DOCSLIB.ORG

The Effect of Connected Mathematics on Student Achievement In

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Effect of Connected Mathematics on Student Achievement In THE EFFECT OF CONNECTED MATHEMATICS ON STUDENT ACHIEVEMENT IN SELECTED MIDDLE SCHOOL GRADES Ruth Gharst Waggoner B.A., Mid America Nazarene University, 1981 M.S., University of Kansas, 1991 Submitted to the Graduate Department and Faculty of the School of Education of Baker University in partial fulfillment of the requirements for the degree of Doctor of Education in Educational Leadership May 6, 2009 Copyright 2009 by Ruth Gharst Waggoner Clinical Research Study Committee ___________________________________________________________ Major Advisor ____________________________________________________________ ____________________________________________________________ ____________________________________________________________ Defended May 6, 2009 ii Abstract The purpose of this study was to examine the effect of Connected Mathematics Project on the mathematics achievement of sixth and seventh grade students in the Olathe School District. The design of this study was an experimental, control group. The treatment variable was the type of mathematics instruction taught in the classroom. Students in the control group received mathematics instruction in a traditional, lecture‐ based setting. The treatment for the experimental group was mathematics instruction using CMP. The study focused on 357 seventh grade students at 5 participating junior high schools. The researcher analyzed scores from a sample of students (n=119) who received two years of mathematics instruction using CMP, a sample of students (n=119) who received one year of mathematics instruction using CMP, and a sample of students (n=119) who received no mathematics instruction using CMP. The study also examined the effects of CMP on students qualifying for special education services and students of low SES. The dependent variable, mathematics achievement, was measured using scores obtained from the 2008 seventh grade Kansas Mathematics Assessment. Additional analyses were conducted on the fifteen mathematics indicators on the seventh grade KMA test. The results of the data analysis showed that while the mean score of students receiving mathematics instruction using CMP were higher than the mean scores of students not receiving mathematics instruction using CMP, the differences were not iii statistically significant at the .05 level. The results also showed the main effect of mathematics instruction on students qualifying for special education services or students of low SES was not statistically significant. However, there were statistically significant differences indicated on mean scores of four of the fifteen seventh grade tested indicators between students with CMP instruction and those with no CMP instruction. iv Dedication This is dedicated to my mother, Dr. Bonnie Gleason, to whom I owe a lifetime of gratitude. You have been my mentor, model and inspiration. Even more, you have always been my friend. If I can be half the teacher and leader you have been, I’ll be content. I hope I have made you proud. v Acknowledgements The support, encouragement and sometimes nudging from advisors, family, and friends have made the completion of this journey possible. There are many to whom I owe a sincere debt of gratitude. First of all, a special appreciation is extended to Dr. Harold Frye, my major advisor, for his assistance, support, and guidance throughout this process. Dr. Frye kept me on track and focused. Without his gentle prodding, I might still be contemplating contents of Chapter One. A warm and heartfelt appreciation is also offered to my doctoral committee: Dr. Ann Sanders, Dr. Randy Pembrook, and Dr. Cathy Donovan. Your guidance and service on my committee were greatly appreciated. Thank you to Peg Waterman for her assistance in planning the methodology and interpreting the results. Her guidance was invaluable. A big thank you goes to my husband, Randy, for surviving this pursuit. “Mr. Mom” showed a great amount of patience and assistance. He sacrificed time and attention to allow me to follow this dream. I also want to thank Sammy and Alex for smiles and hugs throughout the last two years. And, yes Sammy, the dining room table will finally be clean, so you may eat there again. vi Table of Contents Abstract ............................................................................................................................... iii Dedication ............................................................................................................................ v Acknowledgements ............................................................................................................. vi TABLE OF CONTENTS.......................................................................................................... vii List of Tables ....................................................................................................................... ix CHAPTER ONE: INTRODUCTION AND RATIONALE ............................................................. 1 Background and Conceptual Framework .................................................................... 3 Problem Statement ..................................................................................................... 6 Purpose of the Study .................................................................................................. 7 Significance of the Study ............................................................................................. 7 Delimitations ............................................................................................................... 9 Assumptions ................................................................................................................ 