What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving?

This study investigated factors promoting the use of self-constructed diagrams by examining students’ perceptions and daily class activities, and comparing Japanese (n ¼ 291) and New Zealand (n ¼ 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often and scored higher than their Japanese counterparts. Lack of confidence and perceptions of difficulty in diagram use, and viewing diagrams more as a strategy that teachers use, were found to link with lower use. Possible ways of promoting diagram use in math word problem solving are discussed.

[1]  Richard E. Mayer,et al.  Frequency norms and structural analysis of algebra story problems into families, categories, and templates , 1981 .

[2]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

[3]  Susan R. Goldman,et al.  Word problems: research and curriculum reform , 2001 .

[4]  L. Verschaffel,et al.  Do realistic contexts and graphical representations always have a beneficial impact on students' performance? Negative evidence from a study on modelling non-linear geometry problems , 2003 .

[5]  R. Cox.  Representation construction, externalised cognition and individual differences , 1999 .

[6]  Peter C.-H. Cheng,et al.  Why Diagrams Are (Sometimes) Six Times Easier than Words: Benefits beyond Locational Indexing , 2004, Diagrams.

[7]  Claude Janvier.  Problems of representation in the teaching and learning of mathematics , 1987 .

[8]  A. Schoenfeld.  Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint) , 2009 .

[9]  Barbara L. McCombs,et al.  Motivational Skills Training: Combining Metacognitive, Cognitive, and Affective Learning Strategies , 1988 .

[10]  Peter C.-H. Cheng,et al.  Electrifying diagrams for learning: principles for complex representational systems , 2002, Cogn. Sci..

[11]  Patricia A. Alexander,et al.  Learning and study strategies : issues in assessment, instruction, and evaluation , 1988 .

[12]  Wayne D. Gray.  Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society , 2001 .

[13]  D. Kibler,et al.  Exploring the Episodic Structure of Algebra Story Problem Solving , 1989 .

[14]  Lieven Verschaffel,et al.  Mathematics teaching and learning. , 1996 .

[15]  G. Pólya,et al.  How to Solve It. A New Aspect of Mathematical Method. , 1945 .

[16]  P. Pintrich,et al.  Motivational and self-regulated learning components of classroom academic performance. , 1990 .

[17]  学習方略の有効性の認知・コストの認知・好みが学習方略の使用に及ぼす影響 , 1998 .

[18]  K. Holyoak,et al.  The use of diagrams in analogical problem solving , 2001, Memory & cognition.

[19]  R. Hembree.  Experiments and Relational Studies in Problem Solving: A Meta-Analysis. , 1992 .

[20]  Herbert A. Simon,et al.  Why a Diagram is (Sometimes) Worth Ten Thousand Words , 1987, Cogn. Sci..

[21]  Hermann G. Ebner,et al.  Improving cross-content transfer in text processing by means of active graphical representation , 2003 .

[22]  Shaaron Ainsworth,et al.  The effects of self‐explaining when learning with text or diagrams , 2003 .

[23]  Douglas A. Grouws,et al.  Handbook of research on mathematics teaching and learning , 1992 .

[24]  Richard E. Mayer,et al.  Multimedia Learning: The Promise of Multimedia Learning , 2001 .

[25]  Susan E. Newman,et al.  Cognitive Apprenticeship: Teaching the Craft of Reading, Writing, and Mathematics. Technical Report No. 403. , 1987 .

[26]  B. Zimmerman,et al.  Student Differences in Self-Regulated Learning: Relating Grade, Sex, and Giftedness to Self-Efficacy and Strategy Use. , 1990 .

[27]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[28]  P. Cheng.  Electrifying diagrams for learning: principles for effective representational systems , 2002 .

[29]  Steven J. Chrostowski,et al.  TIMSS 2003 International Mathematics Report: Findings from IEA's Trends in International Mathematics and Science Study at the Fourth and Eighth Grades. , 2004 .

[30]  Jacob Cohen,et al.  A power primer. , 1992, Psychological bulletin.

[31]  John Hattie,et al.  Cultural Differences in the Use of Strategies for Self-Regulated Learning , 1996 .

[32]  Christiaan Hamaker,et al.  Using Self-Generated Drawings to Solve Arithmetic Word Problems , 1990 .

[33]  Kenneth R. Koedinger,et al.  A Cognitive Task Analysis of Using Pictures To Support Pre-Algebraic Reasoning , 2002 .