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Metacognitive strategies secondary one students employed while solving mathematics problems
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Type
Thesis
Author
Loh, Mei Yoke
Supervisor
Fan, Lianghuo
Lee, Ngan Hoe
Lee, P. Y. (Peng Yee)
Abstract
Singapore has been lauded for doing well in international comparative studies and, having a world-class mathematics education system. In order for our students to continue to do well in school and be prepared for the future workforce, there is a need to go beyond what has been done. The Singapore Ministry of Education has identified the 21st Century competencies that schools should nurture in our students and metacognition is recognised as one of these emerging competencies. One way that mathematical instructional approaches may be refined to support students in developing these competencies is to promote metacognition in mathematical problem solving. Such effort helps to improve students’ mathematics performance, as well as prepare them for future learning and the future workforce.
Before recommending appropriate measures to better incorporate metacognition in problem solving, it is important to first find out how metacognition has worked through the classrooms and its impact on problem solving since the first problem-solving mathematics curriculum which explicitly addressed metacognition was introduced in 1992.
- What are the metacognitive strategies students frequently employed while solving mathematics problems?
- What is the relationship between metacognition and success in mathematical problem solving?
This study investigates the metacognitive strategies students, after six years of primary mathematics education, employ during mathematical problem solving. Data was collected on 783 students who have completed their primary education during the beginning months of the Secondary One school term.
The study also explores on metacognition in relation to performance in problem solving by topics (Angles and Whole Numbers) as well as by students’ general academic achievement.
The Problem Solving Metacognitive (PSM) framework (p. 98) was developed for this study. It describes the four phases of problem solving and three levels of metacognitive strategies involved in mathematical problem solving. Together, the phases and levels illustrate the types of metacognitive strategies for mathematical problem solving.
The research design used for this study is the mixed methods concurrent research design. Three instruments, survey inventory, problem solving test and task-based interview, were used to collect data.
Some recommendations for classroom practice were distilled from the findings:
1. Infuse the teaching of both general and topic-specific metacognitive strategies.
2. Spend more time in understanding the problem, evaluating the adequacy of given information and building appropriate representations of the problems before devising a plan.
3. Teach heuristics and enhance metacognitive knowledge in applying appropriate heuristics to different problem situations.
4. Enhance the reflection processes such as checking of reasonableness of solutions and evaluating the efficacy of methods employed.
The study also contributes to theoretical implications about research in metacognition in mathematical problem solving. While survey inventory and retrospective self-report are commonly used instruments for data collection in examining students’ metacognitive practices, when used together, they appear not to enhance the interpretative validity of the findings from synthesizing multiple sources of data. However, task-based interview seems to be the most appropriate instrument for examining metacognition in mathematical problem solving. Understanding the limitations of each instrument would lead to a better interpretation of the findings derived.
Before recommending appropriate measures to better incorporate metacognition in problem solving, it is important to first find out how metacognition has worked through the classrooms and its impact on problem solving since the first problem-solving mathematics curriculum which explicitly addressed metacognition was introduced in 1992.
- What are the metacognitive strategies students frequently employed while solving mathematics problems?
- What is the relationship between metacognition and success in mathematical problem solving?
This study investigates the metacognitive strategies students, after six years of primary mathematics education, employ during mathematical problem solving. Data was collected on 783 students who have completed their primary education during the beginning months of the Secondary One school term.
The study also explores on metacognition in relation to performance in problem solving by topics (Angles and Whole Numbers) as well as by students’ general academic achievement.
The Problem Solving Metacognitive (PSM) framework (p. 98) was developed for this study. It describes the four phases of problem solving and three levels of metacognitive strategies involved in mathematical problem solving. Together, the phases and levels illustrate the types of metacognitive strategies for mathematical problem solving.
The research design used for this study is the mixed methods concurrent research design. Three instruments, survey inventory, problem solving test and task-based interview, were used to collect data.
Some recommendations for classroom practice were distilled from the findings:
1. Infuse the teaching of both general and topic-specific metacognitive strategies.
2. Spend more time in understanding the problem, evaluating the adequacy of given information and building appropriate representations of the problems before devising a plan.
3. Teach heuristics and enhance metacognitive knowledge in applying appropriate heuristics to different problem situations.
4. Enhance the reflection processes such as checking of reasonableness of solutions and evaluating the efficacy of methods employed.
The study also contributes to theoretical implications about research in metacognition in mathematical problem solving. While survey inventory and retrospective self-report are commonly used instruments for data collection in examining students’ metacognitive practices, when used together, they appear not to enhance the interpretative validity of the findings from synthesizing multiple sources of data. However, task-based interview seems to be the most appropriate instrument for examining metacognition in mathematical problem solving. Understanding the limitations of each instrument would lead to a better interpretation of the findings derived.
Date Issued
2015
Call Number
QA14.S55 Loh
Date Submitted
2015