9 Research Questions ................................................................................................... 10 Definition of Terms .................................................................................................... 10 Overview of the Methodology .................................................................................. 12 Organization of Study ................................................................................................ 14 CHAPTER TWO: REVIEW OF LITERATURE ......................................................................... 16 Introduction ............................................................................................................... 16 History of Mathematics in the Twentieth Century ................................................... 18 Reform Mathematics ................................................................................................. 23 Connected Mathematics Project ............................................................................... 36 Mathematics Education for Students of Low SES ..................................................... 47 Mathematics Education for Students with Disabilities ............................................. 50 Summary .................................................................................................................... 54 CHAPTER THREE: METHODS ............................................................................................ 55 Introduction ............................................................................................................... 55 Research Design ........................................................................................................ 55 vii Population and Sample.............................................................................................. 56 Sampling Procedures ................................................................................................. 58 Instrumentation ......................................................................................................... 59 Validity ....................................................................................................................... 61 Data Collection Procedures ....................................................................................... 63 Research Questions and Hypothesis ......................................................................... 65 Data Collection and Statistical Analysis ..................................................................... 67 Limitations ................................................................................................................. 67 Summary .................................................................................................................... 67 CHAPTER FOUR: RESULTS ................................................................................................ 69 Introduction ............................................................................................................... 69 Hypothesis Testing .................................................................................................... 70 Additional Analyses ................................................................................................... 78 Summary .................................................................................................................. 102 CHAPTER FIVE: INTERPRETATION AND RECOMMENDATIONS ...................................... 105 Introduction ............................................................................................................. 105 Study Summary ........................................................................................................ 105 Overview of the Problem .......................................................................................
Load more

Recommended publications
  • Chapter 13 National Science Foundation Systemic Initiatives
    Chapter 13 National Science Foundation Systemic Initiatives: How a small amount of federal money promotes ill-designed mathematics and science programs in K-12 and undermines local control of education Michael McKeown Mathematically Correct David Klein California State University, Los Angeles Chris Patterson Education Connection of Texas Since its inception in 1950, the National Science Foundation (NSF) has played a strong, positive role in making American scientific research and technological application the best in the world. Through its funding of peer-reviewed, investigator-initiated research proposals, it has supported basic research in a wide variety of scientific disciplines, such as mathematics, biology, physics, chemistry, geology, astronomy, and psychology. American science owes much to the support it has received, and continues to receive, from NSF. This chapter deals with a program in the Education and Human Resources Division called the NSF Systemic Initiatives Program, not with NSF programs related directly to the support of basic research. We are highly critical of this particular NSF program. Not only do the Systemic Initiatives undermine local control of education, but, as our analysis in this chapter suggests, they also seem to lower academic standards for mathematics education and weaken the educational base for American science. This chapter is composed of three sections. The first section, an overview of NSF Systemic Initiatives, was written by Michael McKeown. The second section, an analysis of the development and 288 Standards Wars features of the Los Angeles Systemic Initiative, was written by David Klein. The third section, an analysis of the development and features of the Texas Statewide Systemic Initiative, was written by Chris Patterson.
