flanker
Task (p = .66). Math anxiety did negatively predict PEA in the Flanker Task (p = .001);
however, this may be due to priming from completing the math task before the Flanker Task.
Lastly, the same analyses from Paper 2 were tested while controlling for PES in the Flanker
Task. Results showed that the main effects did not change. A statistical summary of these

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analyses can be found in the Supplemental Information (see pages 138-139). These preliminary
findings suggest that the same insights would not have been revealed if this dissertation had only
examined the Flanker Task and math anxiety. As noted, though, these are only exploratory
analyses. The study design was not set up for these comparisons, such that the order of task
completion was not counterbalanced, and participants always completed the math task first,
potentially resulting in unwanted task priming. Future investigations should investigate whether
these differences hold with a more appropriate study design.
A major conceptual contribution of this dissertation is a more developed understanding of
the shared mechanisms of emotions and academic learning. Evidence presented here suggests
that children and adolescents’ social-affective experiences with math may contribute to how
successful they are at learning from their mistakes in math. Researchers could continue to build
on these findings and examine whether educational practices aimed to counter math anxiety
improve error monitoring, or in the opposite direction, if changing mindsets about mistakes
mitigates math anxiety. This dissertation also suggests that broader dispositions for meaningmaking about the social world may be paralleled in academic learning. Potentially, by supporting
students’ dispositions of thinking by creating space for reflection in learning, educators could
foster dispositions of mind in students that are beneficial across academic domains.
A methodological strength of this dissertation was the wide age range of participants,
including children and adolescents ages 3 to 18. This study is one of the few investigations of the
behavioral responses of error monitoring across the entirety of pre-, primary, and secondary
education (for exception, see Denervaud, Knebel, et al., 2020; Smulders et al., 2016). This
dissertation also contributes a novel task to study error monitoring in the context of math. This is
the first math task designed specifically for examining PES and PEA in children and adolescents

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and provides a new tool for future investigations in this area of research. Additionally, this
dissertation shows that social-emotional meaning-making can be examined from a relatively
brief task easily implemented in classroom settings.
This dissertation had several limitations, a majority of which were a result of the scale of
data collection. While collecting data while participants were in school allowed for a better
understanding of error monitoring in the context of academic learning and a wider, more diverse
sample, it also presented difficulties with the quantity and quality of data. Testing entire
classrooms of students at once resulted in less attention being given to participants than usually
is in a lab setting. This data collection may have resulted in some students not understanding the
task fully, being distracted by their peers completing it, or just being off task entirely.
Additionally, testing students while they were in school restricted data collection to align with
bell schedules. Given the time constraints, many students did not complete all of the study
activities. As seen in the analyses of the papers, controlling for a measure such as IQ also led to a
decrease in sample size because fewer students completed the measure.
Building upon this dissertation’s results, future work might examine whether behavioral
patterns of error monitoring are evident in other domains of academic learning, such as science
or reading, and how those patterns may relate to other social-affective experiences of learning.
Future investigations could also utilize neuroscientific methods such as EEG and fMRI that
would provide insight into whether the neural correlates of error monitoring are identifiable in
the math task developed for this dissertation. Additionally, future studies could examine whether
pedagogy may shape patterns of error monitoring and how these patterns may relate to socialemotional functioning. Tantalizing evidence from Montessori schools in Switzerland suggests

100
that this is the case (Denervaud, Fornari, et al., 2020; Denervaud, Knebel, et al., 2020). However,
these hypotheses have yet to be explored in a United States sample of students.
In conclusion, this dissertation aids in building a deeper understanding of how capacities
for error mentoring develop and offers new insights into how error monitoring may be one of the
mechanisms by which academic learning and social-emotional functioning are interconnected.
Ultimately, the characterization of these mechanisms holds the promise of informing the
development of educational practices that support children and adolescents’ development in a
holistic way.

101
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Supplemental Information
Overall Sample Characteristics
Table 1.
Participant Breakdown by School
School Type
Zip Code Median
Household Income
Students Eligible for
Free or ReducedPriced Lunch
Students
Identifying as
BIPOC
Number of Participants
Per Paper
1 2 3
Preschool $22,420 - - 5 - -
Preschool $88,415 - - 18 - -
Elementary $48,514 76% 92% 108 91 -
Middle $71,645 31% 73% 123 121 130
High $31,334 61% 85% 45 49 53
TK-12 $53,635 70% 71% 66 53 39
Note. The elementary school category includes a sum of five classrooms across within the same
school district and school district wide data is reported.
Table 2.
Breakdown of Number of Participants Who Completed Each Task by Grade Level
Total Flanker
Task
Math
Task
Math
Anxiety
Positive
Feelings
about
Math
MeaningMaking
Ravens
(IQ) SCAS Gender
n participants
Prek/
Kindergarten 31 31 - - - - 24 - 30
Elementary 135 125 108 107 110 - 75 73 118
Middle
School 158 148 144 151 149 112 143 150 145
High School 64 54 59 59 58 59 48 57 59
Note. Each number represents the number of participants who completed each task by age group.
Paper 3 includes participants in the Middle and High school groups.

