METACOGNITION AS A STRATEGY TO IMPROVING MATHEMATICS PROBLEM SOLVING SKILL

Parhaini Andriani

A.      Background

Transformation and technological change increasingly, unstoppable and unpredictable requires more complex capabilities. Way of thinking in the 21^st century emphasis on creativity, critical thinking, problem solving, decision making and learning. Therefore, to develop the skills of problem solving becomes very necessary.

Problem solving is part of the thought process that includes the most complex of all intelligence functions that require modulation and control over basic skills (Goldstein & Levin: 1987). Thus, it can be said that problem solving is included in high order thinking skills. Other cognitive skills such as creative thinking, critical, analytical, and evaluative certainly be increased if the developing problem solving skills.

Concepts in mathematics essentially built on undefined terms, definitions, axioms (postulates), theorem, lemma, colloraly, and conjecture are arranged in a hierarchical and systematic. Therefore, the learning of mathematics should focus on systems, structures, concepts, principles and tight linkage between other elements. However, although the structure of mathematics can be said to be very rigid, learning can take place in a dynamic where the teacher / lecturer explore higher order thinking skills of students by providing challenging problems. A question is a problem only if the question shows a challenge that cannot be solved by routine procedures which had already known / memorized.

B.       Discussion

1.      Problem solving in Mathematics

Problem solving as a context of doing mathematics is divided into 4 sub-categories, namely: (a) problem solving used as a justification for teaching mathematics; (b) problem solving are used to motivate students; (c) problem solving is used as a recreation; and (d) as a problem solving exercise. When used in the context of problem solving math, the emphasis is on finding an interesting task or problem and relating that can help explain a concept or mathematical procedures.

According to Polya (1988: 5-6), there are four phase to solve a problem. First, we have to understand the problem; wehave to see clearly what is required. Second, we have tosee how the various items are connected, how the unknownis linked to the data, in order to obtain the ideaof the solution, to make a plan. Third, we carry out our plan. Fourth, we look back at the completed solution, we review and discuss it.

2.      Definition of Metacognition Strategy

The term metacognition was introduced by the 1979 Falvell Metacognition is usually defined simply as "thinking about thinking". According to Flavell (1979, 1987), metacognition consists of both metacognitive knowledge and metacognitive or regulation. Metacognitive knowledge refers to acquired knowledge about cognitive processes, knowledge that can be used to control cognitive processes. Flavell further divedes metacognitive knowledge into three categories: knowledge of person variables, task variables and strategy variables (Livingston, 1997: 1).

Schoenfeld, AH (1992: 38-39) defines metacognition which includes several functional categories that can be explored: (a) individual’s declarative knowledge about their cognitive process; (b) self-regulatory procedures, including monitoring and on-line decision making; (c) belief and affects, and their effects in performance.

The difference between cognition and metacognition proposed by Desoete (2001: 3) as in the picture below:

According to NCREL “Metacognition consist of three basic elements: (1) Developing a plan of action (2) Maintaining (monitoring the plan (3) Evaluating the plan.

1.             Before-when you are developing the plan of action, ask yourself:

a.              What in my prior knowledge will help me with this particular task?

b.             In what direction do I want my thinking to take me?

c.              What should I do first?

d.             Why am I reading this selection?

e.              How much time do I have to complete the task?

2.             During – When you are maintaining/monitoring the plan of action, ask

3.             yourself:

a.              How am I doing?

b.             Am I on the right track?

c.              How should I proceed?

d.             What information is important to remember?

e.              Should I move in a different direction?

f.              Should adjust the pace depending on the difficulty?

g.             What do I need to do if I do not understand?  

4.             After –in When you are evaluating the plan of action ask yourself:

a.              How well did I do?

b.             Did my particular course of thinking produce more or less than I had expected?

c.              What  could I have done differently?

d.             How might I apply this line of thinking to other problems?

e.              Do I need to go back through the task to fill in any “blanks” in my understanding?

Based on the opinions above, we can be concluded that metacognition skills are person's thinking skills to realize their own thinking processes related to the skills of planning, monitoring and evaluation in solving the problem. Activity planning skills are beginning to think about how, when and why to act in order to achieve the main objective problems. Skills monitoring is monitoring activities of the cognitive strategies that he used for solving the problem, to recognize the problem and modify the plan. And, skills evaluation is defined as a person looking back at the strategy that has been used and whether the strategy directs the desired results or not.

C.                Conclusion

There are four steps in solving a problem: understanding the problem, devising a plan, carrying out the plan and looking back. These four skills can be developed through metacognition strategies, because metacognition strategies are intimately associated with the ability to understand cognition. This strategy can make students be aware of their own thinking processes related to the skills of planning, monitoring and evaluation in solving the problem.

D.                References

Desoete, A. 2001.Off-line metacognition in children with mathematics learning disabilities.Disertation.FaculteitPsychologie en PedagogischeWetenschappen, Universiteit Gent

Goldstein F. C., & Levin H. S. (1987).Disorders of reasoning and problem-solving ability.In M. Meier, A. Benton, & L. Diller (Eds.), Neuropsychological rehabilitation. London: Taylor & Francis Group.

Livingston, J. A., 1997. Metacognition: An Overview.  Tersedia di: http://gse.buffalo.edu/fas/shuell/cep564/metacog.htm

McIntosh, R. &Jarret, D. 2000. Teaching mathematical problem solving: Implementing the vision.  A Literature Review.Mathematics and Science Education Center.

NCREL.Metacognition.Tersedia di: http://www.ncrel.org/sdrs/areas/issues/students/atrisk/at71k5.htm

Polya. 1988. How To Solve It: A New Aspect of Mathematical Method. Firs Princeton Science Library Edition.

Pepkin K.L. 2004.Creative Problem Solving In Math.Tersedia di: http://www.uh.edu/hti/cu/2004/v02/04.htm

Schoenfeld, A. H., 1992. Learning To Think Mathematically: Problem solving, metacognition, and sense-making mathematics.In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370).Neaw York: MacMillan.