    [Show full text]
  • Mathematics in African History and Cultures
    Paulus Gerdes & Ahmed Djebbar MATHEMATICS IN AFRICAN HISTORY AND CULTURES: AN ANNOTATED BIBLIOGRAPHY African Mathematical Union Commission on the History of Mathematics in Africa (AMUCHMA) Mathematics in African History and Cultures Second edition, 2007 First edition: African Mathematical Union, Cape Town, South Africa, 2004 ISBN: 978-1-4303-1537-7 Published by Lulu. Copyright © 2007 by Paulus Gerdes & Ahmed Djebbar Authors Paulus Gerdes Research Centre for Mathematics, Culture and Education, C.P. 915, Maputo, Mozambique E-mail: [email protected] Ahmed Djebbar Département de mathématiques, Bt. M 2, Université de Lille 1, 59655 Villeneuve D’Asq Cedex, France E-mail: [email protected], [email protected] Cover design inspired by a pattern on a mat woven in the 19th century by a Yombe woman from the Lower Congo area (Cf. GER-04b, p. 96). 2 Table of contents page Preface by the President of the African 7 Mathematical Union (Prof. Jan Persens) Introduction 9 Introduction to the new edition 14 Bibliography A 15 B 43 C 65 D 77 E 105 F 115 G 121 H 162 I 173 J 179 K 182 L 194 M 207 N 223 O 228 P 234 R 241 S 252 T 274 U 281 V 283 3 Mathematics in African History and Cultures page W 290 Y 296 Z 298 Appendices 1 On mathematicians of African descent / 307 Diaspora 2 Publications by Africans on the History of 313 Mathematics outside Africa (including reviews of these publications) 3 On Time-reckoning and Astronomy in 317 African History and Cultures 4 String figures in Africa 338 5 Examples of other Mathematical Books and 343
    [Show full text]
  • An Alternative Route to Teaching Fraction Division: Abstraction of Common Denominator Algorithm
    International Electronic Journal of Elementary Education, 2015, 7(3), 399-422. An Alternative Route to Teaching Fraction Division: Abstraction of Common Denominator Algorithm İsmail Özgür ZEMBAT Mevlana (Rumi) University, Turkey Received: February 2015 / Revised: May 2015 / Accepted: May 2015 Abstract From a curricular stand point, the traditional invert and multiply algorithm for division of fractions provides few affordances for linking to a rich understanding of fractions. On the other hand, an alternative algorithm, called common denominator algorithm, has many such affordances. The current study serves as an argument for shifting curriculum for fraction division from use of invert and multiply algorithm as a basis to the use of common denominator algorithm as a basis. This was accomplished with the analysis of learning of two prospective elementary teachers being an illustration of how to realize those conceptual affordances. In doing so, the article proposes an instructional sequence and details it by referring to both the (mathematical and pedagogical) advantages and the disadvantages. As a result, this algorithm has a conceptual basis depending on basic operations of partitioning, unitizing, and counting, which make it accessible to learners. Also, when participants are encouraged to construct this algorithm based on their work with diagrams, common denominator algorithm formalizes the work that they do with diagrams. Keywords: Teaching fraction division, abstracting common denominator algorithm, curriculum development Introduction Arithmetic operations, and teaching and learning of them have always been an interest for mathematics education community. In his historical analysis, Usiskin (2007) pointed out that operations (especially on fractions) still preserve its importance in school mathematics and they should be given enough emphasis.
    [Show full text]
  • AVAILABLE from ABSTRACT DOCUMENT RESUME Exemplary
    DOCUMENT RESUME ED 434 033 SE 062 877 TITLE Exemplary and Promising Mathematics Programs. INSTITUTION Department of Education, Washington, DC. PUB DATE 1999-00-00 NOTE 71p.; Prepared by the "Math and Science Education Expert Panel." AVAILABLE FROM ED Pubs, P.O. Box 1389, Jessup, MD. Tel: 877-433-7827 (Toll Free); Web site: <http://www.enc.org>. PUB TYPE Reports Descriptive (141) EDRS PRICE MF01/PC03 Plus Postage. DESCRIPTORS *Academic Standards; Demonstration Programs; Elementary Secondary Education; Mathematics Curriculum; *Mathematics Education; *Program Descriptions; *Program Evaluation ABSTRACT Selecting programs, textbooks, and curriculum materials is one of the most important decisions educators make. An Expert Panel on Mathematics and Science was established by the U.S. Department of Education to develop a high-quality, research-based process for selecting programs and to use that selecting process to identify exemplary and promising programs. This booklet describes eight mathematics programs designated as exemplary or promising. A detailed explanation of the submission and selection process and an explanation of how the programs were separated into exemplary and promising categories is included. The four characteristics used for the selection criteria include quality of program, usefulness to others, educational significance, and evidence of effectiveness and success. Each characteristic has multiple criteria with specific indicators of achievement. Each program is described in terms of the four selection characteristics and professional
    [Show full text]
  • Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform Kimberly White-Fredette
