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Evaluation of a two -period double math program on the academic achievement of underperforming seventh grade math students

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Evaluation of a two -period double math program on the academic achievement of underperforming seventh grade math students

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Content EVALUATION OF A TWO-PERIOD DOUBLE MATH: PROGRAM ON THE ACADEMIC ACHIEVEMENT OF UNDERPERFORMING SEVENTH GRADE MATH STUDENTS by Diane Marie Kempley A Dissertation Presented to the FACULTY OF THE ROSSIER SCHOOL OF EDUCATION UNIVERSITY OF SOUTHERN CALIFORNIA in Partial Fulfillment of the Requirements for the Degree DOCTOR OF EDUCATION May 2005 Copyright 2005 Diane Marie Kempley Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3180388 Copyright 2005 by Kempley, Diane Marie All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3180388 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ii ACKNOWLEDGEMENTS To undertake the commitment to pursue a doctorate of education requires the support, understanding, encouragement and drive of many individuals. I dedicate this dissertation to the many people in my life who have made this possible. My husband, Robert, who unselfishly took over all the household response- bilities these past 3 years to make it possible for me to work full-time and complete this dream. M parents, Boyd and Agnes, who instilled the love of learning and the value of an education in all their children and grandchildren, and supported me in many ways over these many years to reach for the stars. Dr. Mike McLaughlin, leader, mentor, and friend. You were always pushing the envelope and encouraging me to take the next step both in my professional life, as well as my educational life. I am forever appreciative of your guidance and support. Te Redding School District Board of Education, Dr. Renae Dreier, Superintendent, and the educators I work with daily, for their continued support and encouragement. Dr. Dennis Hocevar, my dissertation chair, for his steadfast commitment to the Redding Cohort and for his kindness and support over these past 3 years. Dr. Carl Cohn, a fine gentleman and scholar, who took the theory and showed me how what it could look like in practice. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The USC Redding Cohort who bonded together through thick and thin to us all through. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS..................................................................................... ii LIST OF TABLES.................................................................................................... vi LIST OF FIGU RES.......................................... viii ABSTRACT............................................................................................................... ix Chapter Page 1. INTRODUCTION....................................................................................... 1 Evaluation of a Two-Period Double Math Program on the Academic Achievement of Underperforming Seventh Grade Math Students....................................................................... 1 Mission Statement of Mathematics Department................................ 2 Evaluation Research.............................................................................. 3 Rationale for Evaluation....................................................................... 4 Problem Analysis................................................................................... 6 Description of the Targeted Program.................................................. 12 2. REVIEW OF THE RELEVANT LITERATURE.................................... 17 Middle School Reform.......................................................................... 17 The Middle School Student................................................................... 25 Mathematics Achievement History..................................................... 29 What Works to Improve Student Achievement?............................... 32 Time and Learning................................................................................. 35 3. EVALUATION DESIGN........................................................................... 40 Methodology............................... 40 Participants ........... 40 Procedure................................................................................................. 41 Intervention or Manipulation ................................. 42 Procedures............................................................................................... 45 Statistical Analysis ..................... 46 4. RESULTS .......................................................................... 47 Introduction............................................................................................. 47 Participants....................................................... 48 Null Hypothesis................... 48 Pretest D ata............................................................................................. 48 Math Attitude ..................... 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V Chapter Page Grade Point Averages: Pretest Results............................................... 52 Pretest Math criterion Test Results ................................................ 54 Treatment and Control Group Comparison Math Attitude.............. 56 Treatment and Control Group Comparison: Grade Point Average............................................................................................ 59 Pre/Post Comparison on Math Criterion Test..................................... 61 Summary................................................................................................. 64 5. INTRODUCTION........................................................................................ 65 Hypothesis............................................................................................... 65 Results..................................................................................................... 65 Rationale for the Study.......................................................................... 66 Dependent Variable Discussion........................................................... 67 Hypothesis #1................................................................................... 67 Hypothesis #2................................................................................... 68 Hypothesis #3................................................................................... 69 Discussion............................................................................................... 70 Limitations of the Study........................................................................ 74 Recommendations for Further Research and Practice....................... 76 REFERENCES........................................................................................................... 78 APPENDICES........................................................................................................... 83 A. MDTP PREALGEBRA READINESS TEST........................................... 84 B. MDTP SAMPLE PRINTOUT REPORT................................................... 96 C. MATH ATTITUDE SURVEY................................................................... 99 D. PARENT NOTIFICATION LETTER................... 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi LIST OF TABLES Tables Page 1. Student Achievement in Mathematics Data California Standards Test Data: Mathematics-2003-2004........ 3 2. Northstate School District Math Criterion Reference Test Results 2003-2004 School Year...................................................................... 3 3. Mark Distribution by Grades: Mathematics........................................... 4 4. 7th Grade Math Performance G ap ............................................................ 7 5. Math Achievement Comparison between California and the Nation on the NAEP Math Assessment........................................................ 29 6. Math Attitude Reliability Analysis.......................................................... 49 7. Pretest Math Attitude Means and Standard Deviation.......................... 50 8. t Test for Equality of Means: Prettitude Math Survey......................... 51 9. Pretest Grade Means and Standard Deviation......................................... 52 10. Fourth Quarter Pregrades Independent Samples Test........................... 53 11. Test Item Total Number and Title.............................. 54 12. Prettest Math Criterion Test Means and Standard Deviation............... 55 13. Independent Samples Test on Pretest: Criterion T est .......... 55 14. Descriptive Statistics of Post Math Attitude Survey............................. 57 15. ANCOVA Effects on Math Attitude................................... .................. . 58 16. Posttest Math Attitude Means and Standard D eviation........................ 59 17. Descriptive Statistics of Postmath Grades ...... 60 18. ANCOVA Effects on Math Grades..................... 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vii Table Page 19. Means and Standard Deviation for Posttest Grades............................... 61 20. Descriptive Statistics of Postmath Criterion T est.................................. 62 21. ANCOVA Effects on Math Criterion Test Results............................ 63 22. Estimated Marginal Means: Pre/Postmath Criterion Test.................... 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii LIST OF FIGURES Figure Page 1. Math Attitude-Pretest Graph.................................................................... 51 2. Histogram of End of Year 6th Grade Math G rades............................... 53 3. Histogram Displaying Precriterion Test Results.................................... 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix ABSTRACT The purpose of this research was to determine if two periods of daily math instruction would positively impact the academic achievement of underperforming 7th grade math students. A total of 54 students, equally divided between the control and the treatment group, were selected for the study. Student selection was based on three measures which included: (a) end of year 6th grade math grades, (b) ranking of basic or below basic on the Spring, 2004 state math standards test (CST), and (c) results on the end of the district end of the year math criterion test. Evaluation was based on a pre- and posttest summary of two groups of students for one semester. Pre- and posttest evaluation was based on three measures: (a) 6th grade 4th quarter math grade and 1st and 2nd quarter math grades, (b) a Likert scale survey to measure student’s attitudes about math, and (c) a pre/posttest criterion referenced test. An analysis of covariance (ANCOVA) was utilized to determine if there is a statistically significant difference between the control and the treatment groups. The means were adjusted in order to compare the dependent variables of both groups. Results of this study indicated the 2-period double math program did not statistically affect student attitudes about math or their performance on the math criterion test. The results did indicate that the 2-period double math program did significantly impact student’s math grades. There size of the grade effect was large as indicted by their adjusted means, (T= 2.47; C = 1.43). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The study lends itself to other curriculum areas and grade levels. Further research might include the measurement of other variables including but not limited to: (a) teacher training, (b) instructional strategies, (c) classroom management, (d) classroom curricula design, and (e) student performance on the state standards test. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 CHAPTER 1 INTRODUCTION Evaluation o f a Two-Period Double Math Program on the Academic Achievement o f Underperforming Seventh Grade Math Students Spartan Middle School has long been a leader, a school on the “cutting edge” of educational reform. Following the tenets of Caught in the Middle, Carnegie Turning Points (Carnegie Council, 1989), and Taking Center Stage (CDE, 2001), Spartan continually “pursues excellence.” Spartan operates from a shared vision and mission of community beliefs, which together with school goals and priorities, are evaluated and annually approved by the various school community stakeholders. The staff, students, parents, and community work together to: 1. Create a community for learning; 2. Teach a core of common knowledge; 3. Ensure success for all students; 4. Empower staff; 5. Prepare teachers for the middle grades; 6. Improve academic performance through health and fitness; 7. Re-engage families in the education of young adolescents; and 8. Connect Seneca to the community. Spartan Middle School makes a difference by attending to the physical, intellectual, emotional, and social needs of approximately 1,030 students in Grades Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 6-8. Northstate is a city of approximately 70,000 residents in a rural region of Northern California, approximately 160 miles north of Sacramento. The student population is comprised of: 84% Caucasian, 3% Asian, 5% Hispanic, 3% Native American, 3% Black, and 1% other who come from a variety of socioeconomic backgrounds. Approximately 44.5% of our students qualify to participate in the free or reduced lunch program. Spartan has not received accolades for being perfect, but more for how it has responded to problems while continuing to focus on quality education. Spartan proves that effective middle schools emphasize academic integrity while making emotional connection with students. Mission Statement o f Mathematics Department It is essential that students develop an understanding of the symbolic language of mathematics and mathematical reasoning. Students must be proficient in the California State Mathematics Standards: (a) Number Sense, (b) Algebra and Functions, (c) Measurement and Geometry, (d) Statistics, (e) Data Analysis, and (f) Probability. By the end of 8th grade, all students will master operations with whole numbers, decimals and fractions. They will use relationships among units of measurement and properties of two and three dimensional shapes to solve problems. They use statistical techniques to systematically analyze data and probability situations. In addition, they will represent numerical and functional relationships Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. symbolically, and use symbolic representations to solve problems. Algebraic skills and concepts are developed and utilized. Evaluation Research Will a two-period double math program positively impact the academic achievement of underperforming 7th grade math students at Spartan Middle School (Tables 1-3)? Table 1. Student Achievement in Mathematics Data California Standards Test Data: Mathematics-2003-2004 Percentage of students in each performance band by grade Grade Far below basic Below basic Basic Proficient Advanced 6 3% 21% 30% 30% 16% 7 5% 24% 37% 26% 7% 8 6% 19% 31% 31% 14% Table 2. Northstate School District Math Criterion Reference Test Results 2003-2004 School Year Percentage of students scoring above and below 50% on district made criterion test. 60% determined as proficient Grade Above 60% Below 60% 6 56.3% 43.7% 7 35% 65% 8 66.2% 33.8% Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 Table 3. Mark Distribution by Grades: Mathematics Percentage o f students receiving below a 2.0 Grade: 2003-2004 school year Grade First quarter Second quarter Third quarter Fourth quarter 6 23.8% 20.5% 25.8% 28.1% 7 31.9% 29% 18.3% 18.6% 8 29.2% 28.4% 30% 18.6% Note. Advanced math students grades not included. As evidenced by the California Standards Test scores, district criterion reference math test results, and mark distribution by grade, one can see there are a large percentage of students who struggle with mastery of math concepts at the middle school level. Students receive 45 minutes daily o f math instruction. Teachers attribute high failure rate of students to lack of parent support at home, large class sizes, and lack of time to grasp concepts. This resulted in the development of an action research plan to provide additional instructional time for underperforming math students. Rationale fo r Evaluation Math teachers and administration are committed to helping students achieve to their fullest potential. An on-going dialogue with the Math Department has centered on what can be done to assist underperforming math students. Teachers provide before and after school study hall times. The after-school program provides instructional assistants to assist in homework and classroom help in all curricular Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 areas. Forty-five percent of our students utilize bus transportation to and from school, and are thereby, limited in participating in study halls and the after school program unless parents can provide transportation. Administration and math teachers carefully looked at ways to assist students during the school day. The result was a plan to identify those students who are currently underperforming in math and provide them with a second period of math instruction during the school day. Providing students additional math instruction time during the school day, necessitates taking the student out of their elective program until they are performing at a competent level in their regular math program. This is determined by their performance in the regular math program. Participation in the double math period will be based on district criteria test data, teacher referrals, California Standards Test (CST) math scores, and previous math grades. Efforts will be made to schedule the students with the same instructor they have for their regular math class. Class size will be limited to 20-25 students. Instructors will focus on the pre-teaching and re teaching of daily skills and homework assistance. The purpose of this evaluation problem is to evaluate the effectiveness of extended time in math relative to student achievement. The general goal is to determine if extended math time has a positive effect on the academic achievement of seventh grade math students. A secondary goal will be to determine if extended math time will result in students having a more positive opinion about mathematics. