- An exploratory study of secondary two students' mathematics anxiety and mathematical problem solving

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# An exploratory study of secondary two students' mathematics anxiety and mathematical problem solving

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Type

Thesis

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.

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.

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.

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.

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.

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.

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.

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.

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.

Date Issued

2004

Call Number

QA14.S55 Yeo

Date Submitted

2004