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Inquiry Based Mathematics Instruction Versus Traditional Mathematics

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Inquiry Based Mathematics Instruction Versus Traditional Mathematics Cedarville University DigitalCommons@Cedarville Master of Education Research Theses Master of Education Capstones 2010 Inquiry Based Mathematics Instruction Versus Traditional Mathematics Instruction: The ffecE t on Student Understanding and Comprehension in an Eighth Grade Pre-Algebra Classroom Kyle Ferguson Cedarville University Follow this and additional works at: http://digitalcommons.cedarville.edu/education_theses Part of the Junior High, Intermediate, Middle School Education and Teaching Commons, and the Science and Mathematics Education Commons Recommended Citation Ferguson, Kyle, "Inquiry Based Mathematics Instruction Versus Traditional Mathematics Instruction: The Effect on Student Understanding and Comprehension in an Eighth Grade Pre-Algebra Classroom" (2010). Master of Education Research Theses. 26. http://digitalcommons.cedarville.edu/education_theses/26 This Thesis is brought to you for free and open access by DigitalCommons@Cedarville, a service of the Centennial Library. It has been accepted for inclusion in Master of Education Research Theses by an authorized administrator of DigitalCommons@Cedarville. For more information, please contact [email protected]. Inquiry Based Mathematics Instruction Verses Traditional Mathematics Instruction: The Effect on Student Understanding and Comprehension in an Eighth Grade Pre-algebra Classroom A thesis submitted in partial fulfillment of the requirements for the degree of Masters of Education By KYLE L. FERGUSON B.A. Middle Childhood Education, Cedarville University, 2006 2010 Cedarville University Acknowledgments I give thanks to God for giving me the ability and opportunity to complete my M. Ed. I would like to thank Dr. Hwang, Dr. Heaton, Mr. Hess and Dr. Gruber for their input and guidance in helping me through this thesis project. Finally, I would like to thank my wife for her support and encouragement to push on to the end. ii ABSTRACT Ferguson, Kyle L. M.Ed., Education Department, Cedarville University, 2010. Inquiry Based Verses Traditional Mathematics Instruction: The Effect on Student Understanding and Comprehension in an Eighth Grade Pre-Algebra Classroom. This quantitative study provides information obtained through the use of inquiry-based mathematics instruction verses traditional mathematics instruction. The use of each curriculum was implemented into two classrooms of eighth grade pre-algebra students. The study was based on data collected before and after each of the two units of study. Fifty-two suburban eighth grade students represented the sample population. Results of the SPSS analysis showed that both classes made improvement from their pre-test to their post-test for both units but students receiving instruction through inquiry-based instruction showed significantly more improvement on the second unit. These results can be useful for educators considering the adoption of an updated or new mathematics curriculum in their school district. iii TABLE OF CONTENTS Page CHAPTER I: Introduction………………………………………………………………..1 Definition of Terms…………….………………………………………………….6 Statement of Issue………………………………………………………………..10 Scope of Study and Delimitations………………………………………………..11 Significance of the Study………………………………………………………...12 Methods of Procedure……………………………………………………………13 CHAPTER II: Plenary Literature Review…………………………….………………...15 History of Mathematics Education….…………………………………………...15 Implementing Inquiry Based Mathematics curriculums…………………………18 Use of Traditional Mathematics Textbooks……………………………………...19 Teachers’ Beliefs and Conceptions about Mathematics Instruction……………..21 Teachers’ Knowledge of Mathematics…………………………………………..23 Benefits of Traditional Mathematics Instruction………………………………...25 Limitations of Traditional Mathematics Instruction……………………………..26 Benefits of Inquiry Based Mathematics Instruction……………………………..27 Limitations of Inquiry Based Mathematics Instruction………………………….29 Need for the Present Study………………………………………………………31 CHAPTER III: Methodology……..……………………………………………………..33 Rationale for the Method………………………………………………………...34 Population of the Study…………………………………………………………..35 Sample……………………………………………………………………………35 Procedure………………………………………………………………………...36 iv CHAPTER IV: Results: Quantitative Analysis……………..……………………..……38 Overview…………………………………………………………………………38 Results of unit 1.…………………...……………….……………………………39 Results of unit 2………………………………………………………………….42 CHAPTER V: Discussion and Implications…………………………………………….44 Interpretation of the Results………………………….…………………………..44 Potential Applications of the Findings…………………………………………...45 Biblical Integration………………………………………………………………48 Relation of the Results to Literature..