    The Mathematics Educator 2009/2010, Vol. 19, No. 2, 21–31 Why Not Philosophy? Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform Kimberly White-Fredette This article argues that, as teachers struggle to implement curriculum reform in mathematics, an explicit discussion of philosophy of mathematics is missing from the conversation. Building on the work of Ernest (1988, 1991, 1994, 1998, 1999, 2004), Lerman (1990, 1998, 1999), the National Council of Teachers of Mathematics (1989, 1991, 2000), Davis and Hersh (1981), Hersh (1997), Lakatos (1945/1976), Kitcher (1984), and others, the author draws parallels between social constructivism and a humanism philosophy of mathematics. While practicing mathematicians may be entrenched in a traditional, Platonic philosophy of mathematics, and mathematics education researchers have embraced the fallibilist, humanist philosophy of mathematics (Sfard, 1998), the teachers of school mathematics are caught somewhere in the middle. Mathematics teachers too often hold true to the traditional view of mathematics as an absolute truth independent of human subjectivity. At the same time, they are pushed to teach mathematics as a social construction, an activity that makes sense only through its usefulness. Given these dichotomous views of mathematics, without an explicit conversation about and exploration of the philosophy of mathematics, reform in the teaching and learning of mathematics may be certain to fail. The teaching and learning of mathematics is without a radical change in instructional practices going through tremendous changes. The National and an equally radical change in teachers’ views of Council of Teachers of Mathematics’ (NCTM, 2000) mathematics teaching and learning, as well as the Principles and Standards for School Mathematics discipline of mathematics itself.
    [Show full text]
  • A Landscape Paper Science Reform a Survey of Mathematics in the Southeast AND
    A Survey OF Mathematics AND Science Reform IN THE Southeast A Landscape Paper A Survey OF Mathematics AND Science Reform IN THE Southeast: A Landscape Paper SERC @ SERVE Dr. Francena D. Cummings, Director 1203 Governors Square Boulevard, Suite 400 • Tallahassee, FL 32301 • 800-854-0476 Proprietary Document—Written permission required for duplication or use. Associated with the School of Education University of North Carolina at Greensboro First Printing, 2003 Edited by Donna Nalley, SERVE Publications Director Karen DeMeester, SERVE Senior Program Specialist Designed by Tracy Hamilton, SERVE Art Director Photography by This document was produced Shelley Call, Barbara Davis, Donna Nalley, and Tracy Hamilton with funding from the Dwight D. Eisenhower National Programs from Mathematics and Science Select photographs used in this magazine are from Comstock Klips, Corbis, Creatas, Regional Consortia Program, EyeWire Images, Image 100, and/or PhotoDisc. Institute for Education Sciences, U.S. Department of Education, under contact no. R319A000011. Additional photographs provided by Penny Gilmer and classroom teachers (masters and doctoral students at Florida State University). The content of this publication does not necessarily reflect Photographs may not be reproduced without written permission from the photographer or the views or policies of the Institute of Education Sciences, the stock photography company. U.S. Department of Education, nor does mention of trade names, commercial products, or organizations imply endorsement by the U.S.
    [Show full text]
  • May 2001 What Are the Children Learning and Who Decides
    May 2001 THE TEXTBOOK CONUNDRUM What are the Children Learning and Who Decides? Introduction With the quality of education in the United States now the biggest domestic concern, demands for accountability are in vogue. The drive for better schools however, is usually limited to issues of standards, testing, choice and teachers. Missing from most discussions is the role that textbooks play in the achievement of children. A few facts to consider: • In more than twenty states, the state (state board of education, department of education, secretary or commissioner of education, or another specially designated state textbook committee) picks the textbooks for every classroom in the state – either through outright text selection, or recommendations from a short list. To control curriculum, they tie funding to compliance with the states’ textbook adoption policy. • Textbooks supplied to three states, California, Texas and Florida – all of which give significant influence to state agencies for textbook selection – account for 30 percent of the more than $3.3 billion K-12 textbook market in 1998, the most recent year for which statistics are available.i • Four publishers (McGraw-Hill, Houghton Mifflin, Harcourt, and Pearson) control 70 percent of the industry. Size means money means influence in the textbook world. They are a strong, quiet interest group that works behind the scenes and through major education groups to ensure that the process favoring them stays exactly the way it is. The process for putting books in front of children then, looks something like this: The “big three” states draw up textbook adoption policies to which the “big four” publishers try to align their textbook content.
    [Show full text]
  • An Examination of the Potential of Secondary Mathematics
    AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS by Joshua E. Williams B. S., Clarion University, 2000 M. S., Salisbury University, 2006 Submitted to the Graduate Faculty of The School of Education in partial fulfillment of the requirements for the degree of Doctor of Education University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH THE SCHOOL OF EDUCATION This dissertation was presented by Joshua E. Williams It was defended on September 7, 2016 and approved by Dr. Ellen Ansell, Associate Professor, Instruction and Learning Dr. James Greeno, Emeritus Professor, Standford University Dr. Mary Kay Stein, Professor, Learning Science and Policy Dissertation Advisor: Dr. Margaret S. Smith, Emeritus Professor, Instruction and Learning ii Copyright © by Joshua E. Williams 2016 iii AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS Joshua E. Williams, EdD University of Pittsburgh, 2016 The Common Core State Standards for Mathematics (CCSSSM) suggest many changes to secondary mathematics education including an increased focus on conceptual understanding and the inclusion of content and processes that are beyond what is currently taught to most high school students. To facilitate these changes, students will need opportunities to engage in tasks that are cognitively demanding in order to develop this conceptual understanding and to engage in such tasks over a breadth of content areas including probability and statistics. However, teachers may have a difficult time facilitating a change from traditional mathematics instruction to instruction that centers around the use of high-level tasks and a focus on conceptual understanding and that include content from the areas of probability and statistics that may go beyond their expertise and experience.
    [Show full text]
  • Achievement Effects of Four Early Elementary School Math Curricula Findings from First Graders in 39 Schools
    NCEE 2009-4052 U.S. DEPARTMENT OF EDUCATION Achievement Effects of Four Early Elementary School Math Curricula Findings from First Graders in 39 Schools Achievement Effects of Four Early Elementary School Math Curricula Findings from First Graders in 39 Schools February 2009 Roberto Agodini Barbara Harris Sally Atkins-Burnett Sheila Heaviside Timothy Novak Mathematica Policy Research, Inc. Robert Murphy SRI International Audrey Pendleton Project Officer Institute of Education Sciences NCEE 2009-4052 U.S. DEPARTMENT OF EDUCATION U.S. Department of Education Arne Duncan Secretary Institute of Education Sciences Sue Betka Acting Director National Center for Education Evaluation and Regional Assistance Phoebe Cottingham Commissioner February 2009 This report was prepared for the Institute of Education Sciences under Contract No. ED-04-CO- 0112/0003. The project officer was Audrey Pendleton in the National Center for Education Evaluation and Regional Assistance. IES evaluation reports present objective information on the conditions of implementation and impacts of the programs being evaluated. IES evaluation reports do not include conclusions or recommendations or views with regard to actions policymakers or practitioners should take in light of the findings in the reports. This publication is in the public domain. Authorization to reproduce it in whole or in part is granted. While permission to reprint this publication is not necessary, the citation should be: Roberto Agodini, Barbara Harris, Sally Atkins-Burnett, Sheila Heaviside, Timothy Novak, and Robert Murphy (2009). Achievement Effects of Four Early Elementary School Math Curricula: Findings from First Graders in 39 Schools (NCEE 2009-4052). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S.
    [Show full text]
  • Book Report Winning the Math Wars
    Book Report Winning the Math Wars: No Teacher Left Behind Samantha A Peterson Seattle Pacific University 2 Winning the Math Wars: No Teacher Left Behind, is a book written by four Seattle Pacific University scholars, who present a well-articulated and non-biased assessment of the state of mathematics education in the world, in the United States, and specifically in Washington State. The authors divided the book into four chapters, which address the following four topics respectively; what the world is thinking about math education, the American dilemma about math education, math education in Washington State, and ending with a discussion about the implications and conclusions of the math debate. The focus of the book is to present a broad analysis of the math wars and to come to some conclusion about what’s needed in order to realize effective change in the teaching and learning of mathematics. The underlying theme throughout the discussion of reform mathematics is the lack of attention that has been given to the teacher’s role in education reform; “effective reform requires the coordination among standards, assessment, and instruction,” (pg.123). The authors begin by exploring the historical development of the math wars and comparing the United States educational system to that of other cultures. This comparison is helpful because it addresses some of the cultural implications for differences in performance between American students and students from other countries. For instance, Japanese students typically spend far more time on homework and math study. Japanese and American teachers also differ fundamentally in their approach to math teaching.