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 Problem Analysis In the book, Turning Research into Results, Clark and Estes (2002, p. 21), state that in order to improve performance, one must first identify the goal. The California Department of Education has established grade level standards for mathematics. The expectation from the Department o f Education is that all students are expected to master the standards for their grade level. The State of California determines mastery of concepts through the annual State Assessment Program. Based on their testing performance, students are ranked in terms o f proficiency on a 5-point scale: (a) far below basic, (b) below basic, (c) basic, (d) proficient, and (e) advanced. The Department of Education has established the goal that all students in California will rank in the proficient or advanced level on state assessments. The mathematics department at Spartan Middle School believes it is essential that all students must be proficient in the five domains of mathematics: (a) number sense, (b) algebra and functions, (c) measurement and geometry, (d) statistics, and (e) data analysis and probability. The staff has embraced the state mathematics standards and set as its goal to have all students be proficient in mathematics. The performance level of 7th grade math students, as measured by the State assessment results for the 2003-2004 year, indicate that 33% of 7th grade students have met the performance goal of being proficient or advanced (Table 4). The first step in closing the performance gap at Spartan Middle School involves identifying the causes of the gap. According to Clark and Estes (2002), Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 Table 4. 7th Grade Math Performance Gap Area Current desired goal Current Performance (02-03 standardized test results) Gaps to be closed Math 100% at 33% at proficient or 67% to move from far Achievement proficient advanced level. below basic, below level or basic, or basic level to above proficient or advanced levels. “We have to identify the causes of the gap and, therefore, the type of performance improvement program required” (p. 41). Clark and Estes (2003) identify three causes for performance gaps. These include: (a) people’s knowledge and skills, (b) people’s motivation to achieve the goal(s), and (c) organizational barriers that may be causing the gap (p. 43). The staff at Spartan Middle School analyzed students’ assessment results for the purpose of identifying the strengths and weaknesses that need to be addressed. This is completed during staff development days, minimum days, weekly team meetings, and monthly department meetings. Through these meetings staff identified six factors that were possible causes for the performance gap. These include: 1. Lack of prior knowledge or skills for students; 2. Inability of parents to support or assist in math; 3. Failure of students in completing homework, assignments or test preparation; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 4. Limited instructional time; 5. Large class sizes; and 6. Behavioral issues. From the factors identified at meetings with the Math Department, it becomes apparent they fall under the three causes identified by Clark and Estes (2002). First, the knowledge and skills of the students, teachers and parents must be addressed. Student’s knowledge and skill level is evaluated by their math grades and annual district and state testing results. In addition, prior teacher input is solicited to help determine each student’s current skills and knowledge level related to mathematics. Teacher’s knowledge and skills are addressed through training and support. Current staff are involved in the following staff development activities: (a) taking college math classes; (b) attending monthly math meetings on relevant math topics taught by high school instructors; staff development opportunities offered by the district; (c) monthly department meetings; (d) support of retired math teachers; and (e) sharing of professional reading materials related to math. Parent’s skills and knowledge level were identified as a cause of the performance gap. Math teacher’s offer assistance to parents through conferences, e-mail and voice mail. Second, motivation gaps are evident in the causes for the performance gap. Through interviews, teachers felt overwhelmed with the numbers of students not performing at grade level. Teachers believe students lack the motivation to work at increasing their mathematical proficiency due to prior performance or experiences Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 and the lack of understanding of concepts. Parents lacked the motivation due to their need to provide support for their families. During Student Study Teams or Parent Conferences many parents expressed the feeling of incompetence in math based upon their prior experiences. This feeling is often transmitted to the children of these parents in rationalizing why they are not successful in math. Albert Bandura (1977) found that positive people who believe they are capable, will achieve significantly more than those who doubt their abilities. Student’s attitude and efficacy can be a contributing factor in analyzing the performance gap in mathematics. Providing a second period of math instruction for selected students focuses on not only skill acquisition and proficiency, but also building a student’s confidence in mathematics. A third potential cause of the performance gap involves analyzing the organization. In analyzing the academic performance of students in mathematics, teachers believed that time was a primary factor for students not being successful in math. Students at Spartan Middle School have a daily 45 minutes of math instruct- tion. Additional assistance is given to students before or after school, 1 to 2 days a week during study halls. Student may also receive assistance in the after-school homework club. Students who rely on bus transportation to attend school are unable to participate in before and after school study halls or homework club. Teachers’ brainstormed ways the school could provide additional instructional time during the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 school day for those students who struggle in math. The result of this team planning, involved assigning a second math period to students as their elective. Further problem analysis focuses on assessing teacher knowledge and skills. Researchers have identified many variables that affect attribute to teacher effectiveness. Robert Marzano (2003) synthesized this research into three categories: 1. Instructional Strategies 2. Classroom Management 3. Classroom Curriculum Design (p. 76) At Spartan Middle School, it was important for the administration and staff to consider these areas in terms o f their effect on closing the performance gap. Marzano (2003) identifies nine categories of instructional strategies that affect student achievement: 1. Identifying similarities and differences; 2. Summarizing and note taking; 3. Reinforcing effort and providing recognition; 4. Homework and practice; 5. Nonlinguistic representations; 6. Cooperative learning; 7. Setting objectives and providing feedback; 8. Generating and testing hypothesis; and 9. Question cues, and advanced organizers (p. 80) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 A survey of math teachers at Spartan Middle School, will need to be conducted to determine to what degree teachers utilize these instructional strategies in their classroom. The results of this survey will be used to determine if the effectiveness of instructional strategies in addressing the performance gap. Marzano’s Survey Items fo r School-Level Factors (2003), will be administered to math instructors to determine what instructional strategies are utilized in the classroom. Classroom Management has been identified by Marzano (2003), Wang, Haetel, and Walberg (1993) and others as a factor that can influence student achievement. Definitions of classroom management vary among researches. Robert Marzano (2003) defines classroom management into four areas. These include: 1. Establishing and enforcing rules and procedures 2. Carrying out disciplinary actions 3. Maintaining effective teacher and student relationships 4. Maintaining an appropriate mental set for management (pp. 88-89) To determine if classroom management techniques impact student performance in mathematics, a survey will need to be administered to teachers and administrators at Spartan Middle School. Robert Marzano’s (2003), Survey Items for School-Level Factors, will be used to measure the effect of classroom management in the 7th grade mathematics classrooms. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 Classroom curricular design is the third factor identified by Robert Marzano, as impacting student performance. Marzano (2003) identifies classroom curriculum design as, “The sequencing and pacing of content along with the experiences students have with the content” (p. 106). The sequencing and pacing of lesson impacts student comprehension of the content of the lessons, and ultimately, the mastery of the curriculum standards for that subject matter. Much research has been conducted that identifies the effective size of varying types of lesson design and delivery. Based on research, Marzano (2003) identified five action steps to consider in classroom curriculum design. Specifically, Teachers need to identify and articulate the specifics of content; to ensure students have multiple exposures to content; to identify procedures to be mastered; to structure content and tasks using the principles of sameness; and to engage students in complex tasks that require them to address content in unique ways. (p. 120) All five of the components can impact the level of performance. The Marzano (2003), Snapshot Survey o f Effectiveness Factor, will be administered to administrators and teachers at Spartan Middle School to determine if this is an area that impacts the performance gap. Description o f the Targeted Program Spartan Middle School serves approximately 1,030 6th, 7th, and 8th grade students. The school’s educational program is centered around a 7-period day. Students in Grades 6, 7, and 8 are required to take one period each of daily math, science, physical education, history, language arts, reading, and elective. All periods Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 are 45 minutes in length. The school is organized into two teams at each grade level. Each grade level team is made up of CORE teachers who provide language arts, reading, and history instruction in a three-period block of time, one math teacher, and one science teacher. These teams share the same group of students and have a common planning time each day. Exploratory wheel and physical education teachers are not part of the grade level teams. The mathematics program at Spartan Middle School involves two teachers at each grade level and a designated special education teacher in math. All students receive 45 minutes daily of math instruction. Class size averages 33 students per period. Instructors teach six periods of math instruction daily. Each grade level has a minimum of two advanced math sections. Students are selected for advanced math based on a district developed math assessment, teacher j udgment, and performance on state math assessments. Students who are performing significantly below grade level in math, may receive their instruction through the special education instructor. Some students who do not qualify for special education services are provided school- based instruction in math through the special education teacher. These students are identified through a student study team process. State approved standards-based textbooks are provided for all students at Spartan Middle School. Math instructors utilize these instructional materials for planning daily lessons. Most instructional lessons follow an instructional framework that includes seven steps. These are: (a) anticipatory set, (b) objective and purpose, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 (c) input, (d) modeling, (e) checking for understanding, (f) guided practice, and (g) independent practice. Homework is assigned daily by the classroom teacher. There is very little use of manipulatives in the math program. Teachers frequently assess the progress of their students through homework, quizzes and tests. All students are given state required math assessments each spring. A district developed math criterion test is given to students annually. Spartan Middle School offers after-school homework assistance for students with instructional assistants. In addition, intervention services are offered after school by a credentialed teacher. Teachers provide before and after-school study halls for additional assistance. A significant number of our students, 45%, depend on transportation for attendance and are unable to participate in before or after school assistance. Monthly department meetings allow math teachers to work together for articulation. The local high school has provided a department chair to work with the district on articulation. He has provided voluntary in-services for our teachers on mathematics topics. Fall staff development days include professional development days for math instructors. Periodically math teachers are provided opportunities to participate in state and regional math conferences. The school subscribes to math the National Council o f Teachers o f Mathematics Journal for teachers. Teachers frequently attend summer classes in mathematics at the local junior college. Each grade level has a counselor assigned to the grade. The counselor stays with the students all 3 years while at the school. The counselor provides support and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 guidance for the students and acts as a liaison between teachers and families. The counselor conducts weekly team meetings with the staff at her grade level. In working with the staff teachers often express concern over the academic achievement of their students, particularly in math. The current administrator at Spartan Middle School has been in her position for 2 1/2 years. She meets frequently with the Math Department teachers. Math instructors have expressed concern over the large number of students who are not mastering the State standards for their grade level. Teachers express frustration that a large number of students are not completing homework or returning it. Staff express that students who need extra help are not taking advantage of before and after school study halls. Parents have expressed concerns that their children do not understand the math and that they have difficulty explaining it to them. Math teachers feel pressured to cover the State mandated standards. Data presented previously in this chapter has shown an average of 67% o f the students at Spartan Middle School, have performed below the proficient level on the California State Standards Test. Year-end results on the district math criterion test indicate that 35% of students are not proficient in mathematics. In addition, 18.6% of 7th grade students earned below a 2.0 grade in mathematics during the 4th quarter. Teachers attribute this high failure rate to lack o f parent support at home, large class sizes, and lack of time to grasp concepts. Staff discussed many ways they could address helping students be more successful in math. School staff believes that Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 most students who are struggling with math, could be helped with additional time to process the information. This belief becomes the basis of this evaluation dissertation. This study will focus on determining if an additional period of math instruction for underperforming 7th grade students, will increase their academic achievement and positively impact their opinion about mathematics. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17 CHAPTER 2 REVIEW OF THE RELEVANT LITERATURE This section represents a comprehensive review of the relevant literature related to this action research project. Chapter 2 will address the following research (a) middle school reform, (b) middle school age students, (c) history of math achievement at the middle school level, (d) what works to improve student achievement, and (e) time and learning. Middle School Reform The purpose and functions of exemplary middle schools center on the intellectual, social, emotional, moral, and physical developmental needs of young adolescents (Clark & Clark, 1993). According to a research report completed by the National Middle School Association, “Five key components are generally recognized by educators, associations, foundations, state boards of education, and researchers” (NMSA, 2001). These include: 1. Interdisciplinary teaming necessary to provide structure and support for middle school students and staff. Interdisciplinary teaming allows for a positive psycho social environment that allows flexibility and variety (Keefe et al., 1983). Spartan Middle School provides interdisciplinary teaming at all three grade levels. Core teachers, math teachers, and science teachers share a common group of students and have a common planning period. A grade level counselor provides support to the students and teachers and conducts weekly team meetings. