The Effect Constructivist and Traditional Teaching Methods on Students’ Mathematical Achievement By Desiree Solso A Project Submitted to the Faculty of The Evergreen State College In Partial Fulfillment of the Requirement For the degree Master in Teaching 2009 ii This Project for the Master in Teaching Degree By Desiree Solso Has been approved for The Evergreen State College By Masao Sugiyama Member of the Faculty Date iii ABSTRACT In recent years, there has been a debate in the public schools over the different approaches to how mathematics is taught in public schools. In the past, the schools believed that teaching mathematics the traditional way with direct instruction and route memorization of facts and procedures. In recent years, there has been a shift in the educational system in moving towards a more constructivist approach to the teaching of mathematics. School are beginning to adopt new mathematics curriculum with includes the use of manipulatives, small group work and developing cognitive thinking skills. This paper seeks to investigate what effect different mathematical teachings had on student achievement. The research explores both traditional and constructivist teaching to include students with learning disabilities and mathematic assessments’ around the world. In addition, it will investigate constructivist mathematics curriculum and the affect on student mathematical achievement. iv TABLE OF CONTENTS COVER PAGE....................................................................................................... i APPROVAL PAGE ................................................................................................ii ABSTRACT ..........................................................................................................iii CHAPTER ONE: INTRODUCTION ...................................................................... 1 Introduction ....................................................................................................... 1 Rationale........................................................................................................... 1 Controversies.................................................................................................... 2 Definition of Terms............................................................................................ 3 Statement of Purpose ....................................................................................... 5 Summary........................................................................................................... 5 CHAPTER TWO: HISTORICAL BACKGROUND ................................................. 7 Introduction ....................................................................................................... 7 Mathematics in the ancient world...................................................................... 7 18th and 19th century ........................................................................................ 9 Social Constructivist thinking in America .......................................................... 9 Mathematics Educational Revolution, New Math............................................ 11 Mathematics Educational Revolution, Back to Basics -- 1970's...................... 12 Mathematics Educational Revolution, NCTM Standards ................................ 12 Summary......................................................................................................... 13 CHAPTER THREE: CRITICAL REVIEW OF THE LITERATURE....................... 14 Introduction ..................................................................................................... 14 Section One: Student Achievement In Relation to Instruction......................... 15 v Students Ability to Become an Active Participants in their Learning............ 15 Student Perception and Attitude Towards Mathematics.............................. 23 Student Assessments.................................................................................. 31 Section Two: Investigating The Everyday Mathematics curriculum ................ 35 The Everyday Mathematics Curriculum....................................................... 35 Comparing Different Curricula ..................................................................... 43 Section Three: Traditional mathematics.......................................................... 48 Section Four: Constructivism and Traditional mathematical approaches........ 56 Teacher case study on mathematical beliefs............................................... 65 Section Five: Mathematics In Relation to Learning Disabilities and Student Achievement ................................................................................................... 67 Section Six: Mathematics assessments’ around the world.............................. 76 Summary......................................................................................................... 84 CHAPTER FOUR: CONCLUSION ..................................................................... 85 Introduction ..................................................................................................... 85 Summary of Findings ...................................................................................... 85 Student Achievement In Relation to Instruction........................................... 86 Investigating The Everyday Mathematics curriculum .................................. 87 Traditional mathematics .............................................................................. 88 Constructivism and Traditional mathematical approaches .......................... 88 Mathematics in relation to learning disabilities and student achievemen .... 89 Mathematics Assessments’ Around the World ............................................ 90 Classroom Implications................................................................................... 91 vi Suggestions for Further Research .................................................................. 92 Conclusion ...................................................................................................... 93 References ......................................................................................................... 95 1 CHAPTER ONE: INTRODUCTION Introduction Mathematics has the ability to confuse, frighten, and frustrate learners of all ages. If a child has a negative experience in mathematics, that experience has the ability to affect his/her attitude toward mathematics as an adult. Every daily activity includes mathematic procedures, whether people are consciously aware of it or not. Possessing solid mathematical computational ability will help make additional skills come easier to the learner. The current debate in the school system is based on two different approaches to mathematics, constructivist or traditional. Constructivist teaching or constructivism is influenced by Jean Piaget and based upon the student being actively engaged in their learning process. Students build on their prior knowledge or schema, to aid in their learning. (Singer & Revenson, 1999; Marek & Cavalla 1997). Traditional mathematics instruction was influenced by Skinner, holds a scientific approach to learning. Rote memorization, drills, and recitation as the foundation for traditional teaching methods (Skinner, 2002). Traditional mathematics instruction (also referred to as direct instruction) emphasizes learning procedures and number facts and uses drill and recitation to reinforce and assess learning. Rationale The rationale for this project is to discern whether traditional teaching methods or constructivist teaching methods produce a better understanding of the concepts of mathematics in the student learner. This research investigates the effectiveness of both teaching methods and the effect that the methods have 2 on the overall achievement of the student in relationship to instruction, teacher beliefs, and mathematics curriculum. A teacher who comprehends mathematical procedures and is able to teach it in a way that is effective for their students’ learning is important. The purpose of this research is to find the rationale behind the change in the concepts of teaching mathematics. In addition, this research will also investigate the affect that behaviorist and constructivist mathematics teaching on the achievement and understanding of the student. In addition, the research will also explore the mathematical achievement of students with learning disabilities and the affect that constructivist or traditional instruction has on assessment. Furthermore, the research will evaluate constructivist mathematics curriculum in relation to student achievement. Finally, the research explores mathematics around the world and the different instructional styles in other countries in relation to student achievement. Controversies With the change toward teaching mathematics from a constructivist view of learning in recent years, much controversy has erupted. One of the main conflicts over the change to constructivist mathematics is the reluctance of those who have taught traditionally to change the way mathematics has been taught. Teachers who follow the traditional methods of teaching believe that rote memorization and drilling of facts is the only way that a child will learn the mathematical skills needed for higher-level thinking. They believe children will not be able to develop the skills to know how to do addition, subtraction, time tables or other mathematical calculations