    [Show full text]
  • Navigating Reform in Mathematics Teacher Education
    Georgia State University ScholarWorks @ Georgia State University Middle and Secondary Education Dissertations Department of Middle and Secondary Education 5-11-2018 Navigating Reform in Mathematics Teacher Education: Teacher Educators' Responses to edTPA and Professional Organizations' Initiatives Alesia Mickle Moldavan Georgia State University Follow this and additional works at: https://scholarworks.gsu.edu/mse_diss Recommended Citation Moldavan, Alesia Mickle, "Navigating Reform in Mathematics Teacher Education: Teacher Educators' Responses to edTPA and Professional Organizations' Initiatives." Dissertation, Georgia State University, 2018. https://scholarworks.gsu.edu/mse_diss/59 This Dissertation is brought to you for free and open access by the Department of Middle and Secondary Education at ScholarWorks @ Georgia State University. It has been accepted for inclusion in Middle and Secondary Education Dissertations by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. ACCEPTANCE This dissertation, NAVIGATING REFORM IN MATHEMATICS TEACHER EDUCATION: TEACHER EDUCATORS’ RESPONSES TO EDTPA AND PROFESSIONAL ORGANIZATIONS’ INITIATIVES, by ALESIA MICKLE MOLDAVAN, was prepared under the direction of the candidate’s Dissertation Advisory Committee. It is accepted by the committee members in partial fulfillment of the requirements for the degree, Doctor of Philosophy, in the College of Education and Human Development, Georgia State University. The Dissertation Advisory Committee and the student’s Department Chairperson, as representatives of the faculty, certify that this dissertation has met all standards of excellence and scholarship as determined by the faculty. _________________________________ David W. Stinson, Ph.D. Committee Chair _________________________________ _________________________________ Janice B. Fournillier, Ph.D. Pier A. Junor Clarke, Ph.D. Committee Member Committee Member _________________________________ Joyce E.
    [Show full text]
  • Review of Evaluation Studies of Mathematics and Science Curricula and Professional Development Models
    Abstract This report identifies mathematics and science curricula as well as professional development models at the middle and high school levels that are effective based on their success in increasing student achievement. The goal of the study was to provide some choice to districts and schools that wanted guidance in selecting a curriculum and that wished to use effectiveness as a selection criterion. Unexpectedly, most middle and high school mathematics and science curricula did not have studies of student achievement with comparison groups, and it proved especially difficult to find effects in either math or science for subgroups by sex, minority status, and urban status. Findings strongly suggest that science curricula is more effective when it is inquiry-based, although math curricula can be effective when standards- or traditional-based. REVIEW OF EVALUATION STUDIES OF MATHEMATICS AND SCIENCE CURRICULA AND PROFESSIONAL DEVELOPMENT MODELS By Beatriz C. Clewell Clemencia Cosentino de Cohen The Urban Institute and Patricia B. Campbell Lesley Perlman Campbell-Kibler Associates, Inc. with Nicole Deterding Sarah Manes Lisa Tsui The Urban Institute and Shay N.S. Rao Becky Branting Lesli Hoey Rosa Carson Campbell-Kibler Associates, Inc. Submitted to the GE Foundation December 2004 Acknowledgments A number of individuals contributed to this effort in various ways. We were fortunate to have the assistance of Gerhard Salinger of the National Science Foundation; Jo Ellen Roseman of Project 2061 at the American Association for the Advancement of Science (AAAS); Joan Abdallah at AAAS; and several staff members at the Center for Science Education at the Education Development Center—Barbara Berns, Jeanne Century, Joe Flynn, Elisabeth Hiles, Jackie Miller, Marian Pasquale, and Judith Sandler —in helping us identify science curricula that might have evaluation studies.
    [Show full text]