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TEACHER IMPLEMENTATION OF REFORM-BASED MATHEMATICS
AND IMPLICATIONS FOR ALGEBRA READINESS:
A QUALITATIVE STUDY OF 4TH GRADE CLASSROOMS
by
Stephen Korb Sher
____________________________________________________________________
A Dissertation Presented to the
FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF EDUCATION
August 2011
Copyright 2011 Stephen Korb Sher
Object Description
| Title | Teacher implementation of reform-based mathematics and implications for algebra readiness: a qualitative study of 4th grade classrooms |
| Author | Sher, Stephen Korb |
| Author email | stepheks@usc.edu;ssher@sbcglobal.net |
| Degree | Doctor of Education |
| Document type | Dissertation |
| Degree program | Education (Leadership) |
| School | Rossier School of Education |
| Date defended/completed | 2011-06-13 |
| Date submitted | 2011-08-25 |
| Date approved | 2011-08-25 |
| Restricted until | 2011-08-25 |
| Date published | 2011-08-25 |
| Advisor (committee chair) | Garcia, Pedro |
| Advisor (committee member) |
Rousseau, Sylvia Castruita, Rudy |
| Abstract | This study looked at 4th grade classrooms to see how teachers implement NCTM standards-based or reform-based mathematics instruction and then analyzed it for the capacity to improve students’ algebra readiness. The qualitative study was based on classroom observations, teacher and administrator interviews, and teacher surveys. The study took the perspective of instruction as interaction and mathematics as a sense making activity. The NCTM Process Standards were used to evaluate learning activities. The Adding It Up, Strands of Mathematical Proficiency served as a qualitative metric for assessing the likeliness of the instruction to better prepare students in mathematics, specifically for algebra. Together, these standards are the basis for the Common Core State Standards for Mathematical Practice. The study also looked for student engagement in important mathematical content and ideas, particularly those necessary to prepare students for algebra. Furthermore, the study looked for rigor and an opportunity for students to struggle with important mathematics. ❧ The study observed teacher created Cognitively Guided Instruction (CGI) lessons and lessons from Contexts for Learning replacement units. Teachers implemented reform-based mathematics instruction in two ways, in distinct reform-based lessons and integrating some of the reform-based pedagogy in their traditional text-based lessons. Observation lessons revealed that students were genuinely engaged in the Process Standards for over 90% of the instructional time. Learning engaged children in understanding mathematics in the context of real-life situations, accurate computation and algebraic reasoning were stressed. Classroom sociomathematical norms were developing around the Process Standards, which served as distributed scaffolding to support children in their conceptual understanding. The study found evidence to support a bridge between social constructivist theory and reform or standards-based practice. ❧ The study determined that students engaged in qualitatively different activities from traditional classrooms which should positively impact algebra readiness. Learning emphasized important mathematical content and ideas necessary for success in algebra. Students were developing conceptual understandings of arithmetic which were explicitly connected to standard computation methods. ❧ Student solutions expressing mathematical relationships were always conveyed in both words and standard mathematical notation, and frequently in expressions or equations. The study concluded that students were making progress in each of the five Strands of Mathematical Proficiency, providing them more of the tools needed for algebra.The study found that students' engagement with the Process Standards and their trajectory in the Strands of Mathematical Proficiencies will not only serve students wishing to enter the STEM fields, but provide skills useful for academic, career, and personal facets of their life. Commonly mentioned 21st century skills, such as problem solving, critical thinking/reasoning, effective communication, flexible application of knowledge, and creativity are addressed in the Process Standards and Strands of Mathematical Proficiencies, now combined in the CCSS Standards for Mathematical Practice. |
| Keyword | algebra readiness; Cognitively Guided Instruction; Common Core State Standards for Mathematical Practice.; NCTM Process Standards; reform-based mathematics; standards-based mathematics |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Sher, Stephen Korb |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-SherStephe-275.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Full text | TEACHER IMPLEMENTATION OF REFORM-BASED MATHEMATICS AND IMPLICATIONS FOR ALGEBRA READINESS: A QUALITATIVE STUDY OF 4TH GRADE CLASSROOMS by Stephen Korb Sher ____________________________________________________________________ A Dissertation Presented to the FACULTY OF THE USC ROSSIER SCHOOL OF EDUCATION UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF EDUCATION August 2011 Copyright 2011 Stephen Korb Sher |
