One of the aims of mathematics education in schools in Singapore is to enable students to acquire thinking and problem solving skills and to make effective use of these skills to formulate and solve problems (MOE, 2007).
The existing curriculum framework for mathematics designed by the Ministry of Education (MOE) lists metacognition as one of the components on which the development of mathematical problem solving ability depends.
According to the MOE (2007), metacognition can be defined as the realization of, and the ability to regulate one’s thinking processes, in particular the choosing and application of problem-solving strategies. The MOE believes that it is important to provide students with metacognitive experience in order to help them develop their problem solving abilities.
Note: The above paragraphs are adapted from my minor research paper, Examining Supports for Metacognition in Singaporean Lower Secondary Mathematics Textbooks, NIE, 2011. All rights reserved.
Related links:
(1) Metacognition – The secret to learning and problem-solving;
(2) Metacognition and problem-solving;
(3) Metacognition enhances learning;
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Metacognition enhances learning
Various studies have revealed that metacognition helps to enrich students’ learning in different domains. For example, it has the potential to increase students’ capacities for independent learning (Ganz & Ganz, 1990).
Research also shows that knowledge of metacognition, such as being familiar with one’s strengths and weaknesses and searching for ways to overcome the latter, contributes to more effective learning (Bransford, Brown, & Cocking, 1999). Research also suggests that metacognition improves one’s chances of success when it comes to completing activities that rely heavily on thinking processes (Garner & Alexander, 1989; Pressley & Ghatala, 1990).
Many studies in metacognition have concluded that those who have advanced metacognitive abilities are more adaptable and steadfast in problem solving (e.g., see Artzt & Armour-Thomas, 1992; Swanson, 1990). Studies have also shown that one’s ability to plan and monitor a problem-solving process requires several metacognitive skills such as regulation and evaluation of thought processes (Mayer, 1999), and the use of metacognitive skills has the potential to identify the more able students from the less able ones (Pellegrino, Chudowsky & Glaser, 2001).
In addition, research has shown that one’s individual and group learning skills can be improved through the acquisition of metacognitive competencies (White & Frederiksen, 2005). Recent studies have also revealed that students who often fail to choose appropriate strategies, monitor or regulate their work, or articulate their thought processes are more likely to perform poorly in mathematics (e.g., see Lucangeli & Cabrele, 2006; Carlson & Bloom, 2005).
Note: The above paragraphs are adapted from my minor research paper, Examining Supports for Metacognition in Singaporean Lower Secondary Mathematics Textbooks, NIE, 2011. All rights reserved.
Related links:
(1) Metacognition – The secret to learning and problem-solving;
(2) Metacognition and problem-solving;
(3) Is Metacognition part of the Singapore Math curriculum?
_______________________________________
TUITION CLASSES:
_______________________________________________________________
EDUCATIONAL SERVICES:
______________________________________________________________
By EX-MOE TEACHERS & EXPERIENCED TUTORS
@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.
Metacognition and mathematical problem solving
Metacognition is a crucial element in problem-solving, which is itself a key component in mathematics learning. To monitor and regulate one’s cognitive processes in problem-solving, Polya (1945) describes a four-step method: first, one has to comprehend the problem by sub-dividing it into more manageable parts and recognize any given data, conditions and variables to be found; second, one devises or selects a strategy to find the connections between the known data and the unknowns to be found; third, one executes the plan, scanning, regulating and examining each step; and, finally, after obtaining the solution, one evaluates the results which may involve re-visiting the previously taken steps.
Building on Polya’s work, Schoenfeld (1987) describes effective mathematical problem-solving as being contingent on how one uses four types of knowledge/skills: (1) resource knowledge, which is knowledge about one’s abilities and cognitive processes including knowledge of how to perform tasks or procedures; (2) heuristics, which are specific problem-solving methods or strategies; (3) regulatory processes, which includes the organisation and selection of resources and strategies; and (4) beliefs, which includes perceptions of and assumptions about mathematics (Gama, 2004).
Note: The above paragraphs are adapted from my minor research paper, Examining Supports for Metacognition in Singaporean Lower Secondary Mathematics Textbooks, NIE, 2011. All rights reserved.
Related links:
(1) Metacognition – The secret to learning and problem-solving;
(2) Metacognition enhances learning;
(3) Is Metacognition part of the Singapore Math curriculum?
_______________________________________
TUITION CLASSES:
_______________________________________________________________
EDUCATIONAL SERVICES:
______________________________________________________________
By EX-MOE TEACHERS & EXPERIENCED TUTORS
@ BLK 644, BUKIT BATOK CENTRAL, #01-68. S(650644).
CALL 65694897 OR SMS 98530744 OR 97860411.