Mathematical problem solving : a focus on metacognition - Yeap, Ban Har. (2009)
The main purpose of the study that forms the basis of this dissertation is to understand the role of metacognition in mathematical problem solving among a group of secondary one students in a Singapore secondary school. The three specific aims are: (1) to observe patterns of behaviours when students solve mathematical problems, (2) to observe types of metacognitive behaviours during mathematical problem solving, and (3) to understand the role of metacognition during problem solving. The study also aims to provide some recommendations for classroom practice to develop metacognition and problem solving ability. The research study was conducted in two major phases. The first phase involved construction of problem solving protocols for a purposive sample of ten students. The problem solving protocols were mainly constructed from verbal protocols transcribed verbatim from audio recording of students solving a mathematical problem by the thinking aloud method. Students' written responses, field notes from researcher's observations and field notes from interview sessions were used to resolve ambiguities in the verbal protocols. The problem solving protocols were analyzed using two different frameworks. A modified version of Foong's (1993) taxonomy of problem solving behaviours was used to identify the types of metacognitive behaviours that students show during mathematical problem solving. Flavell's (1981) model of cognitive monitoring was used to emerge the role that metacognition play during mathematical problem solving