Academic journal article International Education Studies

The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis

Academic journal article International Education Studies

The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis

Article excerpt

Abstract

The purpose of the study was to meta-synthesize research findings on the effectiveness of problem posing and to investigate the factors that might affect the incorporation of problem posing in the teaching and learning of mathematics. The eligibility criteria for inclusion of literature in the meta-analysis was: published between 1989 and 2011, reported problem posing as an intervention, employed experimental research design, and provided data necessary to compute effect sizes. The large positive effect sizes (Hedges' g) showed that problem posing activities provide considerable benefits for: mathematics achievement, problem solving skills, levels of problems posed, and attitudes toward mathematics. Several noteworthy limitations of this study were discussed.

Keywords: mathematical problem posing, teaching strategies, meta-analysis

1. Introduction

In recent years, mathematical problem posing has been gaining considerable attention as a useful cognitive activity along with problem solving. The National Council of Teachers of Mathematics (NCTM) highlighted the importance of problem posing as a classroom intervention strategy for reforming school mathematics. Mathematics educators have acknowledged problem posing as a worthy intellectual activity based on constructivist theories of teaching and learning (Silver, 1994). According to English (1997), when students pose their own problems, they can enhance their mathematical knowledge, stimulate critical thinking, and improve computational skills by exploring their curiosity about specific mathematics concepts.

Problem posing is considered a developmental tool for critical thinking (English, 1997; Lowrie, 2002) because it can help students extend what they know in order to develop mathematical fluency and engage them in higher-order thinking (NCTM, 2000). In order to create an effective problem, posers must have imaginative skills that can be developed through the process of problem solving (Kilpatrick, 1987). Lavy and Bershadsky (2003) stated students not only needed to think mathematically but also think creatively when reformulating and generating a new mathematical problem. These researchers believed that students who were engaged in problem posing activities became enterprising, creative, and active learners.

2. Problem Posing in the Teaching and Learning of Mathematics

Research on problem posing has been shown to have positive outcomes on students' knowledge, problem solving skills, problem posing abilities, creativity, and disposition toward mathematics (e.g., Cai, 1998, 2003; Cai & Hwang, 2002; English, 1997, 1998; Lavy & Bershadsky, 2003; Moses, Bjork, & Goldenberg, 1990; Silver, Mamona-Downs, Leung, & Kenney, 1996; Stoyanova, 1999; Yuan & Sriraman, 2011). For instance, Lavy and Bershadsky (2003) discovered that the use of problem posing activities contributed to the development of an individual's mathematical knowledge. In this study, the What if not? strategy (Brown & Walter, 2005) was adapted into two learning workshops on complex solid geometry. The results showed that students have deeper understanding of geometry and strengthen some interrelated mathematical concepts which supported Moses et al.'s (1990) ideas of restructuring and connecting knowledge based on prior ones with the use of problem posing activities.

In addition, a number of empirical works reported the effects of problem posing activities on attitudes and beliefs about mathematics and mathematics instruction. In their study, Barlow and Cates (2006) found that when teachers incorporated a problem-posing intervention, classrooms became more student-centered and students were more actively involved in creating and solving their own problems. On the other hand, problem posing gave students ownership of the problems they had generated or formulated (Cunningham, 2004; Grundmeier, 2003; Within, 2006). Cunningham stated that when students created new problems, they increased their sense of responsibility as they constructed their own knowledge while critiquing and refining problems with their classmates. …

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