Publication: An exploratory study of secondary two students' mathematics anxiety and mathematical problem solving
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Date
2004
Authors
Yeo, Joseph Kai Kow
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Abstract
This exploratory study attempted to identify interrelationships between and among mathematics anxiety, test anxiety and problem-solving performance of Secondary 2 students in Singapore, categorise the mathematics-anxiety levels of these students into five levels, and explore their mathematical problem-solving performance in each level. The research also studied the heuristics and mathematical problem-solving framework used by the students in each of the mathematics-anxiety levels to solve problems. It delved further into characteristics of high mathematics-anxiety students and explored their reasons and feelings with regards to choices of problems as well as the difficulties they faced when solving problems.<br><br>A total of 621 Secondary 2 students from Singapore schools participated in Phase I of the study. Of these 621 students, 112 high mathematics-anxiety students were selected to participate in Phase II of the study. The sample was representative of the general student population in Singapore schools.<br><br>The design involved the development and use of paper and pencil instruments to collect data from the 621 Secondary 2 students during Phase I and from a sub-sample of 112 students during Phase II. During Phase I, the individual reflections of the 621 students on their problem-solving processes were recorded. Interviews were carried out with 56 students during Phase II of the study.<br><br>The results of the study showed that there was a positive correlation between test- and mathematics-anxiety scales while test anxiety did not associate with non-routine mathematical problem-solving test. The mathematics anxiety and Problems Test scores showed a marginal linear relationship. The varied performance of the Secondary 2 students on the five problems items also suggests that different mathematics-anxiety levels students may perform differently on different problems. It appears that the students at the low mathematics-anxiety level performed better on a non-routine mathematical problem-solving test than the high mathematics-anxiety students. Particular mathematical problem-solving heuristics were found to be used by students from mathematics-anxiety levels 1 to 5 to solve non-routine mathematical tasks. Although they were found to differ in the repertoire of heuristics, the difference was only marginal. The Secondary 2 students were found to rely on individual problem-solving frameworks to guide them when solving problems. The framework of the different mathematics-anxiety levels students was found to be similar, brief, and specific in nature.<br><br>The reasons given by high mathematics-anxiety students when choosing a problem to solve first were: "easiest problem", "familiar problem", "minimum working required", and "understand the problem". The main reasons for choosing to solve a particular problem last were: "difficulty of the problem", "multiple steps required", "more time required", and "lack of understanding". The feelings manifested by high mathematics-anxiety students when choosing a problem to solve first were more positive. However, with a problem that they chose to solve last, they felt anxious, stressed, tensed, irritated, frustrated, angry, fearful, and bewildered. It was found that the difficulties experienced by high mathematics-anxiety students when obtaining a solution were : (a) lack of comprehension of the problem posed, (b) lack of strategy knowledge, (c) inability to translate the problem into mathematical form, and (d) inability to use the correct mathematics.