117
Paper 1 Supplemental Information
Figure 1.
Distribution of Post-Error Slowing During the Flanker Task Broken Down by Grade Level in
Paper 1

118
Figure 2.
Distribution of Number of Errors with Response in the Flanker Task in Paper 1
Table 3.
Paper 1 ANOVAs Testing Relationships between Grade Level and PEA or PES with and without
Controlling for IQ
Note. Gender is coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

119
Table 4.
Paper 1 Linear Regression Models Testing Relationships between Grade Level and PEA or PES
with and without Controlling for IQ
Note. Grade level was dummy coded with the Preschool/Kindergarten level as the reference.
Gender was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.
Table 5.
Paper 1 ANOVAs Testing the Moderating Effect of Grade Level on the Relationship between
PES and PEA with and without Controlling for IQ
Note. Gender is coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

120
Table 6.
Paper 1 Linear Regression Models Testing Relationships between PES and PEA with and
without Controlling for IQ within Grade Levels.
Note. Gender is coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

121
Paper 2 Supplemental Information
Figure 3.
Distribution of Math Anxiety Scores in Paper 2

122
Figure 4.
Distribution of Positive Feelings about Math Scores in Paper 2

123
Figure 5.
Distribution of SCAS Generalized Anxiety Scores in Paper 2

124
Figure 6.
Distribution of Math Anxiety and Positive Feelings about Math Scores +/- 1 SD in Paper 2

125
Table 7.
Paper 2 Linear Regression Models Testing the Effect of PES on PEA in the Math Task with and
without Controlling for IQ
Note. Grade level was dummy coded with the Elementary School level as the reference. Gender
was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not included in the
model.
Table 8.
Paper 2 ANOVAs Testing Relationships between Grade Level and PEA or PES with and without
Controlling for IQ
Note. Gender was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

126
Table 9.
Paper 2 Linear Regression Models Testing Relationships between Grade Level and PEA or PES
with and without Controlling for IQ
Note. Grade level was dummy coded with the Elementary School level as the reference. Gender
was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not included in the
model.
Table 10.
Two-way ANOVAs of Grade Level and Math Anxiety Predicting PEA in the Math Task in Paper
2 with and without Controlling for IQ and Generalized Anxiety
Note. Gender was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

127
Table 11.
Paper 2 Linear Regression Models Testing Relationships between Math Anxiety, Positive
Feelings about Math, Grade Level, Gender, IQ, Generalized Anxiety and PEA or PES
Note. Grade level was dummy coded with the Elementary School level as the reference. Gender
was coded as Male = 1 and Female = 2. FAM = feelings about math. “ – ” indicates that the
predictor was not included in the model.

128
Paper 3 Supplemental Information
Figure 7.
Distribution of Math Anxiety and Positive Feelings about Math Scores in Paper 3
Figure 8.
Distribution of SCAS Generalized Anxiety Scores in Paper 3

129
Figure 9.
Distribution of Transcendent and Concrete Meaning-Making Scores in Paper 3
Table 12.
Linear Regression Models Testing Relationships Between Meaning-Making, Math Anxiety, and
Positive Feelings about Math in Paper 3
Note. MM = meaning-making. FAM = feelings about math. “ – ” indicates that the predictor was
not included in the model.

130
General Conclusion Supplemental Information
Table 13.
Comparison of PES in the Flanker and Math Task
Table 14.
ANOVAs Testing Relations between Flanker and Math Task PES and PEA
Note. Gender was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not
included in the model.

131
Table 15.
Linear Regression Models Testing Relations between Flanker and Math Task PES and PEA
Note. Grade level was dummy coded with the Elementary School level as the reference. Gender
was coded as Male = 1 and Female = 2. “ – ” indicates that the predictor was not included in the
model.

Abstract (if available)

Abstract Error monitoring (EM) is the cognitive, affective process by which individuals notice and react to errors. EM is known to be instrumental in academic learning, however, it remains unclear how EM develops during the school-aged years and how EM may differ in academic contexts and relate to social-emotional functioning. In this dissertation, I employ a cross-sectional study design to investigate developmental patterns of EM in preschool through high school and examine relationships between EM in math, emotions about math, and broader dispositions of social processing in older children and adolescents. Participants were 396 students in preschool through 12th grade. Participants completed a combination of developmentally appropriate study activities, including EM tasks and questionnaires. I show that EM patterns differ across the school-aged years and that children engage in EM as early as preschool (Paper 1). Further investigating how patterns of EM develop in an academic context, I demonstrate that social-affective experiences during math moderate the effectiveness of children and adolescents’ EM during a math task (Paper 2). Bridging adolescents’ dispositions of social processing and social-affective experiences and EM in math, I show that adolescents who engage in more transcendent, reflective thinking also enjoy math more, and conversely, adolescents who engage in more concrete, reactive thinking, experience more math anxiety and demonstrate less adaptive patterns of EM (Paper 3). These findings suggest EM as a potential mechanism connecting social-emotional functioning and learning. This dissertation speaks to the need to educate the "whole child" in schools.

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Asset Metadata

Creator Pueschel, Ellyn Bethany (author)

Core Title Development of error monitoring in preschool to 12th-grade students and relations in late childhood and adolescence to social-affective processing and emotions about math

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Psychology

Degree Conferral Date 2023-12

Publication Date 10/02/2023

Defense Date 08/17/2023

Publisher Los Angeles, California (original), University of Southern California (original), University of Southern California. Libraries (digital)

Tag adolescence,Childhood,error monitoring,math,math anxiety,meaning-making,OAI-PMH Harvest,social-emotional development

Format theses (aat)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Immordino-Yang, Mary Helen (committee chair), Copur-Gencturk, Yasemin (committee member), Grammer, Jennie (committee member), Moll, Henrike (committee member), Morales, Santiago (committee member)

Creator Email ellypueschel@gmail.com,pueschel@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113719244

Unique identifier UC113719244

Identifier etd-PueschelEl-12407.pdf (filename)

Legacy Identifier etd-PueschelEl-12407

Document Type Dissertation

Format theses (aat)

Rights Pueschel, Ellyn Bethany

Internet Media Type application/pdf

Type texts

Source 20231004-usctheses-batch-1100 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright.

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA

Repository Email cisadmin@lib.usc.edu