Mathematical Problems In Mathematics: Mathematical Problem-Solving Performance

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Mathematical Problem-Solving Performance
The ability to solve mathematics problems develops slowly over a very long period of time because it requires much more than merely the direct application of some mathematical content knowledge. Problem-solving performance indicates the factors which are knowledge acquisition and utilization, control, beliefs system, affects, and socio-cultural contexts (Lester, F., 1987). Knowledge Acquisition and Utilization. It is safe to say that the overwhelming majority of research in mathematics education has been devoted to the study of how mathematical knowledge is acquired and utilized. By "knowledge" I mean both informal and intuitive knowledge as well as formal knowledge. Included in this category are a
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This domain includes individual feelings, attitudes and emotions. Mathematics education research in this area often has been limited to examinations of the correlation between attitudes and performance in mathematics. Not surprisingly, attitudes that have been shown to be related to performance include: motivation, interest, confidence, perseverance, and willingness to take risks, tolerance of ambiguity, and resistance to premature closure. To distinguish between attitudes and emotions I choose to regard attitudes as traits, albeit perhaps transient ones, of the individual, whereas emotions are situation-specific states. An individual may have developed a particular attitude toward some aspect of mathematics which affects her or his performance (e.g., a student may greatly dislike problems involving percents). At the same time, a particular mathematics task may give rise to an unanticipated emotion (e.g., frustration may set in when a student finds that he or she has made little progress toward solving a problem after working diligently on it for a considerable amount of time). The point is that an individual's performance on a mathematics task is very much influenced by a host of affective factors, at times to the point of dominating the individual's thinking and actions (Lester, F.,…show more content…
In recent years, the point has been raised within the cognitive psychology community that human intellectual behaviour must be studied in the context in which it takes place. That is to say, since human beings are immersed in a reality that both affects and is affected by human behaviour, it is essential to consider the ways in which sociocultural factors influence cognition. In particular, the development, understanding, and use of mathematical ideas and techniques grow out of social and cultural situations. Some of the researchers argues that children bring to school their own mathematics which has developed within their own socio-cultural environment. This mathematics, which he calls "ethnomathematics," provides the individual with a wealth of intuitions and informal procedures for dealing with mathematical phenomena. Furthermore, one need not look outside the school for evidence of social and cultural conditions that influence mathematical behavior. The interactions that students have among themselves and with their teachers, as well as the values and expectations that are nurtured in school shape not only what mathematics is learned, but also how it is learned and how it is perceived. The point then is that the wealth of socio-cultural conditions that make up an individual's reality plays a prominent role in determining the individual's potential for success in doing mathematics both in and out of school. These five categories overlap (e.g., it

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