Peer Instruction as a Way of Promoting Spontaneous Use of Diagrams When Solving Math Word Problems

Peer Instruction as a Way of Promoting Spontaneous Use of Diagrams When Solving Math Word Problems Yuri Uesaka (yuesaka@p.u-tokyo.ac.jp) Department of Educational Psychology, Graduate School of Education The University of Tokyo, Japan Emmanuel Manalo (e.manalo@auckland.ac.nz) The Student Learning Centre, The University of Auckland, New Zealand Abstract reasoning strategies when some prerequisite conditions are met (e.g., Stern, et al., 2003; see also the review by Cox, It appears, however, that school students do not appreciate the efficiency that diagram use brings to problem solving as much as teachers and researcher do. A number of problems about students’ use of diagrams have been reported, which include lack of spontaneity in their use (e.g., Ichikawa, 1993, 2000; Uesaka, Manalo, & Ichikawa, in press), inappropriate construction (e.g., Cox, 1996; Uesaka & Manalo, 2006), and failure to draw correct inferences even when appropriate diagrams have been used (e.g., Cox, These problems concerning students’ use of diagrams have not been sufficiently examined in previous studies. The present study focused on the lack of spontaneity with which students use diagrams in math word problem solving: a teaching method for promoting spontaneity was developed and evaluated. Although using diagrams is generally considered one of the most effective strategies for solving math word problems, research and educational practice reports indicate that students lack spontaneity in their use of diagrams. In an attempt to address this problem, the present study investigated the hypothesis that creating situations whereby students have to teach other students how to solve math word problems with the use of diagrams would promote those students’ subsequent spontaneous use of diagrams. Experimental classes were conducted with 57 8th-grade students for five days. Participants in the experimental condition were all given opportunities to explain to other students in their group their way of solving the math word problems given. In contrast, in the control condition, only some of the students were given opportunities to make presentations in front of the class about their way of solving the problems. In both conditions, the teacher encouraged diagram use during the instructions provided. The main finding was that, in the post-instruction assessment, those in the experimental condition evidenced greater spontaneous use of diagrams in attempting to solve the math word problems given. This finding suggests that, as a consequence of the peer teaching experience – which provided opportunities for the use of diagrams as communication tools – participants internalized diagrams as tools for problem solving. The protocol of peer interaction was also analyzed to better understand the mechanisms involved in this effect. 1.1 Students’ Lack of Spontaneity in Diagram Use Research reports relating to educational practices suggest that students’ failure to spontaneously use diagrams occur despite plenty of exposure to appropriate use of diagrams. Ichikawa (1993), for example, reported in a tutoring case study an 8th-grade girl who did not spontaneously use diagrams in a test situation and failed to solve the problem given – despite previously being taught how to solve similar problems with the use of diagrams. Ichikawa (2000) described the extent to which this problem is found among students. Dufour-Janiver, Bednarz, & Belanger (1987) also noted the lack of spontaneity in diagram use among students and observed that this problem occurs even though math teachers use a lot of diagrams in class. Uesaka, Manalo, & Ichikawa’s (in press) empirical study confirmed this tendency particularly among Japanese students. If students do not (or cannot) use diagrams in situations where they would be deemed appropriate, they (the students) would clearly be disadvantaged. Although in some educational contexts suitable diagrams are provided or suggested, in the majority of cases – including ‘real world’ situations – students are required to construct and use diagrams by themselves according to necessity. In light of the previously identified problems, it would seem that interventions additional to traditional classroom instructions Keywords: Diagram Use, Math Word Problem Solving, Peer Instruction Introduction Diagrams are generally considered as one of the most effective tools in problem solving. For example, Larkin and Simon (1987) showed that diagrammatic representations are superior to sentential representations because they help reduce mental computational loads associated with searching and processing. Other studies have also empirically demonstrated that diagrams effectively promote the performance of many types of tasks (e.g., Ainsworth & Th Loizou, 2003; Cheng, 2002; Koedinger & Terao, 2002; Larkin & Simon, 1987; Mayer, 2003; Polya, 1945; Schoenfeld, 1985; Stern, Aprea, & Ebner, 2003). As a sub-category of diagrams, those that are self- constructed are especially effective. Although some studies have suggested that self-constructed diagrams do not always promote success in problem solving (e.g., Van Essen & Hamaker, 1990), the findings of recent studies mostly indicate that self-constructed diagrams provide powerful