……………………………………………51 Strengths of the Study……………………………………………………………52 Limitations of the Study………………………………………………………….53 Suggestions for Future Research………………………………………………...54 APPENDICES…………………………………………………………………………...56 APPENDIX A: Pre-Test/Post Test Unit 1……………………………………….56 APPENDIX B: Pre-Test/Post Test Unit 2……………………………………….58 REFERENCES…………………………………………………………………………..59 v Chapter 1 Introduction If most people were asked to recall how they were taught mathematics they would most likely recall engaging in rote memorization of mathematical concepts as the teacher demonstrated the procedures to solve certain problems on the board. Following the lesson the teacher would give a “drill and kill” homework assignment over the same concepts that were covered in class. The next day would consist of the same procedures but over a different concept. This method of mathematics instruction would continue on day after day. Over the past several years, however, debate has taken place over how to effectively teach math and whether the traditional method is as effective as it once was. Skills students were required to have in order to function in society in the 20th century are different than the skills required of students in the 21st century. With this change in skill requirement comes a need for change in how students are taught (Chapko & Buchko, 2004). Students today find it difficult to understand what it is they need to know and many times why they need to know it. A common question asked in a mathematics classroom is “why do I need to know this?” or “When will I ever use this?” Answering this “need to know” question has been coined the term inquiry. Inquiry goes much deeper than asking simple questions such as, “is it going to rain today?” Inquiry is a process of learning that is driven by questioning, thoughtful investigating, making sense of information and developing new understandings (Diggs, 2009). Traditional methods of math instruction do not allow for much questioning, investigating or individual development of understanding. Inquiry based mathematics instruction allows for all of this to take place in the classroom and opens up the doors for students to answer their own questions by exploring meaningful real-life problems that incorporate several mathematical 1 concepts into one problem. What might this inquiry based mathematics instruction look like in a mathematics classroom? We all know there is only one right answer for a math problem, but there is obviously more than one way to obtain that right answer. Inquiry math is different from traditional math in that students work with partners and whole-group instruction to construct mathematical explanations that make sense to them. Students are presented with opportunities to verbally explain their thinking processes to the teacher and class, and it is this exchange of ideas that provides the foundation for true understanding of mathematical concepts (Chapko & Buchko, 2004, p. 33). Traditional math works in the short term, but students who cannot remember what the teacher did on a certain step or do not understand why the teacher used a particular procedure will inevitably forget. Inquiry math focuses on conceptual development as opposed to procedural development in traditional math. A teacher using inquiry math will establish the problem on which the students are going to be working. Once students understand what the problem is, they begin working on coming up with a solution while working with partners or small groups. Inquiry math allows students more opportunity to think about and explain their mathematical thinking. Communicating math is done in many ways using inquiry math but the predominant one is through written communication. Writing in mathematics courses is a concept that many mathematics educators would agree needs to be incorporated more into mathematics instruction. Writing allows individuals to think about their reasoning, express ideas and concepts that make better sense to them in their own words and share their ideas with others (Burns, 2004). Writing is an assessment that gives teachers valuable insight into a child’s thinking that can be used for intervention and future planning (McCarthy, 2008). Unfortunately, the pressures of high stakes testing and the reliance 2 on multiple choice tests have limited mathematics instructors in the venues in which they can teach. Writing is a powerful tool that not only helps to improve students’ writing abilities, but also helps students clarify and extend their knowledge in the area of mathematics (Manning and Manning, 1996). Outside of the classroom, students do not typically use mathematical terminology in their everyday language. In fact, most students do not even talk about mathematics naturally outside of the classroom. Because of this, math teachers are challenged to help students learn how to write and communicate their
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