Bar Diagramming in School Mathematics: A Review of the Literature 公开
Sanders, Zendre' Yvette (2017)
Abstract
Bar Diagramming in School Mathematics:
A Review of the Literature
By
Zendre' Yvette Sanders
This thesis is a review of the extant empirical literature about the school mathematics practices of bar diagramming, strip diagramming, tape diagramming, the Model Method, and bar modeling. For a few decades, policy makers, curriculum designers, and educators in several of the nations that have repeatedly ranked as top performers in mathematics have prioritized the introduction and featuring of these diagrammatic classroom practices. As incorporation of these diagrammatic practices has increased, so has the need to provide stakeholders with additional information about the effective and ineffective handling of diagrams in the classroom. In response to this need, I conducted a review of the empirical literature surrounding these diagrammatic practices. A total of 16 studies across 15 research articles met the literature search criteria. Major findings are as follows: (1) Bar diagrams can represent mathematical concepts in ways that show their connection to other mathematical concepts. (2) Bar diagrams can simultaneously show the informal, qualitative aspects of a concept and the formal, quantitative aspects of the concept. (3) Bar diagrams allow students to become comfortable with operating upon unknowns, undoing operations, and maintaining balance across the equal sign. (4) Habituation to the visual nature of bar diagrams and circumvention of algebra via arithmetic can cause some students problems. Further research about how stakeholders can better employ bar diagramming to develop and deepen students' understanding of problem structure and students' appropriation of algebraic concepts and principles is suggested.
Keywords: bar diagramming, bar modeling, diagrammatic reasoning, instructional technique, mathematics instruction, school mathematics, the Singapore Model Method, strip diagramming, tape diagramming
Table of Contents
Table of Contents
Statement of the Problem 1
Purpose of the Literature Review 2
Significance of the Review 3
Literature Review Search Strategy 4
Definition of Key Terms 6
Bar diagram 6
Bar diagramming 7
Delimitations 8
Limitations of the Review 8
Review of the Literature 8
Researchers' Analyses of Participants' Assessment Scores 13
Researchers' Examinations of Participants' Mathematical Work
17
Researchers' Analyses of Interview Data 26
Researchers' Analyses of Classroom Conversation 33
Researchers' Examinations of Teaching Sessions and Students'
Session Work 36
Researchers' Examinations of Neuroimaging 37
Literature Review Findings 41
Benefits of Bar Diagrams for Representing Mathematics 42
Detriments of Bar Diagrams for Representing Mathematics 43
Challenges with Bar Diagrams for Representing Mathematics 44
Benefits of Bar Diagrams for Supporting Students' Problem Solving
45
Detriments of Bar Diagrams for Supporting Students' Problem Solving
46
Challenges with Bar Diagrams for Supporting Students' Problem
Solving 47
Benefits of Bar Diagrams for Supporting Students' Growth in
Mathematical Understanding 47
Detriments of Bar Diagrams for Supporting Students' Growth in
Mathematical Understanding 49
Challenges with Bar Diagrams for Supporting Students' Growth in
Mathematical Understanding 50
Conclusion 50
Suggestions for Further Research 51
Final Word 52
References 54
List of Appendices
Appendix A: Countries Ranking Fifth or Higher on the Mathematics
TIMSS and Whether Their Curriculum Features Bar Diagramming
59
Appendix B: Boaler's Model Depicting the Interrelationship Among
Knowledge, Practice, and Identity 60
Appendix C: List of Empirical Studies under Review 61
Appendix D: Bar Diagrams Can Depict How the Same Situation Can Be
Discussed with Different Mathematical Language Corresponding to
Different but Related Concepts 64
Appendix E: Bar Diagrams Can Represent Algebra Equations in
Addition to Arithmetic Equations 65
Appendix F: Table A1. Studies' Locations, Sample Characteristics,
and Relevant Research Findings 68
List of Tables
Table 1. Preliminary Search Hits for Empirical Studies about Bar
Diagramming 5
About this Master's Thesis
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