What kinds of perceptions and daily learning behaviors promote students’ use of diagrams in mathematics problem solving? Yuri Uesaka a, * , Emmanuel Manalo b , Shin’ichi Ichikawa c a Department of Educational Psychology, Graduate School of Education, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan b The Student Learning Centre, The University of Auckland, New Zealand c Department of Educational Psychology, Graduate School of Education, The University of Tokyo, Japan Abstract 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 question- naire 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. Ó 2007 Published by Elsevier Ltd. Keywords: Math word problem solving; Self-constructed diagrams; Cross-national comparison; Student strategy use 1. Introduction 1.1. Math word problem solving and the importance of diagram use In mathematics education, the development of students’ abilities in solving math word problems has been an important topic (see, e.g., Polya, 1945; Reed, 1999; Schoenfeld, 1985, 1992). Some researchers have described solv- ing math word problems as one of the most difficult areas for students (e.g., Reed, 1999; Yoshida, 1991). Standards published by the National Council of Teachers of Mathematics in the US (NCTM, 2000) and the National Curriculum of Japan published by the Japanese Ministry of Education (1998) both focus on the importance of learning tasks relating to real-world situations e the very area that the majority of math word problems deal with. As noted, solving math word problems is not easy for many students and, because of this, many studies have looked into and proposed ways for overcoming the difficulties that some students encounter. One approach is to cultivate stu- dents’ internal resources e in other words, to develop their knowledge of heuristics and skills in strategies use * Corresponding author. Tel.: þ81 3 5841 3923; fax: þ81 3 5841 3919. E-mail address: yuesaka@educhan.p.u-tokyo.ac.jp (Y. Uesaka). 0959-4752/$ - see front matter Ó 2007 Published by Elsevier Ltd. doi:10.1016/j.learninstruc.2007.02.006 Learning and Instruction 17 (2007) 322e335 www.elsevier.com/locate/learninstruc