Elements Of Metacognition

There are three correlated elements of metacognition in the field of learning and instruction, particularly solving mathematical problems.

1. Metacognitive knowledge: knowledge about one’s own cognition or thinking process (e.g. what does an individual know about his own thinking?) (Lester, 1994);

2. Metacognitive beliefs: beliefs and perceptions (e.g. what thoughts an individual carries during work in mathematics and how they help in solving mathematics problems?) (Schoenfeld, 1992).

3. Executive control: monitoring of activities during problem solving (e.g. How well does an individual reflect and uses his reflection in solving a problem? (Lester, 1994).

Executive control or self-regulation denotes the procedures in planning, monitoring and

For example one knows that short-term memory has its limits, is mortal but can be helpful in retaining information (De Corte et al, 1996).

Metacognitive knowledge means one’s own cognitive abilities; own cognitive strategies and knowledge about what to do under which conditions (Flavell, 1979). It also mathematically refers to the students beliefs about the nature of mathematics and processes and techniques they use in doing mathematics. Metacognitive knowledge obliges one to accurately and precisely define his thought or awareness. Effective use of this knowledge helps in problem solving and indecent perception about it requires a lot of hard work in problem solving. So one’s tactics and understandings to solve a problem is related to how precisely he judges his knowledge (Flavell and Wellman, 1977). Metacognitive knowledge and skills are very useful in Mathematics classrooms especially if the students are trained properly. Veenman, van Hout-Wolters, and Afflerbach (2006) concluded that students at early-school years have a very basic level of meta-cognition, but it becomes more sophisticated and academically oriented toward the end of primary

• The person category consists of one’s beliefs about oneself and others as intellectual beings. For example young children’s guess about their motor tasks performance is superior to on memory tasks Markman (1979).

• The task category includes knowledge about the difficulty and requirements of tasks, as well as knowledge about reasons and conditions, that make some tasks more difficult than others, for example good reader consider reading as a search for meaning while poor reader think it just a decoding activity (Canney and Winograd, 1979).

• The strategy category covers knowledge of overall and detailed cognitive strategies. The strategies a person has “at the ready” to implement in a flexible way to effectively complete a task; for example, knowing how to activate previous knowledge before reading a technical article, using a glossary to look up unfamiliar words, or knowing that sometimes one has to reread a paragraph several times before it makes