Metacognitive awareness of problem solving among primary and secondary school students

The ability to solve mathematics problems is the central focus of the Singapore mathematics curriculum. This curriculum postulates that metacognition is one of the five key factors that can facilitate success in problem solving. Metacognition means that the problem solvers become aware of their own problem solving process, take control of this process, and seek help whenever necessary. One component of the CRPP-funded project entitled Developing the Repertoire of Heuristics for Mathematical Problem Solving (MPS) examines metacognitive awareness among a sample of P5 and S1 students. The questionnaire on metacognition asks about what the students do during problem solving and their levels of enjoyment and confidence while solving problems. This was administered as a “pretest” around April 2004, and a “posttest” several months later. There were few changes in students’ metacognitive awareness between the two tests. Their responses were fairly general, lacking in deep awareness of personal metacognition. Many students wrote about trying to understand the problem, but very few mentioned about checking their work. Most students expected the teachers to teach and explain more and better, but few could give specific suggestions. If metacognition were to become a standard learning and problem solving process as intended by the Singapore mathematics curriculum framework, structured programs that aim to inculcate various aspects of metacognition need to be developed and researched. THE STUDY The ability to solve mathematics problems has been the central focus of the Singapore mathematics curriculum since late 1980. To successfully solve various types of problems, in particular the non-routine ones, a motivated student has to apply four types of mathematical competencies, namely, specific mathematics concepts, skills, processes, and metacognition. Some studies have been conducted on metacognition and problem solving behaviours among Singapore students (Foong, 1993; Tay et al., 2006; Teong, 2003). In addition, Teong (2003) designed an explicit metacognitive instruction called CRIME (Careful reading; Recall possible strategies; Implement possible strategies; Monitor; and Evaluation) to be used in a computer-based environment. Low-achieving P5 pupils trained under her scheme outperformed the control group in solving word problems. Tay and his team (2006) reported that after explicit lessons on mathematics heuristics, a cohort of high ability Secondary 3 students under the Integrated Programme (IP) had changed their attitudes towards problem solving and mathematics. This paper provides further findings about metacognitive awareness as reported by some Singapore Primary 5 (P5) and Secondary 1 (S1) students after they had solved some mathematics problems (see Wong & Tiong, 2006a, about the use of heuristics). This is part of the CRPP project entitled “Developing the Repertoire of Heuristics for Mathematical Problem Solving” (MPS). The findings about metacognition can contribute towards understanding its role in problem solving, an important issue that mathematics This conference proceedings may be used for private study or research purpose only.