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 2. Advisory programs that promote developing close and trusting relationships between adults and students. According to George and Shewey (1994), advisory programs help create positive school climates as well as enhancing students’ self-concept and preventing school dropouts. Spartan Middle School conducts bi monthly advisory sessions which focus on current issues related to young adolescents. 3. The National Middle School Association, (1995), promotes varied instruction for students at the middle school level. This could include: integrating learning experiences with real life issues; engaging students in problem solving debates; providing experiences that promote collaboration, cooperation, and community; and seeking to develop good citizenship. This can be accomplished by use of multi-age grouping strategies, cross-age tutoring; and use of block or flexible scheduling. Spartan Middle School partners community “School to Career” businesses that engage students in real life situations. Approximately 50% of students participate in the annual “Take Your Child to Work Day.” Those not attending, participate in career day opportunities provided by private and public community agencies at the school site. 4. Exploratory programs were identified as a necessary component of middle schools. Exploratory programs allow students at the middle school level to experience academic, vocational and recreational subjects. Spartan Middle School offers a quarterly exploratory program for students in Grades 6 and 7. Programs Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 included are: (a) foreign language, (b) computer technology, (c) fine arts, (d) performing arts, and (e) speech. 5. Research indicates that transition programs are essential for middle school students entering and exiting middle school. Maclver, (1990), found that 88% of students begin middle grades in a new school and that transition may be over whelming for students. Providing a transition program for these students is essential. Spartan Middle School provides a comprehensive transition program for students entering middle school. The principal visits each of the feeder schools and shares the program offered at Spartan. Students take a field trip to the middle school in the spring of their 5th grade year to experience the school first hand. At-risk students are identified by their 5th grade teachers and invited to a 1-week summer academy to help them adjust to the middle school life. Fifth grade parents are encouraged to visit the school during the day or at an evening parent information night to meet the staff and find out about the programs offered. The local high school sends their counselors to the middle school to meet with the 8th grade students and schedule them for their high school classes. The California Department of Education began a research study on middle school in the late 1980s establishing a Middle Grades Task Force. The task force set as their agenda to develop a report specifically aimed at addressing the intellectual, physical, psychological, and social development of early adolescents. The task force met over a year to learn what makes effective schooling in the middle grade level. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 Caught in the Middle: Educational Reform for Young Adolescents in California Public Schools (1987) was published to provide direction for school districts, administrators and teachers in addressing the needs of this very unique age. The reform document focused on five areas: (a) curriculum and instruction, (b) student potential, (c) organization and structure, (d) teaching and administration, and (e) leadership and partnership. The task force postulates, “The success of the educational reform movement depends on meeting the needs of middle school students-both academically and socially. Failing to address these needs jeopardizes efforts for educational excellence and, more importantly, for these students’ own future success,” (1987, p. v). This document provided the blueprints for designing middle schools throughout California. The Carnegie Corporation (1989) of New York issued, Turning Points: Preparing American Youth fo r the 21st Century. This report outlined the need to “strengthen the academic core of middle schools and establish caring, supportive environments, which value adolescents” (p. 10). This report called for transforming the educational practices for the middle school adolescent. Eight recommendations were made by this task force that included: 1. Create a community for learning through small learning environments. The recommendation aims at providing an environment where young adolescents can build trusting relationships with adults and students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 2. Teach a core of common knowledge focuses on teaching adolescent students to think critically as well as develop healthy lifestyles and become active and productive citizens. 3. Ensure success for all students. The findings in this report state, “Tracking students by achievement level is an almost universal practice in middle grade schools .... Lower tracts are often dull and repetitive, leading at best to minimum competencies (Carnegie Council, 1990, p. 4). The recommendations call for grouping students for learning, providing for flexible scheduling and expanding opportunities for learning. 4. Empower teachers and administrators is recommendation number four. The report calls for giving teachers creative control over how they achieve curriculum goals. In addition it is recommended that schools build governance committees made up of teachers, administrators, students, support staff and parents. The goal is to “promote trust, respect, and a community of purpose essential for learning” (Carnegie Council, p. 18). Finally, a recommendation is made for designating teacher leaders in each department to ensure a conducive learning environment. 5. Preparing teachers for the middle grades is identified as an essential recommendation. Teaching adolescent students requires competent teachers who are trained in addressing the unique needs of middle school students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 6. Recommendation number six calls for middle schools to address the academic performance of middle school students through better health and fitness opportunities. Middle school is the time when students are experimenting and exploring. This study found “70%-80% of all youth in need of mental health services may not receive these services” (Carnegie Council, p. 20). Providing counselors and health services for middle school adolescents is a necessary component of this recommendation. 7. At a time when adolescents are attempting to assert their own identity, families need to play an important part during these unique years. Middle schools need to promote parent involvement through participation in school governance, keeping them informed, and offering opportunities for parents to support learning at home and at school. 8. Middle Schools need to reach out to the school community organizations to provide for a shared responsibility in ensuring middle school students success. This recommendation calls for promoting opportunities for youth service, access to health and social services, expanding career guidance opportunities for students, and supporting the middle school program. In 2001, the California Department of Education (2001) published, Taking Center Stage: A Commitment to Standards-Based Education fo r California’ s Middle Grades Students. Building on the foundation of Caught in the Middle and Turning Points, this document focuses on standards, assessment, and accountability and their Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 implications for middle school instruction. This document outlines seven key elements and recommendations needed to ensure the success of all students in mastering state standards. These seven elements include: 1. Rigorous academic content and performance standards; 2. Curriculum and instruction; 3. Assessment and accountability; 4. Student interventions; 5. Professional development; 6. Parent and community partnerships; and 7. Health and safety (pp. 2-4). The information gathered in these three key reform documents is utilized in developing the organizational structure and instructional program for students at Spartan Middle School. The former principal of Spartan Middle School, served on the Middle Grades Task Force in the development of Taking Center Stage. As principal, he was instrumental in implementing many of the recommendations for educational reform including, the school— within a school concept, grade level teaming, advisory, and creating counseling positions at each grade level to provide support for students and teachers. Research from these three documents is considered in developing the two-period math program for under-performing middle school students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 Aimed at closing the achievement gap in students, the federal government passed the No Child Left Behind Act of 2001. This new law focused on increasing accountability for all states, school districts, and schools; greater choice for parents and students; more flexibility in state and local educational agencies; and a stronger emphasis on reading. In reference to mathematics, the U. S. Department of Educa tion (n. d.) attests, “America’s schools are not producing the math excellence required for global economic, leadership and homeland security in the 21st century.” The government suggests the solution to these problems is to “ensure schools use scientifically based methods with long-term records of success to teach math and measure student progress.” In addition, the mandate calls for schools to “establish partnerships with universities to ensure that knowledgeable teachers deliver the best instruction in their field” (USDE, n.d.). This federal legislation requires all students in Grades 3 through 8 to be tested annually in math and reading/language arts. Each state had to submit an accountability plan that meets the federal requirements of No Child Left Behind. All schools, including middle schools must make adequate yearly progress (AYP) on state assessments. Under the federal law, schools not making adequate yearly progress can be subject to improvement or corrective action that can include restructuring measures (U. S. Department of Education, 2001). Spartan Middle School embraces the federal NCLB mandate and works to align curriculum and instruction to state standards. The school and district has made their AYP goals this past year. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 The Middle School Student The next part of the research will look at the unique attributes of the middle school adolescent. This is particularly important in designing any instructional program that meets the needs of young adolescents. Much research has been written about the changes young adolescents go through during the middle school years. The reform documents mentioned in the first part of this chapter all address the unique personalities of middle school students. According to Peter Scales (1991), the early adolescent is characterized by seven key developmental needs. These seven needs are: (a) positive social interaction with adults and peers, (b) structure and clear limits, (c) physical activity, (d) creative expression, (e) competence and achievement, (f) meaningful participation in families and schools, and (g) communities opportun ities for self-direction. In his book, Teaching Ten to Fourteen Year Olds, Chris Stevenson (1992) writes, “Every child wants to believe in himself as a successful person; every youngster wants to be liked and respected; every youngster wants physical exercise and freedom to move; and youngsters want life to be just” (pp. 4-8). Jacquelyn S. Eccles and Alan Wigfield has complied many research studies relating with adolescent development. In the book, What Current Research Says to the Middle School Practitioner (cited in Irvin, 1997), these authors summarize the major changes and relate them to middle level student’s achievement motivation and performance. These include changes in the child’s intellectual, physical, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 psychological, social and moral and ethical development. Citing research from B. B. Brown, 1990, Eccles and Midgley, 1989, Keating, 1990, Simmons and Blyth, 1987 they state, “Young adolescent development is characterized by increases in desire for autonomy, peer orientation, self-focus and self-consciousness, salience of identity issues, concern over heterosexual relationships and capacity for abstract cognitive activity” (Irvin, 1997, p. 25). Middle school educators need to keep the unique needs of the middle school adolescent in mind when helping them achieve to their fullest potential. Robert Marzano (2003) looked carefully at the research related to student- level factors that contribute to student achievement. In his book, What Works in Schools: Translating Research Into Action, Marzano synthesized the research into three factors that influence student achievement. These include: (a) home environ ment, (b) learned intelligence and background knowledge, and (c) motivation (p. 124). In his summary Marzano states, “Both research and theory indicate that student-level factors account for the lion’s share of variance in student achievement” (p. 125). It is Marzano’s belief that the negative effects of the three elements listed can be overcome. For the purpose of this document, this portion o f the paper will focus on the impact student motivation has on student achievement. There are five major bodies of research related to motivation and achievement that will be discussed in this section. Those include: (a) drive theory, (b) attribution theory, (b) self-worth theory, (c) emotions, and (d) self-efficacy. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 Drive theory, the first mentioned, involves balancing the students striving for success and the fear of failure. John Atkinson (1957), was first to postulate this theory. His work was further investigated by David McClelland (1995). According to this theory, people become either success oriented or failure avoidant. Students who become failure avoidant often develop avoidance techniques that can place blame on other reasons beyond ability. The second theory related to student motivation was conceived by Bernard Weiner (1972) and called the “attribution theory.” According to Weiner, how students perceive the causes of their successes or failures is a better indicator of motivation and persistence than is a learned success or failure. Marzano (2003) writes, “There are four causes individuals attribute to their successes: ability, effort, luck, and task difficulty” (p. 146). Weimer (1972) indicates that effort has the strongest effect on student achievement. Covington (1992) states, “If students believe their failures occur for a lack o f trying they are more likely to remain optimistic about succeeding in the future” (Marzano, 2003, p. 146). Covington and Berry (1976), articulated a third theory related to motivation called “self-worth theory.” This theory assumes there are several factors that influ ence a student’s sense of worth. These factor’s include their performance level, their self-estimates of ability, and the degree of effort expended (Butler & McMunn, 1999). A student’s self-worth depends upon his/her accomplishments. The implication is that if students cannot become successful as some valued activity, this Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 may diminish, their self-worth. In the book, Educational Psychology: Windows on Classrooms, author’s Paul Eggen and Don Kauchak (2003), state self-worth is strongly linked to ones’ perceptions of ability. Some learners will procrastinate, blame others, and engage in other self-handicapping behaviors to protect their perceptions of high ability. Many researchers have investigated the role emotions play in motivation. Joseph LeDoux (1996) looked carefully at the role emotions play in motivation and student achievement. He found that emotions can impact one’s values and beliefs related to their influence on human behavior and thereby impact motivation. When discussing the role motivation plays in student achievement, one must consider the influence of self-efficacy. According to Albert Bandura (1994), “Self- efficacy is defined as people’s beliefs about their capabilities to produce designated levels of performance that exercise influence over events that affect their lives” (p. 1). Bandura (1977) asserts that people who are positive and believe they are capable and effective will achieve at a significantly higher rate than those who doubt their own abilities. The major reform documents, Caught in the Middle, Turning Points, and Taking Center Stage have all considered adolescent development in making their recommendations for organizing and designing effective middle school. Spartan Middle School has worked to incorporate the recommendations from these reform documents. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 Mathematics Achievement History When looking at the research in mathematics, one must consider the historical data related to student achievement in mathematics. This section of chapter 4 will focus on two research documents related to mathematics: the National Assessment of Educational Progress (NAEP) and the Third International Mathematics and Science Survey (TIMSS, 1999). The National Assessment of Education Progress (NAEP) has provided national testing data since 1969. Over the years, NAEP has tested student in various subjects including reading, mathematics, science, writing, U. S. history, geography, civics and the arts (NCES, 2004). “In 2003, NAEP conducted national and state assessment in mathematics in Grades 4 and 8” (p. 1). Nationally, math achievement in Grades 4 and 8 was higher in all performance bands than in previous years. While California schools have continued to improve in math achievement they continue to score below the national average. The table below shows the comparison of California and the national average of 8th grade math performance on the 2003 NAEP assessment. Table 5. Math Achievement Comparison between California and the Nation on the 2003 NAEP Math Assessment Below Basic Basic Proficient Advanced National average 24% 45% 28% 4% California 33% 42% 22% 3% Note. NCES-2004 Mathematics Highlights Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 In his February 6, 2003 presentation at the Mathematics Summit in Washington DC, Tom Loveless (2003) from the Brookings Institution, presented the latest NAEP findings and recommendations. Mr. Loveless asserts the reason student performance levels on the NAEP test are below average is that students are not learning how to compute. Basic skills knowledge is important, according to Mr. Loveless for three main reasons: (a) basic skills serve equity, (b) basic skills are necessary to advance in math, and (c) basic skills predict adult earnings (p. 2). The Third International Mathematics and Science Survey (TIMSS) was considered by some as evidence that the United States was not doing a good job of educating students in science and math. This study, conducted in 1999, involved a comparison of the educational systems in 41 countries. The findings of this report showed that while United States 4th grade students compared similarly to other countries, 8th grade and 12th grade students performed significantly less than students in the other countries (Marzano, 2003). According to Tom Loveless (2003), “TIMSS offers us a good opportunity to use scientifically collected data on some 50 countries to find a more promising answer to the question o f what we should do to improve the mathematics education of all children so that we truly do not leave any of them behind” (p. 3). Related to this research, his report concluded: 1. Students who had high levels of educational resources at home had higher mathematics achievement. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 2. There was a positive correlation between educational expectations and mathematics achievement. 3. An average of 15% of students were convinced they could not do math. Students who had a positive self-concept about math scored higher achievement levels. 4. The United States was one of three participating countries not having a national mathematics curricula. 5. The percentage of instructional time for math, on an average, decreases from Grades 6 to 8. 6. Higher achievement rate is related to higher levels of teacher confidence in mathematics. 7. Classes that emphasized reasoning and problem-solving had higher achievement levels than those with less emphasis (TIMMS 1999, International Math Report). Tom Loveless found all high performing mathematics countries had two common features in place. First, all countries had a coherent mathematics curri culum. Loveless (2003) defined coherent as, “A curriculum that leads students through a sequence of topics and performance over the grades that reflects the logical and sequential nature of knowledge in mathematics.” Secondly, Loveless found that all high achieving countries had a curriculum that was focused and demanding. This curriculum “helps students move particular knowledge and skills toward an Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 under-standing of deeper structures, more complex ideas and mathematical reasoning including problem solving” (p. 3). Both reports provide information about math achievement for students in the California and the United States respectfully. The reports indicate a need for improvement in the area of mathematics achievement among our adolescents. Suggestions from these reports should be taken into consideration when developing programs or instructional practices for these students. What Works to Improve Student Achievement? Much research has been conducted with the focus on identifying key factors that can increase student achievement. This portion of the research chapter will focus first on general factors that influence student achievement and then relate the research specifically to mathematics and the middle school student. Robert Marzano, (2003), studied 35 years of research related to student achievement and summarized those findings into three major categories: (a) school-level factors, (b) teacher-level factors, and (c) student-level factors. School-level factors focus on the organizational structure of the school. Marzano (2003) identifies five factors that affect student achievement related to the school. These include: 1. Guaranteed and viable curriculum; 2. Challenging goals and effective feedback; 3. Parent and community involvement; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 4. Safe and orderly environment; and 5. Collegiality and professionalism (p. 15). Teacher-level factors focus primarily on the independent decisions made by teachers that most influence student achievement include: (a) instructional strategies, (b) classroom management, and (c) classroom curricular design (p. 10). Marzano (2003) found from his study of research that the most important factor affecting student learning is the teacher (p. 72). Student-level factors are identified as the third areas of influence on student achievement. Marzano (2003) synthesized the research into three critical factors: home environment, learned intelligence or background knowledge, and motivation (p. 124). Marzano is careful to note that while student-level factors are probably the most influential in affecting student achievement, the negative side of the three factors can be overcome (p. 125). In a recent EdSource Report (2004), researchers Carol Studier and Mary Perry focused on the middle school students and their needs. These researchers identified four areas education needs to focus on for middle school students to meet the high academic standards of the state and the nation. First, they state, professional development and on-going support, is needed for teachers as they learn and design effective instruction focusing on the rigorous standards they are held accountable for. Second, extra support needs to be in place for struggling or at-risk students. Flexible schedules that include block scheduling, drop schedules or rotating schedules can Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 allow for in-depth studies and addressing the needs of the middle school student. Third, schools need to provide ways to promote student engagement that result in their being involved in the middle school program. These researchers note this can be achieved through the inclusion of exploratory classes and extracurricular activities that engage students in school. Fourth, schools need to create organizational structures that includes interdisciplinary teaming. This will allow for a smaller learning community that can focus on meeting the needs of the individual student while fostering positive relationships with teachers and fellow students. Identifying factors specifically related to improving student math achieve ment was the focus of a 10-year study by California Professors’ James Stigler and James Hiebert (2004). These researchers viewed random samples of 8th grade math lessons from different countries. These classroom videos came from the 1995 and 1998 TIMMS studies. The aim of the study was to identify key instructional practices that may impact student achievement. The authors of the study identified three ideas that can improve our teaching of mathematics. These include: 1. The focus of teaching students mathematics should be on instructional practices and lesson design. Stigler and Hiebert (2004) refer to this as the culture of teaching. The authors state, “We must find a way to improve the standard operation procedures in U. S. mathematics classrooms.” The authors further assert, “The ways in which teacher and students interact about the subject, can be more powerful than the curriculum materials the teachers use” (p. 16). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 2. Teachers need to be given the training and the time to analyze lessons in order to improve them. The authors state, “Analysis of classroom practice . . . gives teachers the opportunity to analyze how teaching affects learning and to examine closely those cases in which learning does not occur. It also gives teachers the skills they need to integrate new ideas into their own practice” (Stigler & Hiebert, 2004, p. 16). 3. “Teachers need access to examples” (Stigler & Hiebert, 2004, p. 16), the authors assert. Examples allow the teachers to find ways they can integrate them into their instructional practices. Teachers need to see the theories and applications of research as well as alternative practices in place in order to improve their own practices. This can be accomplished through professional development, observation, and coaching. Time and Learning The topic of time and its effect on learning is a critical component of this evaluation study. This portion of the chapter will focus on several research studies related to extended learning time and mathematics achievement. Research conducted by the National Center for Improving Student Learning and Achievement in Mathematics and Science, located at the Wisconsin Center for Educational Research (2002) found that, “Learning the concepts and skills in a mathematical domain requires students be engaged in a rich set of structured activities over time” (p. 2). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 Lewis and Seidman (1994) compared the amount o f time 8th grade students in the United States and Japanese student spent, both in school and out of school, on math. They found that Japanese student spent 30% more time on math than the United States students. They concluded that a significant increase in student’s math achievement could be gained by increasing the school year and assigning math homework over the summer. Gilby, Link, and Mulligan (1993) looked at 8,400 elementary students over 3 years and concluded that small positive gains in math achievement were made by students how had extra hours of math instruction each week. Tevfik Aksoy and Charles R. Link (1997) conducted a 3-year study to find out if increasing the amount of time in learning activities affects math achievement. These researchers looked at the effect of increased instructional time in school, the effect of increased time on math homework, and the effect of the amount of time students spend watching television. The authors found the following results: 1. Longer daily math periods are associated with increased math achievement. 2. Extra hours spent on math homework increase student’s math test scores. 3. Watching television has a negative impact on student math achievement (p. 274). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 Kathleen Cotton (2001) studied 57 research studies related to educational time factors for the Northwest Regional Educational Laboratory in 2001. Many researchers and theorists credit John B. Carroll’s (1963) work related to educational time factors. Carroll, author of A Model o f School Learning, professed that a student’s time needed for learning depends on five factors: 1. Aptitude. The amount of time an individual needs to learn a given task under the optimal instructional conditions. 2. Ability. Capacity to understand instruction. 3. Perseverance. The amount of time the individual is willing to engage actively in learning. 4. Opportunity to learn. The time allowed for learning. 5. Quality o f Instruction. The degree to which instruction is presented so as not to require additional time for mastery beyond that required by the aptitude of the learner (pp. 723-733). This research was further clarified in terms of how time is being used in the school. In the monograph, Improving Student Achievement by Extending School: Is It a Matter o f Time? (Aronson, Zimmerman, & Carlos, 1999), the researchers studied the relationship of time to learning. Specifically the authors looked at three types of time: (a) allocated time, (b) engaged time, and (c) academic learning time. Allocated time refers to the time students are required to attend school. Engaged time refers to the time students are engaged in learning activities. Academic learning Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 time is defined at the time when students are actually learning. These researchers concluded: 1. There is little or no relationship between allocated time and student achievement. 2. There is some relationship between engaged time and achievement. 3. There is a larger relationship between academic learning time and achievement (Aronson et al., 1998, p. 4). Academic learning time involves focusing on three primary factors. These include: (a) improving teachers’ classroom management skills so there is less loss of instructional time due to discipline interruptions, (b) matching curriculum and instruction so it builds upon students’ thinking, and (c) implementing challenging and engaging instructional activities that increase student motivation. Much research focused on time factors and student characteristics. Cotton, 2001, found the following specific findings from researches she studied: 1. Increasing allocated or engaged time is more beneficial to lower- ability students than to higher-ability students. 2. Increasing time-on-task reduces the anxiety and enhances the achievement of highly anxious students. 3. Increasing time-on-task is more beneficial in the more highly structured subjects, such as mathematics and foreign languages, then in less structured ones, such as language arts and social studies (pp. 8-9). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This chapter focused on five essential elements related to this evaluation dissertation: (a) middle school reform, (b) middle school age students, (c) math achievement history, (d) what works to improve student achievement, and (e) the relationship between time and learning. All five of these factors play a critical part in evaluating the achievement of underperforming 7th grade students through a two- period math program. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 CHAPTER 3 EVALUATION DESIGN Methodology This chapter will focus on the methodology utilized to evaluate the effects of a two period- double math program on the academic achievement of underperforming 7th grade math students. This evaluation research project will follow a quantitative research design. Because there is a variance in the criterion for placement between individual students that cannot be completely controlled by this study, it will be considered quasi-experimental. Three dependent variables were studied: (a) math grades, (b) criterion-referenced test results, and (c) a Likert scale survey to measure student attitudes about math. This chapter will outline the methodology to be used in this study. Participants The participants selected for both the control group and the treatment group were underperforming 7th grade math students attending Spartan Middle School for the 2004-2005 school year. Students selected for the study were based on three criteria: 1. Students receiving below a 2.0 grade point average in 6th grade math (second semester); 2. Students performing at the basic or below basic level on the spring 2004 California Standards Test in mathematics; and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 3. Students performing below the proficiency rate on the end o f year (spring 2004) district math criterion assessment. Procedure There were approximately 330, 7th grade students in attendance at Spartan Middle School. Two groups were identified for this study. The number of participants in this experiment was limited to a total of 54 students, 27 for the control group, and 27 for the experimental group. The placement of the students in each group was based on random assignment. Factors considered for placement included prior math grades, spring 2004 California Standards Test (CST) math ranking, 6th grade math teacher recommendation, and parent recommendation. The treatment group substituted their elective for a second period of math instruction. Parents were notified their son/daughter was placed in a double math period and given the option of not having their child participate. Students in the treatment program were required to participate in the double math offering for a minimum of one quarter of the 2004- 2005 school year. Exit from the “double math” program was determined by teacher judgment and proficiency in the regular one period math program. During the first quarter o f double math, 7 students were exited from the program for behavior reasons. Seven students entered during the 1st quarter. Fifteen students entered double math during the second quarter. Students in the control group did not receive an additional period of math during the school day. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 Intervention or Manipulation Students selected for the treatment group were placed in two periods of math daily for a m ini mum of one-quarter of the fall term. Students in the treatment group were placed in a regular math class, and then receive a second period of math instruction in a smaller group. Instruction focused on pre-teaching and re-teaching of content standards, and homework assistance by one of the 7th grade math instructors. Class size did not exceed 25 students. Students in the control group receive one period of daily math instruction. Double math and regular math classes meet 45 minutes each day. The design utilized three measures for evaluation. A criterion reference math test was administered to all 7th grade students in the study in the fall of the year. This same assessment was re-administered at the end of the first semester to complete a pre- and posttest design. The math criterion test utilized for this study is the MDTP Pre-Algebra Readiness Test (MDTP, 2004). This test is designed to be given to students the year preceding their first course in algebra. This assessment was developed and field tested by the Mathematics Diagnostic Testing Project supported by the California State University and the University of California. The purpose of this criterion test, and the others that MDTP produce, is to assist teachers in “preparing students for success in the further study of mathematics by identifying strengths and weaknesses in their students’ conceptual understanding and procedural skills.” Test development and reliability of test items were completed through Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 extensive field-testing. Included in the test development process is a review of item statistics to ensure that the items test appropriate knowledge and skills, that each item discriminates reasonably well between stronger and weaker students, an that the difficulty levels of the items are not too widespread. To ensure the consistency of an item the biserial “r” is used as a statistical measure. Content validity of the individual items are reviewed to the student’s performance at the end of the course. Comparison of overall test preformed by subpopulations with the performance on each of the five quintals of students based on the total test score with the perform ance of other quintals is used for item discrimination (Mathematics Diagnostic and Testing Project, 2003). The MDTP pre-Algebra readiness test consists of 40 math questions covering a range of prerequisite skills necessary for students to master prior to entering 8th grade algebra class. This assessment is to be administered in one, 45-minute setting. Student answer sheets are sent to the MDTP project for scoring and data analysis. Each math teacher and this researcher were provided with multi-page summaries of results. Included in the results are the following items: 1. Class results by topic represented by both raw scores and percentages correct. 2. Graphic display of class results. 3. Item analysis reports for each subtest. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 4. Individual student results. 5. Individual student letters. Permission was granted by MDTP to utilize this criterion test for this study. Appendix A reflects a copy of the entire assessment. Appendix B shows a sample of the printout reports provided. The second measure pre-post design involved the administration of a Likert scale developed by this researcher. This survey was administered during the first week of school and was re-administered during the first week of December. This survey focuses on five areas: (a) math anxiety, (b) self-esteem, (c) value, (d) level-of effort, and (e) perceived utility. A copy of the survey is included in Appendix C. An independent group’s t test will be used to compare pre-post means for the experi mental and control groups. The statistical procedure of ANCOVA will be used to adjust the means between the experimental and the control groups. A third measure consisted of a compression of 1st and 2nd quarter math grades for both the control and experimental groups. Teacher grades are based upon classroom performance, homework, and test results. Grades are entered on a 5-point scale. A comparison of the student’s math grade for 1st and 2nd quarter will be used to determine if there is a statistical difference between the control and treatment groups. To provide this information an independent group’s t test will be used to compare pre-post means for the experimental and control groups. The statistical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 procedure of ANCOVA will be used to adjust the means between the experimental and the control groups. Procedures Student data were gathered for all incoming 7th grade students during the summer of 2004. Data gathered included: (a) 2003 California Standards Test Math performance rank, (b) 2004 end of year math grade, (c) results o f the 6th grade math criterion test, (d) teacher recommendations, (e) parent recommendations, and (f) special education needs. Students receiving special education services were eliminated from the group due to their receiving services in the special education program. Students were purposely selected based on the criteria. Letters were sent to the parent of students in the treatment group notifying them that their son/daughter will be scheduled into a second period of daily math instruction (Appendix D). Efforts were made to have treatment group students receive services from their same regular math instructor. Due to schedule conflicts this was not always possible. Two 7th grade math teachers were involved in this study. Each teacher was assigned 6 periods of daily 7th grade math instruction including one section of double math as well as one section of 7th grade advanced math. Both teachers jointly plan and present lessons for their students based upon a common instructional focus calendar. Students returned to school on August 26, 2004. All 7th grade students were administered the Likert scale opinion survey in September, 2004. This survey Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 included assessment of (a) math anxiety, (b) self-esteem, (c) value, (d) level of effort, and (e) perceived utility. The two 7th grade teachers administered the criterion- referenced test to all 7th grade students on September 10, 2004. Posttest assessments utilizing the Likert Scale survey and the MDPT pre- Algebra Readiness criteria test were administered again during December of 2004. First quarter and 2nd quarter grades were gathered as part of the study. A compare- son will be made between the control group and the treatment group to test if there is any significant difference in grades received— average for 1st and 2nd quarters. Statistical Analysis The independent variable in this study is the two-period math program. The dependent variables are the MDTP Pre-algebra Readiness test, the Likert scale opinion survey and the average of the student’s 1st and 2nd quarter math grades. To examine the hypothesis of this study, this researcher compared the performance of the experimental and control groups in respect to the three dependent variables. An analysis of covariance (ANCOVA) was utilized to determine if there is a statistically significant difference between the control and the treatment groups. The means were adjusted in order to compare the dependent variables o f both groups. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 CHAPTER 4 RESULTS Introduction The purpose of this study was to evaluate the effects that two periods of daily math instruction have on the academic achievement of underperforming 7th grade math students. In addition, the effect additional math instruction time had on student’s attitudes about mathematics was also evaluated. Evaluation was based on a pre- and posttest summary of two groups of students for one semester. The control group received 45 minutes of daily math instruction. The treatment group received 45 minutes of daily math instruction, plus an additional period of math instruction focusing on pre-teaching, re-teaching and homework assistance from the regular math instructional program. Selection of students participating in the control or treatment groups were based on three criteria: (a) 6th grade math grades, (b) California Standards Test (CST) ranking, and (c) the end of year 6th grade district criteria test results. Students in the treatment group participated in the double math program for a minimum of one quarter, 44 days. Pre- and posttest evaluation was based on three measures: (a) first and second quarter grades, (b) a Likert scale survey to measure student’s attitudes about math, and a (c) pre/posttest criterion referenced test. This chapter describes the research findings of the study. An analysis of covariance (ANCOVA) was utilized to determine if there is a statistically significant Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 difference between the control and the treatment groups. The means were adjusted in order to compare the dependent variables of both groups. Participants There were approximately 330, 7th grade students in attendance in 7th grade at Sequoia Middle School. Two groups were identified for this study. Fifty-four students were randomly selected for the study, 27 in the treatment group and 27 in the control group. The placement of the students in each group was based on random assignment. The participants selected for both the control group and the treatment groups were underperforming 7th grade math students enrolled at Spartan Middle School during the 2004 fall semester. Underperforming was measured by previous year’s math grades, previous year’s criterions test results, and proficiency ranking on the Spring 2004 California Standards Math test. Null Hypothesis There is no statistically significant difference between the control group and the treatment group in terms of math attitude, math grades, and performance on a math criterion referenced test. Pretest Data Math Attitude A Likert scale was utilized to measure four areas related to math attitude: (a) math anxiety, (b) self-esteem, (c) value, (d) level-of effort, and (d) perceived utility. A reliability analysis was run on the 25 items of the survey to determine Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. which items are most likely to produce the same results each time it is administered. Table 6 shows the results of the reliability analysis of the survey. Table 6. Math Attitude Reliability Analysis Mean SD Corrected item total correlation 1. Question 1 2.54 .69 .48 2. Question 2 2.46 .79 .36 3. Question 3 1.52 .84 .36 4. Question 4 2.43 .84 .53 5. Question 5 2.46 .77 .28 6. Question 6 2.22 .79 .44 7. Question 7 2.37 .78 .38 8. Question 8 2.04 1.10 .21 9. Question 9 2.19 .95 .54 10. Question 10 1.50 .88 .26 11. Question 11 2.72 .90 .29 12. Question 12 1.74 .73 .30 13. Question 14 2.67 .87 .26 14. Question 15 2.07 .80 .26 15. Question 16 1.98 .79 .45 16. Question 17 2.17 .84 .36 17. Question 19 2.63 .83 .37 18. Question 20 2.15 .81 .49 19. Question 21 2.63 .94 .38 20. Question 23 2.26 .96 .12 The Likert scale math attitude survey contained 25 questions. Five questions were determined to be unreliable, and therefore, were eliminated from the results. The average mean of the trimmed questionnaire was 44.71 with a variance of 57.48. The standard deviation was 7.52. The alpha coefficient was .79 indicating a high Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 internal consistency of the Likert scale questions after the five unreliable items were eliminated. Table 7 shows the means and standard deviations. The treatment group in this study consisted o f 27 students enrolled in two periods of daily math instruction. The treatment group’s average mean on the pretest math attitude survey was 2.37 with a standard deviation of .37. The control group consisted of 27 students enrolled in one period of daily math instruction. The control group’s mean on the pretest attitude survey was 2.10 with a standard deviation of .34. The math attitude survey used a Likert scale (SA = 1, A = 2, D = 3, SD = 4) to gather responses from the students in five math areas: (a) math anxiety, (b) self-esteem, (c) value, (d) level-of- effort, and (e) perceived utility. The survey was scored so that high numbers indicate a more positive math attitude. Table 7. Pretest Math Attitude Means and Standard Deviation Group Mean SD Std. Error Mean Treatment 2.37 .37 .07 Control 2.10 .34 .07 The t test for equality of means, shown in table 8 indicates the means do differ significantly at the .05 level (p - .008) on the math attitude survey pretest, and therefore, confirms that the control group had a more favorable opinion o f math before the study began. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 Table 8. t Test fo r Equality o f Means: Preattitude Math Survey t d f Sig. (2-tailed) Mean difference Std. error difference Equal variances assumed 2.74 .52 .008 .267 .097 Figure 1 shows the pretest math attitude survey results. As indicated by the graph, the majority of answers on the pre-math attitude survey fell below the theoretical scale mean (2.50). There was a positive skew ness to the results signifying very few students reported exceptionally positive attitudes towards math. MATHAT U. MATHAT Figure 1. Math attitude— pretest graph. Std. Dev = .38 Mean = 2.24 N = 54.00 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 Grade Point Averages: Pretest Results End of year, 4th quarter math grades were obtained for use in this study. Grades were averaged to obtain a mean score. Grades were coded: 0 = F; 1 = D; 2 = C; 3 = B; and 4 = A. Table 9 shows the mean grade point averages and the standard deviation of the spring 2004 6th grade math scores for both the treatment and the control groups. The mean of the treatment group was 1.12 with a standard deviation of 1.16. The control group mean was 1.65 with a standard deviation of .62. The results indicate there was a -.53 difference in the mean between the control and the treatment groups. Table 9. Pretest Grade Means and Standard Deviation Std. error Group Mean SD mean Treatment 1.12 1.16 .23 Control 1.65 .62 .12 Table 10 shows the independent samples test results for the 4th quarter 6th grade grades for the control and the treatment groups. An Independent Samples Test was conducted compare the means of the treatment and the control group. The f-test for equity of means is at the .045 level, which indicates the means do differ significantly at the .05 level. Grades were higher on the control group before the study began. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 Table 10. Fourth Quarter Pre-grades Independent Samples Test Sig. Mean Std. error t d f (2-tailed) difference difference Equal variances assumed -2.06 .50 .045 -.53 .26 Figure 2 displays the results of the criterion test given as a pretest in the Fall. The majority of the answers on the pre-grade results signify the grades fell between a 1.0 and a 3.0 grade point average at the end of 6th grade math year. Std. Dev= 1.12 Mean = 1.95 N = 52.00 0.00 .50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 AVGGPA Figure 2. Histogram of end of year 6th grade math grades. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 Pretest Math Criterion Test Results Students in both the control and the treatment group were administered a 40 question pre-Algebra Readiness math criterion test. This test measures one’s math knowledge in six areas. The math areas assessed were: (a) fractions, (b) decimals and percents, (c) integers, (d) literal symbols, (e) proportional reasoning, (f) co ordinate plane, (g) graphical representations and data analysis, and (h) measurement of geometric objects. Pretest scores were based upon the number correct in each section. This criterion test was administered during one class period. Table 11 shows the six concepts covered and the number of test items on the pre-Algebra readiness test administered to both groups. Table 11. Test Item Total Number and Title Test item description Number of items on test Fractions, decimals, and percent 12 Measurement and geometric objects 6 Coordinate plane, graphical representation, data analysis 5 Integers 7 Literal symbols 5 Proportional reasoning 5 Table 12 shows the pretest math criterion means and standard deviation results. The math criterion test statistics show the mean average the treatment group and the control group received on the pre test given in the fall o f 2004. The mean of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Table 12. Prettest Math Criterion Test Means and Standard Deviation Std. error Group Mean SD mean Treatment 2.6 .96 .19 Control 3.0 .90 .17 the treatment group was 2.6 with a standard deviation o f .96. The mean of the control group was 3.0 with a standard deviation o f .90. The difference between the treatment group mean and the control group mean was -.4. This shows that the control group scored higher on the math criterion pretest. Table 13 shows the results of the criterion pretest administered to the control and the treatment groups. An Independent Samples Test was conducted to compare the means of the treatment group and the control group on the pre math criterion test. The t-test for equity of means indicates the means do not differ significantly at the .05 level ip - . 12) on the math criterion pretest assessment. Table 13. Independent Samples Test on Pretest: Criterion Test Sig. Mean Std. error t d f (2-tailed) difference difference Equal variances assumed -1.6 .52 .12 -40 .25 Figure 3 shows a visual representation of the pretest results on the math criterion test administered to both the control and the treatment groups. The results Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 Figure 3. Histogram displaying pre-criterion test results. indicate a peaked distribution indicating a negative kurtosis that is positively skewed. The graph signifies that the pretest criterion results scores fell in a range between 2.0 and 4.0. Treatment and Control Group Comparison: Math Attitude The pre/posttest comparison test results will be presented for each of the three variables: (a) math attitude, (b) math grades, and (c) math criterion test results. An analysis of covariance will be presented followed by an explanation of the results. Because this study focused on three dependent variables, each variable will be looked at independently to determine if the treatment had a significant effect on the variable. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 The ANCOVA will be utilized to determine the impact of the treatment on each variable. Table 14 shows the unadjusted mean and standard deviation between the treatment and the control group. The unadjusted mean is 2.14 and the standard deviation is .44. The effect size was computed by finding the difference between the means of the treatment and the control group and dividing that difference by the standard deviation of the control group. The effect size was .69 indicating the treatment may have had a practical impact on the student’s math attitude (p > .50), but the result has to be qualified because the differential drop out rates may have resulted in pretest differences between the treatment and control groups. In the next section, ANCOVA will be used to statistically control for pretest differences. Table 14. Descriptive Statistics o f Post Math Attitude Survey Group N Mean SD Treatment 24 2.24 .54 Control 25 2.04 .29 Total 49 2.14 .44 This study began with identifying 27 students for each of the two groups. Six students moved or were not present at the time of the posttest leaving 24 students in the treatment group and 25 students in the control group who participated in a pre/ posttest analysis o f the math attitude survey. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 15 shows the results of the test of effect between groups on the post math attitude survey. The adjusted math attitude posttest survey means were used as the dependent variable to determine if the two-period double math program had a statistically significant impact on the math attitude of underperforming seventh grade math students. The sum of squares for the group effect is .01. The F ratio rate was .14 indicating observed significance at the .71 level. These results indicate the treatment did not have statistically significant effect on student’s math attitude {p > .05). Table 15. ANCOVA Effects on Math Attitude Source Type III sum o f squares d f F Sig. Preattitude 1.80 1 11.90 .001 group error .01 1 .14 .710 total 6.93 46 233.19 49 Table 16 shows the posttest means and standard deviation on the math attitude survey. Utilizing the adjusted postattitude survey results as a dependent variable, the mean o f the treatment group is 2.16. The control group’s mean is 2.12. The difference in the means between the treatment and the control group is .04. This indicates that the double math treatment had no practical impact on the math attitude of underperforming 7th grade students when pretest differences are held constant statistically. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 Table 16. Posttest Math Attitude Means and Standard Deviation Group Mean Standard error Treatment control 2.15 .083 2.12 .081 Treatment and Control Group Comparison: Grade Point Average Pregrades for both groups were obtained from student records. The student’s 4th quarter math grade was utilized as their pretest math grade. Posttest math grades were gathered by averaging first and second quarter math grades. Grades for 26 students in the treatment group and 26 students in the control group were able to be obtained for this study. Table 17 shows the posttest unadjusted means for the treatment and the control groups on math grades. The average unadjusted mean for the control and treatment group was 1.95 with a standard deviation of 1.12. This table indicates the treatment group earned a higher grade point average than the control group at the end of the study. The effect size was computed by dividing the difference of the means by the standard deviation. This resulted in a large effect size of 1.11. This effect size indicates the double math period had a large effect on student’s grades (p > .50), but this result has to be qualified because the differential drop out rates may have resulted in pretest differences between the treatment and the control groups. In the next section, ANCOVA will be used to statistically control for pretest differences. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 Table 17. Descriptive Statistics o f Postmath Grades Group N Mean Standard deviation Treatment 26 2.40 1.24 Control 26 1.51 .80 Total 52 1.95 1.12 Table 18 shows the results of the test of effect between the groups on the grades of students in the study. The adjusted posttest grades means were used as a dependent variable to determine if a two period math program had a statistically significant impact on the student’s grades. The sum of squares for the group is 12.95. The F ratio was 12.71 indicating significance at the .001 level. This significance indicates the treatment did have a statistically significant impact on student’s grades (p < .05). Table 18. ANCOVA Effects on Math Grades Source Type III sum of squares d f Mean square F Sig. PREGRADE 4.50 1 4.50 4.42 .041 GROUP 12.95 1 12.95 12.71 .001 Error 49.95 49 1.02 Total 261.73 52 Table 19 shows the means and standard deviation for the posttest grades. Using the adjusted posttest grades as a dependent variable the mean of the treatment Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 group was 2.47. The control group’s mean was 1.43. The difference in the means between the treatment and the control group was 1.04. These results indicate the treatment group’s grades did have a significant and practical impact on student’s grades when pretest differences are held constant statistically. Table 19. Means and Standard Deviation for Posttest Grades Standard Group Mean error Treatment 2.47 .20 Control 1.43 .20 Pre/Post Comparison on Math Criterion Test The MDTP Math Criterion test (MDTP, 2004), was administered to all students in the treatment and the control group. The pretest was administered in the fall on 27 students in each group. The posttest was administered to 23 students in each group. The difference in numbers between the pre- and posttest results was due to student absences or transfers to other schools during the study. Table 20 shows the unadjusted means for the treatment and control groups on the math criterion test. The average unadjusted mean for the control and treatment group was 3.08 with an average standard deviation o f .97. This table indicates the control group scored higher on the pre/post math criterion test. The effect size was computed by dividing the difference of the means by the standard deviation. This Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 Table 20. Descriptive Statistics o f Post Math Criterion Test Group N Mean SD Treatment 23 2.93 .80 Control 23 3.22 1.11 Total 46 3.08 .97 resulted in an effect size of .26.indicating the treatment may not have had a practical impact on the student’s math attitude (p = > .50), but this result has to be qualified because the differential drop out rates may have resulted in pretest differences between the treatment and the control groups. In the next section, ANCOVA will be used to statistically control for pretest differences. Table 21 shows the results of the test of effect between groups on the math criterion assessment test. The adjusted post criterion test means were used as a dependent variable to determine if the two-period math program had a statistically significant impact on the criterion test results of the students in the study. The sum of squares for the group is .004. The F rate was .055 indicating significance at the .816 level. These results indicate the treatment did not have a significant impact on student’s math criterion test results (p > .05). Table 22 shows the means and standard deviations on the math criterion post test for both groups. The adjusted post math criterion test was utilized as a dependent variable to compute the marginal means of the pre/post criterion test results for the treatment and the control group. The treatment group’s mean was Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Table 21. ANCOVA Effects on Math Criterion Test Results Source Type III sum of squares D f F Sig. Criterion pretest 13.380 1 20.650 .000 Group .004 1 .055 .816 Error 27.860 43 Total 477.530 46 3.05. The control group’s mean was 3.11. The difference between the treatment and the control group’s means was -.06. These results indicate that the double math treatment had no significant or practical impact on the criterion tests results of underperforming 7th grade students when pretest differences are held constant statistically. Table 22. Estimated Marginal Means: Pre/Post Math Criterion Test Group Mean Standard error Treatment 3.05 .170 Control 3.11 .170 Summary This purpose o f this study was to evaluate the effectiveness of a two-period double math program on the academic achievement and math attitude of under performing 7th grade students. A treatment and a control group were established Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 utilizing end of year math grades, end of year math criterion test results, and proficiency ranking on the math portion of the California Standards Test. Placement in the two groups was based on random assignment. This study utilized three variables to determine the effectiveness of the results. These three variables includes (a) a 25 question Likert Survey to measure math attitude, (b) analysis of first and second quarter math grades, and (c) performance on the MDTP Math Criterion pre- Algebra Readiness Test. Students in both the control and the treatment group were administered all there variables before the study (pretest) and at the conclusion of the study (posttest). The study was conducted for one semester, 85 days. The results of the study indicate the following findings: 1. The two-period double math program did not statistically affect students attitudes about math. 2. The two-period double math program did significantly affect student’s math grades. 3. The two-period double math program did not significantly affect the student’s performance on the MDTP pre-Algebra Readiness Criteria Test. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 CHAPTER 5 INTRODUCTION The purpose of this study was to evaluate the effects that two periods of daily math instruction had on the academic achievement of underperforming 7th grade math students. In addition, the effect additional math instruction time had on student’s attitudes about mathematics was also evaluated. Evaluation was based on a pre- and posttest summary of two groups of students for one semester. Pre- and post test evaluation was based on three measures: (a) 6th grade 4th quarter math grade and 1st and 2nd quarter grades, (b) a Likert scale survey to measure student’s attitudes about math, and (c) a pre/posttest criterion referenced test. An analysis of covariance (ANCOVA) was utilized to determine if there is a statistically significant difference between the control and the treatment groups. The means were adjusted in order to compare the dependent variables of both groups. Hypothesis Providing a two-period double math program for underperforming 7th grade math students will result in significant academic achievement and a more positive math attitude. Results The results of the study indicate the following findings: 1. The two-period double math program did not statistically affect student attitudes about math. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 2. The two-period double math program did significantly affect student’s math grades. 3. The two-period double math program did not significantly affect student performance on the MDTP Pre Algebra Readiness Criteria Test. The results of this study provide a basis for further discussion. There was a statistically significant impact on the math grades of students who participated in the double math program. However, the study concluded that there was no significant difference between the control and the treatment group in terms of math attitude or performance on the math criterion test. Chapter 5 will begin by discussing the rational and purpose of the study. This will be followed by a summary of the findings on each of the three dependent variables in the study. A discussion o f the research applicable to the study will follow. Next, this chapter will discuss the limitations of the study as well as consider broader implications. This chapter will conclude with recommendations for further research. Rationale fo r the Study The study of evaluating the effects of a two-period double math program on the academic achievement of underperforming 7th grade math students began with a staff discussion on how we can improve student performance in math. Spartan Middle School staff routinely utilizes student data to evaluate the effectiveness of their program and continually look for ways to improve student performance. Over the past 3 years, the Math Department has seen a decrease in student achievement in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 math. The California Standards Test results for 2003-2004 indicate that 64% of the 7th grade math students scored below the proficient level. In frequent discussions teacher perceived the poor performance in student math achievement was due to three main reasons: (a) lack of support at home, (b) large class sizes, and (c) lack of time to grasp concepts. Teachers looked at what they had control over and indicated they could make a difference in student’s math achievement given more time and smaller class sizes. This study looked at the research related to middle school reform, middle school age students, math achievement, ways to improve student achievement, and the relationship between time and learning. The research and dialogue with teachers resulted in this study. Selection of students for the study was based on previous math performance (grades); end of year results on the exit criterion math test-6th grade, and proficiency ranking on the California Standards Test, 2004. Students selected were (a) earning below a 2.0 GPA in math at the end of 6th grade, (b) scoring below the grade level proficiency level on the end of the year math criterion test, and (c) scoring at the basic or below basic level on the spring 2004 California Standards Test. Placement in the treatment and control group was random. Dependent Variable Discussion Hypothesis #1 Participation in a two-period double math period will result in a more positive attitude about math for underperforming 7th grade math students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Twenty-five questions made up the Likert scale math attitude survey. The survey measured (a) math anxiety, (b) self-esteem, (c) value, level-of-effort, and (d) perceived utility. Through a reliability analysis, five questions were eliminated from the data collection. The pretest means indicated that the control group had a more positive attitude about math at the beginning of the study. During the study, six students were not present or had moved from the two groups leaving 24 students in the treatment group and 25 in the control group. These students were given the same Likert scale survey to see if the double math program had an impact on student attitudes about math. An analysis of effect size was computed on the adjusted means of both groups. This effect size (.69) indicated the treatment group may have had a practical impact on the student’s attitudes but the result has to be qualified because of the differential drop out rates in both groups. An ANCOVA analysis was conducted on the effects of math attitude. The results of this analysis indicated there was no statistical significant impact on student’s attitudes about math (p < .05). Hypothesis #2 Participation in a two-period double math program will result in improved grades for underperforming 7th grade math students. This study focused on three dependent variables to indicate if a two-period double math program would affect student achievement in underperforming 7th grade math students. The second variable looked at was student’s grades. This researcher gathered the end of year 6th grade math grades o f all students in the study. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 These grades served as pretest information. First and second quarter 7th grade math grades were averaged to provide posttest analysis. Grades serve as one indicator of student performance. Teachers in this study use daily homework, test scores, and classroom participation to determine quarterly grades. Student’s in both groups are given the opportunity to make up missed work or failed tests to improve their grade point averages. The pretest results of the treatment and the control group indicated initially the control group initially had a higher grade point average than the treatment group as measured by the end of year 6th grade math grades. The adjusted test results at the end o f the study, indicate the treatment group earned a higher mean average than the control group. The effect size was computed which confirmed there was a large difference between the treatment group and the control group in grades. The effect size on student grades was 1.11 indicating the double math period had a large effect on student’s grades. An ANCOVA analysis was conducted on the math grades pre/post test results indicating the treatment had a statistically significant impact on student’s grades. Hypothesis #3 Participation in a two-period double math program will result in improved math concept mastery as measured by a math criterion test given to underperforming seventh grade math students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 A third variable was utilized to measure the effect that a two-period double math program had on math concepts of underperforming 7th grade math students. This measure was a pre-Algebra Readiness test designed to be given to students the year preceding their first course in algebra. This assessment was developed by the Mathematics Diagnostic Testing Project supported by California State University and the University of California (Wells, 2000). Six areas were assessed on the math criterion test. Twenty-seven students in each groups were administered the math criterion test in the fall. Scores were computed on the pretest to establish the average mean of both groups. The control group scored higher on the pre math criterion test (T - 2.6; C - 3.0). Adjuster test comparison scores were analyzed and the unad justed means indicated the control group scored higher on the criterion test than the treatment group. Twenty-three students in each of the groups were administered the post criterion math test. To control for pretest differences an ANCOVA analysis was conducted to determine if there was a statistically significant effect on the treatment group in terms of the math criterion test results. The results indicate the treatment did not have a statistically significant impact on student’s math criterion test results. Discussion Understanding the unique needs of the middle school student is an important part of designing an effective academic program in which all students are successful. Caught in the Middle, a document published by the California Department of Education (1987) was published to provide educators the research tools necessary to Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 design an effective middle school program for young adolescents. Followed by Turning Points: Preparing American Youth fo r the 21st Century (Carnegie, 1989), and Taking Center Stage (CDE, 2001), these documents all call for addressing the intellectual, physical, psychological, and social development of early adolescents. To address the academic achievement of young adolescents, all three documents call for grouping students for learning, providing flexible scheduling, and expanding learning opportunities. Providing an increased amount of instructional math time for students fell within these parameters. Research tells us student’s attitudes about math play a key roll in his/her math achievement. Much research has been conducted relating to the role motivation has on achievement. Marzano (2003) states, “Both research and theory indicate that student-level factors account for the lion’s share of variance in student achievement” (p. 125). Five areas of research relate to motivation and achievement. These include: (a) drive theory, (b) attribution theory, (c) self-worth theory, (d) emotions, and (e) self-efficacy. Atkinson (1957) and McClelland (1995) researched the role drive theory impacts student motivation. According to this theory, students either become success oriented or failure avoidant. Attribution theory described by Bernard Weiner (1972), involves how students perceive the causes of their successes or failures. Covington and Berry (1976) studied the role self-work theory played in student motivation. They indicated many factors can influence one’s self-worth and that self-worth depends Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 upon one’s accomplishments. Eggen and Kauchak (2003) further indicate that self- worth is strongly linked to one’s perceptions about ability. LeDoux (1996) studied the role emotions play in motivation. He indicated emotions can impact one’s values and beliefs and thereby impact one’s motivation. Self-efficacy as defined by Bandura (1994) influences how one perceives their capabilities. This study focused on assessing the impact student’s attitudes play on his/her math achievement. Through a 25-question Likert scale, this researcher conducted a pre/posttest analysis to see if student’s attitudes about math could be influenced through an additional math period. Loveless (2003) studied the Third International Mathematics and Science Survey results to determine what educators could do to improve mathematics education for all children. His published report, TIMMS (1999), International Math Report, identified seven findings related to math achievement. In reference to this study, Loveless, found that the percentage of instructional time in math decreased from Grades 6 through 8. In addition, he found that students who have a positive self-concept about math scored higher achievement levels. Increasing instructional time and measuring student’s attitudes about math was part of this study. Marzano (2003) identified student factors including home environment, learned intelligence or background knowledge, and motivation as having a significant impact on student achievement. He further indicates the negative side of these factors can be overcome (pp. 124-125). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 In a recent EdSource Report, Studier and Parry (2004) indicated that extra support for middle school aged students is essential. These researchers indicate that flexible scheduling, block scheduling, drop schedules or rotating schedules can allow for increased learning time where needed. Many research studies have been conducted on the impact of time and learning. The Wisconsin Center for Educational Research (2002) found “learning the concepts and skills in a mathematical domain requires students to be engaged in a rich set o f structured activities over time” (p. 2). Lewis and Seidman (1994) found that Japanese students spent an average of 30% more time on math than students in the United States. Aksoy and Link (1997) studied the effect of increased time on math achievement. They concluded, “Longer daily math periods are associated with increased math achievement” (p. 274). Further research by John B. Carroll (1963) found that five factors influenced the effect o f time on learning. These included: (a) aptitude, (b) ability, (c) perseverance, (d) opportunity to learn, and (e) quality of instruction (pp. 723-733). These factors cold have an impact on the students in this study. Kathleen Cotton (2001) studied 57 research studies on time and learning and concluded three findings: 1. Increasing allocated or engaged time is more beneficial to lower- ability students than to higher-ability students. 2. Increasing time-on-task reduces the anxiety and enhances the achievement of highly anxious students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 3. Increasing time-on-task is more beneficial in the more highly structured subjects, such as mathematics and foreign languages, then in less structured ones, such as language arts and social studies (pp. 8-9). This study focused on providing increased learning time for underperforming 7th grade math students thereby resulting in increased academic achievement. The results o f did not completely agree with the research findings. The next part of this chapter will focus on the limitations of the study. Limitations o f the Study The evaluation of a two-period double math program on the academic achievement of underperforming 7th grade math students resulted in mixed findings. While the treatment group was impacted significantly in terms of increased grades, there was no statistical difference between the treatment group and the control group in terms of math attitude or performance on the math criterion test. These findings warrant looking at what limitations might have impacted the results o f this study. The first limitation to the study that may have impacted the results could be related to mortality. The study took place over one semester, 85 days. Students in the treatment group were required to be in the two-period double math program for a minimum of 44 days— one quarter. At the beginning of the study, there were 27 students placed in each of the groups. Absences and students moving during the study resulted in a decline in the participation rate. At the time o f the posttest on math attitude, there were 24 treatment and 25 control group participants. There were Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 2 students in each group who received grades for the 1st and 2n d quarter. The criterion posttest was administered to 23 students in each of the two groups. While these numbers do not seem to indicate a high mortality rate during the study the loss of students may have had a statistical impact on the results. A second limitation of the study may be related to the consistency of the treatment. Two math teachers served as instructors during the study. Each teacher had one section of double-math. While they both planned their lessons together, delivery of instruction may have been a threat to validity, which could impact the results of the study. In addition, some students were cross-teamed for the double math period. This means that due to scheduling a student may have had one teacher for the regular math class and the other for the second math period. A third limitation that may have impacted the results of the study has to do with the length of the study. The study took place over one semester or 85 days. A year-long study may be in order to better determine if the treatment works. This is especially true of the math criterion test, which assesses year-long math concepts. In addition, this researcher would speculate that students would improve over a longer period of time for the study. I attribute this to the power of relationship building between the student and the teacher. Marzano (2003, p.72) found the most important factor affecting student learning is the teacher. This study did not take into effect teacher’s skills or knowledge or the instructional strategies that were utilized. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 One must always look to the internal validity of the study. In this case, it is important to consider if there was something besides the treatment that may have caused the outcome. Two of the three variables, grades and attitude survey can be somewhat subjective and therefore may have been influenced by something other than the treatment. Recommendations for Further Research and Practice This study lends itself to other curriculum areas besides math. In addition, it could be used at different grade levels or for a longer period of time. Further research might consider that other variables may influence the outcome of this study. Marzano (2003) indicated that the most important factor affecting student learning is the teacher (p.72). Further research might consider teacher training, instructional strategies, classroom management and classroom curricular design as variables that could influence the outcome o f the study. The results of this study were shared with the Math Department at Spartan Middle School. In general, the plan is to continue to provide an opportunity for students to participate in a double math offering at all grade levels. This spring, staff will work on redefining criteria for placement into the program and developing clear student expectations. Attempts will continue to be made to place in the double math program with their regular math teacher. The math department is currently developing a new district criterion test that can be given throughout the year to better Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 inform instruction. In addition, the staff is researching materials and best practices for working with underperforming math students. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 REFERENCES Aksoy, T., & Link, C. R. (2000). A panel analysis of student mathematics achieve ment in the U. S. in the 1990's: Does increasing the amount of time in learning activities affect math achievement. Economics o f Education Review 19, 261-277. Aronson, J., Simmerman, J., & Carolos L. (1998). Improving student achievement by extending school: Is it a matter o f time? San Francisco, CA West Ed. Bandura, A. (1994). Self-efficacy. In V. S. Ramachaudran (Ed.), Encyclopedia o f human behavior (Vol.4, pp. 71-81). New York: Academic Press. Bandura, A. (1977). Self-efficacy: The exercise o f control. New York: W.H. Freeman. Butler, S., & McMunn, N. (1999). Theories o f motivation: Self-worth theory o f achievement motivation. Retrieved May 4, 2004, from http://www. serve, org/ assessment/student/ California Department o f Education (CDE). (1987). Caught in the middle: Educational reform fo r young adolescents in California public schools. Sacramento, CA: California Department o f Education. California Department of Education (CDE). (2001). Taking center stage: A commitment to standards-based education fo r California’ s middle grades students. Sacramento, CA: California Department of Education. Carnegie Council on Adolescent Development. (1990). Turning points: preparing American youth fo r the 21st century. Washington, DC: Carnegie Council on Adolescent Development. Carroll, J. B. (1963). A model of school learning. Teachers College Record, 65(8), 723-733. Clark, R. E., & Estes, F. (2002). Turning research into results: A guide to selecting the right performance solutions. Atlanta, GA: CEP Press. Clark, S. N., & Clark, D. C. (1993). Middle level school reform: The rhetoric and the reality. The Elementary School Journal, 93(5), 447-460. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Cotton, K. (2001). Close-up #8 educational time factors. Northwest Regional Educational Laboratory. Retrieved February 8, 2004, from http://www. nwrel. org/scpd/$irs/4/cu8. html Covington. M. V. (1992). Making the grade: A self-worth perspective on motivation and school reform. New York: Cambridge University Press. CSU/UC Mathematics Diagnostic Testing Project. (2004). MDTPpre-algebra readiness test. California: Regents of the University of California and the Trustees of the California State University. Case #PR40A04, test type #0814004 (pp. 1-10), Los Angeles, CA. Eggen, P., & Kauchak, D. (Eds.). (2003). Educational psychology: Windows on classrooms. Upper Saddle River, NJ: Prentice Hall Publishing. George, P., & She wey, K. (1994). New evidence fo r the middle school. Columbus, OH: National Middle School Association. Irvin, J. L. (Ed.). (1997). What current research says to the middle level practitioner. Columbus, OH: National Middle Schools Association. Keefe, J. H., Clark, D. C., Nickerson, N. C., & Valentine, J. W. (1983). The middle level principalship: The effective middle level principal. Reston, VA: National Association of Secondary Principals. Gilby, E. M., Link, C. R., & Mulligan, J. G. (1993). Flow versus stock models o f learning: a panel analysis. Working paper No. 92-06, Economics Department, University of Delaware. Lewis, K. A., & Seidman, L. S. (1994). Reassessing the view that American schools are broken. Economics o f Education Review, 13(3), 215-226. Loveless, T. (2003). Trends in math achievement: The importance o f basic skills. Paper presented at the Washington D.C. Mathematics Summit. Retrieved May 6, 2004, from http://www/ed/gov/print/rschstat/research/progs/ mathscience/loveless. html Maclver, D. J. (1900). Meeting the needs of young adolescents: Advisory groups, interdisciplinary teaching teams, and school transition programs. Phi Delta Kappa, 71, 451-464. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 Marzano, R. (2003). What works in schools: Translating research into action. Alexandria, VA. ASCD Publications. Mathematics Diagnostic Testing Project. (2003, January 9). Field-testing and test development criteria. Retrieved November 17, 2004 from http://mdtp. ucsd. edu/development. shtml National Center for Educational Statistics (NCES). (n.d.). The nation’ s report card. Retrieved May 18, 2004, from http://ness. ed. gov/nationsreportcard National Middle School Association (NMSA). (1996). Westerville, NMSA Research Summary #4. Exemplary middle schools. Retrieved May 2, 2004, from: http://www.nmsa. org/research/resum4. htm NMSA Research Summary #4 Exemplary Middle Schools. (2001). Research Summaries. Ohio, National Middle Schools Association. Retrieved May 2, 2004, from http://www.nmsa.org/research/ressum4.htm Romberg, T. A. (2002). 30 years of mathematics education research. WCER Highlights, 14(3), 1-4. Scales, P. (1991). A portrait o f young adolescents in the 1990's. Minneapolis, MN: Search Institute/Center for Early Adolescence. Stevenson, C. (1992). Teaching ten to fourteen year olds. White Plains, NY: Longman. Stigler, J. W., & Hiebert, J. (2004). Improving mathematics. Educational Leadership, 6(5), 12-17. Studilier, C., & Perry, M. (2004, March). California’s Middle Grade Students. Palo Alto, CA: EdSource Report. TIMS S. (1999). International Mathematics Report-Executive Summary. Retrieved May 4, 2004, from http://isc. be. edu/timssl999i/math_achievement _report.html. U. S. Department o f Education. (2004). The nation’ s report card: Mathematics highlights 2003. Washington, DC: Department of Education. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 U. S. Department of Education, (n.d.). Overview Executive Summary o f NCLB. Retrieved May 3, 2005, from http://www.ed.gov/nclb/overview/ intro/execsumm. html U. S. Department of Education, (n.d.). Overview executive summary o f NCLB. Retrieved May 3, 2004, from http://www.ed.gov/nclb/overview/intro/ execsumm.html Wells, B. (2000, October). D is for diagnostic. Mathematics Diagnostic Testing Project, University o f California, Los Angeles. [MDTP Newsletter.] Mathematics Department, Los Angeles, CA. Weimer, B. (1972). Theories o f motivation: Form mechanism to cognition. Chicago, IL: Rand McNally. WCER Highlights. (2003, Fall). 30 years o f mathematics education research. Madison, WI: University of Wisconsin. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 APPENDICES Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A MDTP PRE ALGEBRA READINESS TEST Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CSU/UC M A TH EM ATIC S DIAG NO STIC TESTIN G PROJECT PREALGEBRA READINESS PR- < 1 This diagnostic test should be given to students near the beginning o f a course im m ediately preceding their first course in algebra. 2004 A suggested time for this test is approximately 45 minutes. INSTRUCTIONS 1. Wait until you are told to start before beginning the test, 2. Work each problem and then on the answer sheet mark the space which corresponds to your answer. The test booklet, the answer sheet, and all scratch paper must be turned in when the test is finished. DO NOT WRITE IN THIS BOOKLET. 3. For each problem you are to select the best response from the given choices. 4. For you and your teacher to make the best use of the test results, you should not guess. If you cannot answer a question, leave it blank. 5. If you find certain problems very time consuming, leave them temporarily. Come back to them after you have gone through the entire test if you have time. 6. Calculators are not needed and may not be used in this test. These materials have been prepared with th e su p p o rt of the California S tate University, th e U niversity o f California, and th e California Academic Partnership Program . Copyright @ 2004 T he Regents of the University of C alifornia and T he T rustees o f the California S ta te University. PR40A04 . T est T ype 0814004 Prealgebra R eadiness T est — 40q. - 45 mm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PREALGEBRA READINESS TEST - 40 QUESTIONS - 45 MINUTES 1 . 104 x 88 = (A) 1,232 (B) 8,032 (C) 8,152 (D) 9,152 2. If a = 9 and 6 = 4, what is the value of 2a — b? (A)'- 10 (B) 14 (C) 25 (D) 72 3. 4 +20 = 2 + 2 = (A) 6 (B) 9 (C) 14 (D) 16 4. Cara earns $3 per hour babysitting. If h represents the number of hours Cara worked babysitting last week, which of the following represents the number of dollars she earned last week? (A) 3 + h (B) | (C) 3/i (D) 21/i 5* The table to the right shows the number of plants that can grow in a garden of a given area. How many plants can grow in a garden that has an area of 24 square feet? (A) 30 (B) 32 (C) 34 (D) 36 Garden Area (square feet) Number of Plants 12 16 18 24 24 30 40 Using the circular spinner „ shown to the right, what is the probability that on any spin the arrow will land in area T ? (A) JL 16 (B) (C) (D) GO ON TO THE NEXT PAGE. PR40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 7. At a carnival, 8 tickets cost $5. How much do 40 tickets cost? (A) $25 (B) $37 (C) $53 (D) $64 8. The temperature at 3:00 PM was 35°F. The temperature had dropped 45 degrees by 9:00 PM. What was the temperature in degrees Fahrenheit at 9:00 PM? (A) ’-4 5 (B) -10 (C) 0 (D) 10 9. 1 to 2^? Which of the following is equal t (A) \ (B) \ (C) H (D) H 10. What is the volume, in cubic units, of the rectangular box shown to the right? (A) 15 (B) 100 (C) 120 (D) 148 6 4 11. 23 + 32 = (A) 12 (B) 14 (C) 15 (D) 17 12. If 3x — 6 ;= 15, then x = (A) -1 (B) 3 (C) 7 (D) 11 GO ON TO THE NEXT PAGE. PR40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 13. Which of the following shows the numbers in the box to the right listed in increasing order? (A) 0, i -1 , 1-7 (B) -1, 0, 1.7, i (C)^ -1 , 0, i 1.7 (D) 1.7, 0, i , -1 0, -1 , 1.7, 14. Which of the following is the prime factorization of 60? (A) 6 x 10 (B) 5 x 12 (C) 2 x 2 x 15 (D) 2 x 2 x 3 x 5 15. Which graph shows all integers less than 5 and greater than — 4? -5 0 5 -5 0 5 (C) - ^ 4 - 4 — + ♦ -5 0 5 / j Q \ iCjfl ^ | | | | | | | || | l | ) | | l l| ^ ^ l 1^1 1 ^ 1 | |S tr -5 0 5 16. What number is 50% of -Z 5f (A) 0.06 (B) 0.6 (C) 6 (D) 60 GO ON TO THE NEXT PAGE. PE40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17. On the number line shown to the right, P M Q point M is the midpoint of PQ. What ^ * 7 • •------- ► number is located at point Q ? ~ (A) 7 (B) 8 (C) 12 (D) 14 In right triangle ABC shown to the right, what is C the degree measure of ZC ? 18. A B 14 + 7 W I (B) 1 ~ ( C O g (D ) 20. Juan has scores of 85, 83, and 93 on three math tests. What is Juan’ s average (mean) test score on these math tests? (A) 85 (B) 87 (C) 88 (D) 89 21. What fraction is equal to 40%? < A ) | < B ) | ( o | m i GO ON TO THE NEXT PAGE. PR40A04 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 22. The sum of a number x and 4 is less than 12. Which of the following inequalities represents this statement? (A) x + 4 < 12 (B) i + 4 > 12 (C) Ax < 12 (D) Ax > 12 o -j _2 32.+ 53 = (A) g i (B) gjj (C) 9 (D) 9^ 24. A B CD j ^ j ^.................j , ft | ' | - 2 - 1 0 1 2 On the number line shown above, which point could represent — 1.2? (A) A (B) B (C) C (D) D 25. What is the perimeter, in centimeters, of the figure shown to the right? 2 cm □ □ (A) 15 (B) 30 (C) 31 (D) 41 3 cm 5 cm f X 5 cm Q_ GO ON TO THE NEXT PAGE. PR40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26. Expressed as a decimal, 3% is (A) 0.03 (B) 0.3 (C) 3.0 (D) 30.0 27. The number of students who participated in sports during each of five months last year is shown to the right. In which month did the number of participants increase the most from the number the previous month? (A) February (B) March (C) April (D) May 180 I 150 0) " B 120 so <«-( o u <D d 90 30 Jan Feb Mar Apr May 28. A number k is greater than 3. Which of the following is true about — ? (A) It is between 0 and ^ (B) It is between i and 1. o (C) It is equal to 1. (D) It is greater than 1. 29. In the coordinate plane shown to the right, which point could have coordinates (3, — 2)? (A) A (B) B (C) C (D) D B . O D GO ON TO THE NEXT PAGE. PR40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 30. David bought a baseball card for $40. Since then, the card has increased in value by 25%. What is the value of David’ s card now? (A) $10 (B) $48 (C) $50 (D) $65 3 31- If x H — = 1, then which point on the number line could be a;? 4 A B C D |i'.n . . . ■ —. | I . i ^ i i i ‘ "j ^ ■ ■ j . .. | _1 _ I 0 - 1 l i 2 2 2 2 (A) A (B) B (C) C (D) D GO ON TO THE NEXT PAGE. PR40A04 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 3 2 . The chart to the right shows the number of sit-ups Annie did starting May 1. If this jg trend continues, how many ^ sit-ups is Annie expected to do on May 11? 15 (A) 12 i 4 (B) 13 13 12 (C) 14 11 Number of iq (D) 15 Sit-ups g 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 Day 33. Which of the following best estimates the sum — + i? £ d < J t* (A) 0.4 (B) 0.5 (C) 0.8 (D) 1.1 34. Which of the following shows the numbers in the box to the right listed from smallest to largest? .307, .4, .31 (A) .4, .31, .307 (B) .31, .4, .307 (C) .31, .307, .4 (D) .307, .31, .4 GO ON TO THE NEXT PAGE. PR40A04 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 35. In the figure shown to the right, what is the value of x ? (A) 140 (B) 100 (C) 60 (D) 50 36. 6 21 In the proportion — = — , the value of k is (A) 25 (B) 35 (C) 126 (D) 210 37. A square has perimeter of 36 feet. What is its area in square feet? (A) 81 (B) 36 (C) 16 (D) 9 38. 1 o l 5 4 ~ ~ q 1 13 3 <*> 3 - (C) - (D) _ GO ON TO THE NEXT PAGE. PR40A04 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 39. The radius of the circle shown to the right is 3 inches. What is the area of this circle, in square inches? (A) 37r (B) 9ft (C) 1 2 7 T (D) 367r 40. A team won 5 and lost 2 of their first 7 games. The team continued to win at this rate and won w games in the 28-game season. Which of the following proportions could be used to determine w ? b £ b l < ° > b i <°) b i END OF EXAMINATION PR40A04 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 APPENDIX B MDTP SAMPLE PRINTOUT REPORT Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. Sample M D T P p r in to u ts: Each teacher r e c e iv e s a summary of c la s s performance in f i v e parts*. 1) Summary of cla s’s by to p ic s 2) Item A n alysts by numbers o f stu d en ts 3) Item a n a ly s is by percentage o f stu d en ts* 4) A lphabetized l i s t o f stu d en t r e s u lts * 5) Histogram s showing item r e s u lts by top ic* Each stu d en t r e c e iv e s h is or her r e s u lts in' the form o f a le t t e r * * Included on th is sh eet C a l i f o r n i a S ta te U n lv e r& i t y / U n l v e r s i ty of C a l i f o r n i a MATHEMATICS DIAGNOSTIC TESTING PROJECT U n i v e r s i t y o f C a l i f o r n i a , Los Angelas Sep t ember 2 0, 1PB4 I n d iv id u a l S tu d e n t R a s u lt* School I n s t r u c t o r Courts Natural High SchoolDownhi11 Geometry l a s t Date Test Type Nuinber of Item s S(J ’ V 7 7 4 4 3 7 4 3 H Of 1 terns L a s 1 1 ter S tuden t T o ta l ARTH. POLY LINR QUA0 QRPH RATU EXPS GEOM WORD A t temp te< ADAMS J *29 5 S *3 *2 3 *2 3 3 33 4 6 A L i e r n a *33 6 3 6 *2 *1 S *4 *2 *2 50 30 ANDERSON P 41 5 6 6 4 4 7 3 3 SO 50 ARARAT 1 K G ,3 6 3 6 *4 *2 *i 3 6 *2 5 so so 01 PAULO S N o te * & denotea «1* score *2 *3 a2 be 1©w m a s te r y . *1 * 1 3 *1 2 3 30 30 A lphabetized l i s t o f stu d en t r e s u lts C a l i f o r n i a S ta ts Un I v e rs I t y / U n I v e rs I t y of C a l i f o r n i a MATHEMATICS DIAGNOSTIC TESTING PROJECT Un I ver * 11>* of C a l i f o r n i a , Los AngeIe a September 20, 17B4 Graph i c Di s p 1a> o f C la s s R e s u lts Grouped by Top c , O rdered by ‘ A C o rre c t T e s t Test Schoo1 I n s t r u c t o r Course Date Type N a tu r a l High School Downhi) i Geometry 9 /6 /S 6 BA50/82 tffft ARYH C o rre c t Ite m * PQLY C o rre c t 21 ** « « * « * « « A 69, 23 « ** 15X 2 * * * * * * * * * ’** 54'A 13 * * * * * * * * * 46V, 29 * * * * * * * * * * * 54V, 14 «««#**««« 46V. 6YA 22 * * * * * * * * * * * 54X IS 69V. 12 * * * * * * * * * * * * * * 69V, 7TA } * * * * * * * * * * * * * * * * * * 92 'A 3 * * * * * * * * *•» **» » *** 8SV , 6 92V. tem LINR Correc t Ite m QUAD C o rre c t \6 » » * * » * * * 39 V . SO * * * * * 23X 32 » * *« * « * « 39V 19 * * * * * * * * 38X 44 » **» *» »» « 4 6Y, 29 * •* » » « « > * 4 6V, 27 * * * * * * * * * * * S4X 47 * * * * * * * * * 46'A 36 * * # *n *w **» j** 627. 26 » * * * * * « * * # * * » * # VTA 42 » * « * # * # * * * * # * * « ♦ VTA lew GRPH C o rre c t Ite m SATL C orrec t 23 *4* 1SX 40 * * * * * * 31V. 45 * * * * * * 31V. 30 * * * * * * * * * 44V. 20 * * * * * * * * * * * S4V 33 * * * * * * * * * * * * 42V. 17 *« » « * * * « * * * » 62V. 33 * * * * * * * * * * * * * * 6PV. 27 * * • * « * * * » * » * • * * 77 V. tew SXPS Correc t Item GEOM C o rre c t 11 * * * * * 23V. 46 * * * * * * * * * * * * 6TA 1 3 »»««««#» 38X 18 s * * * * * * * * * * * * * 69V. 10 * * * * * * * * * * * 54V. 48 * » * * « * » * * * * * » » 69V, 29 * * * * X » * * X « * # * * 6YA y * * » * * * * * * « « » * » * * • BS* 4 * * * * * * * * * * * * * * * 7TA 24 * * * * * * * * * * * * * * * VTA 38 * * * * * * » » # » * * * » * 77'/. tern WORO C o rre c t 4V « » * » * » * * * 46V, 31 * * * * * * * * * * * S4X 41 » * * # * * » » * » « »{4 y , 4 3 » * * * » # » * » * * y4X 34 * * # . * * » * * * * * * * * * » * * * * 100 V . Histograms showing item r e s u lts by top ic Reproduced w ith permission o f th e copyright owner. Further reproduction prohibited without permission. b'a 1 1 f om i 1 a S ta t s U n l v e r s l t y / U n l v e r » l t y o f C a l i f o r n i a MATHEMATICS DIAGNOSTIC TESTING PROJECT U n i v e r s i t y o f C a l i f o r n i a , L o t A ngeles September 20, 1984 N a tu ra l High School A nytown, CA 90874 Tot ADAMS J Here are the r e a u K a o f the d ia g n o s t ic t e s t In w h ic h you have r e c e n t l y ta k e n . Your score was * 1emen t a r y &1gebr a 29 c o r r e c t o u t of a t o t a l o f w h ic h Is 3875. 50 Your Score M a s te ry T o ta l Level P o s s ib le C o n g ra tu la tio n * .* Your r« * u 1 1 * In d ic a t e th a t you have done w e ll in each o f the f o l lo w in g top le s t A r I t h m e t ic 5 Polynoflil at f u n c t io n s and e q u a tio n s 3 G ra ph in g and the c o o r d in a te p lan e 3 R a tio n a l e x p r e s s io n s 3 G eo m e tric measurement '3 Word p roblem s 3 5 7 3 7 3 4 3 5 3 4 < ' 3 5 How ever, your .re tu t t * in d i c a t e you need re v ie w top 14 > In the f o l tow ing Q u a d ra tic e q u a tio n s 2 3 4 Y our r e s u l t * In d ic a t e you need s u b s t a n t ia l r e v i top J c si ew i n the f o l 1 owlng L in e a r e q u a t io n * and I n e q u a l i t i e s ! a b s o lu te v a lu e 3 E xponent* and square r o o t s 2 5 7 3 7 We hope th a t you W i l l f i n d t h i s I n f o rm a tio n h e l p f u l . Please c o n ta c t your te a c h e r f o r s p e c i f i c a c t i v i t i e s and a ssignm ents w hich w i l l a id in any n ec e s s ary r e v ie w . L etter to stud en t C a l i f o r n i a S ta te Uni ver s i t y/Un I v e r a1 t y o f C a l i f o r n i a MATHEMATICS IMAI3N0STIC TESTING PROJECT U n lv # r s it y of C a lifo rn ia - ^ Loa A n g e la * September 2 0, 19-84 Item A n a ly a l* by P ercentage of S tu d e n ts - page 1 of 2 Te & t Teat School in s t r u c t o r C o u rts Date Type N a tu ra l High SchoolDownhI11 Geometry 9 /4 /8 4 BA50/82 Number o f s tu d e n ts ! 13 ITEM KEY TOPIC CORRECT OMIT I C POLY 92 0 2 D ARTH 34 0 3 A ARTH BS 0 4 A EXPS 77 0 1 3 C ARTH 77 8 6 L POLY 92 U V » GEOM 85 0 0 0 EXPS 33 3 S ' A AR7H . 49 0 1U A EXPS 34 0 I i C LXPS 23 0 12 £ POLY 49 0 13 A POLY 44 0 14 B POLY 44 G 13 1 ; ARTH 49 . 0 14 8 LtNR 38 IS 1 / 1 1 GRPH 42 (1 18 B GEOM 49 0 19 fe l QUAD 38 0 20 0 GRPH 54 0 21 C ARTH 44 0 22 D POLY 34 0 23 C POLY 15 D 24 A EXPS 77 15 22 E GRPH 15 0 A B C D ■ ' E 0 8 #92 0 0 8 23 15 #54 0 *85 0 0 8 8 *77 0 0 15 e 0 15 #77 0 0 0 0 B 0 #92 C l #85 8 3 0 33 8 0 *38 8 *69 0 IS 0 IS »34 23 13 0 3 8 ti 0 42 *23 8 3 IS 0 *49 #44 23 b D 23 31 #44 0 8 8 3 8 0 - 15 #49 8 *38 8 23 8 8 31 0 0 *42 8 *49 0 0 23 31 #38 15 8 8 0 0 23 #34 23 15 15 *44 8 15 38 8 0 *54 0 38 38 #1 5 0 8 *77 0 e 0 0 15 31 0 38 #15 N o te } * d en ote s Key. Item a n a l y s i s by p e r c e n ta g e o f s tu d e n ts APPENDIX C STUDENT OPINION SURVEY Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 STUDENT OPINION SURVEY SPARTAN MIDDLE SCHOOL Here are some opinions that students have expressed about math. Indicate how much you agree with each of these 25 opinions as it relates to your experience at this school by circling the number of your choice. Before you start the survey, please circle if you are enrolled in one period of math or one period of math and math lab. Please circle your math teacher’s name. I am currently enrolled in: 1 math period 1 period math and math lab My math teacher is: Mrs. Rose Mrs. East Key: 1 = Strongly agree, 2 = Agree, 3 = Disagree, 4 = Strongly disagree 1. I am a good math student. 1 2 3 4 2. I like working with numbers. 1 2 3 4 3. I know it is important for me to learn math. 1 2 3 4 4. I can easily apply math concepts in real life. 1 2 3 4 5. Learning math is interesting. 1 2 3 4 6. I ask questions when I don’t understand. 1 2 3 4 7. I understand math concepts when they are presented in class. 1 2 3 4 8. Taking a math test stresses me. 1 2 3 4 9. I use math outside of class. 1 2 3 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 10. I believe some people are better at math than others. 1 2 3 11. I talk about math with other students outside of class. 1 2 3 12. When I work hard in math class, I do a better job. 1 2 3 13. Math is my favorite subject. 1 2 3 14. I can explain math concepts to others. 1 2 3 15. The work in my math class really makes me think. 1 2 3 16. I am learning math skills that I will need to succeed. 1 2 3 17. When I have difficulty understanding the math topic, I feel comfortable going to the teacher for help. 1 2 3 18. I stop trying when I get stuck on a problem. 1 2 3 19. I help others with their math. 1 2 3 20. I try different ways to solve math problems. 1 2 3 21. I can explain how I solve math problems. 1 2 3 22. When I become confused in math class, I stop listening. 1 2 3 23. I become nervous and forget important math concepts during math tests. 1 2 3 24. When I do badly on a math test, I blame others. 1 2 3 25. I am a word person rather than a numbers person. 1 2 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX D PARENT NOTIFICATION LETTER Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 July 15,2004 Dear Parents: In reviewing your child’s records, we find th at_______________________________is struggling with math concepts. Next year we are offering a “double math” program for struggling 8th grade math students. What this means is your child is offered the opportunity to have 2 math periods daily. They will be enrolled in the regular math program and then receive a second math program that will focus on missing skills. This second math class will be taught by a credentialed math teacher and will have approximately 20 students in the classroom. The focus will be on building math concepts for success in the regular classroom. This second math class will replace your child’s elective choice. Please notify the school by calling our Registrar at XXX-XXXX extensionXXX, before August 4th, if you wish your child to be enrolled in this opportunity. Sincerely, Spartan Principal Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Asset Metadata

Creator Kempley, Diane Marie (author)

Core Title Evaluation of a two -period double math program on the academic achievement of underperforming seventh grade math students

School Rossier School of Education

Degree Doctor of Education

Degree Program Education

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

Tag Education, Mathematics,Education, Secondary,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Hocevar, Dennis (committee chair), Cohn, Carl (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-347692

Unique identifier UC11336010

Identifier 3180388.pdf (filename),usctheses-c16-347692 (legacy record id)

Legacy Identifier 3180388.pdf

Dmrecord 347692

Document Type Dissertation

Rights Kempley, Diane Marie

Type texts

Source 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 au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA