Yeo Kai Kow, Joseph
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- PublicationOpen Access
- PublicationRestrictedAn exploratory study of secondary two students' mathematics anxiety and mathematical problem solvingThis 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.
- PublicationOpen AccessDevelopment of mathematics pedagogical content knowledge in student teachers(2007)
;Cheang, Wai Kwong ; ;Chan, Eric Chun MingLim-Teo, Suat KhohMathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the development of MPCK in their pre-service teachers. As part of a research study on the development of MPCK in primary school beginning teachers, a 16-item instrument was developed to measure some aspects of the MPCK for teaching mathematics at primary level. The instrument was administered to the 2005 intake of the Postgraduate Diploma in Education student teachers at the National Institute of Education, Singapore just at the beginning of their programme. As they complete their methodology course in February 2006,the instrument was administered again. This paper discusses the findings concerning their performance in these two tests, with reference to the overall performance as well as topic specific and MPCK construct-specific performance. The findings indicate that student teachers at the beginning of their programmes are generally quite weak in their mathematics pedagogical content knowledge, as might be expected. There was significant improvement in all aspects of their MPCK on completion of their mathematics pedagogy course. 1233 1489
- PublicationOpen AccessAnxiety and performance on mathematical problem solving of secondary two students in Singapore(2005)Researchers have highlighted the significance of affective factors and their influences on problem-solving performance. Moreover, it was been reported that research on the cognitive processes in mathematical problem solving has been over-represented resulting in a neglect of non-cognitive factors such as emotions and anxiety. Therefore, the purpose of this study was to identify interrelationships among mathematics anxiety, test anxiety and problem-solving performance. A total of 621 Secondary 2 students from ten secondary schools in Singapore participated in the study. The data showed a positive relationship between mathematics anxiety and test anxiety. In addition, mathematics anxiety and performance on a nonroutine mathematical problem solving test showed a marginal linear relationship whereas test anxiety had almost no relationship with the performance on the nonroutine mathematical problem solving test.
- PublicationOpen AccessDo high ability students have mathematics anxiety?This exploratory study investigates the level of mathematics anxiety among 116 high ability Secondary Two students. These students were from the top 10% of the Secondary Two students in Singapore. Mathematics Anxiety was measured using the Fennema-Sherman Mathematics Anxiety Scale (MAS) (Fennema & Sherman, 1978) which consisted of twelve items which were divided into four categories. The categories were Thinking about Maths, Taking Maths Test, Learning Maths, and Solving Maths Problems. Descriptive statistics on the four categories were reported. The results suggest that Mathematics anxiety did exist among this group of 116 high ability students in two secondary schools. The results also showed that 57 girls in this study exhibited a higher level of Mathematics Anxiety than the 59 boys.
- PublicationUnknownLanguage matters in mathematics: Singaporean primary classrooms booklet 1
- PublicationUnknownExcel as a tool to enhance learning of probability(2003-11)
;Wong, Desmond Kin MunProbability is often an immensely challenging topic for students at the secondary level. The main difficulty for these students often lies in their inability to relate the theories learnt in classroom to their everyday lives. It is for this reason that lessons on the topic of Probability, especially those at the introductory level, rely heavily on hands-on activities. As empirical probabilities will only converge to the results predicted by theory, implementation of hands-on activities is, inherently, ridden with problems and difficulties. The problem is so acute that ‘mistake-prone’, ‘repetitive’ and ‘time consuming’ are but a few phrases which students have associated with traditional hands-on activities. This apparent lack of meaningful hands-on activities has motivated the authors to develop an IT-based discovery activity for the topic of Probability at the secondary level. Microsoft’s Excel has been embraced by the authors in automating the counting and calculations involved in obtaining experimental probabilities which would otherwise be cumbersome to obtain. To enhance the appeal of the discovery, the authors have used the game of Monopoly as the theme of analysis. This paper provides pertinent details of the discovery activity. It also describes the benefits and possible barriers to successful implementation of the activity.
- PublicationUnknownEffects of computer-assisted instruction on the learning of quadratic curves by secondary two students(1995)This study sets out to investigate the effects of two modes of instruction on the learning of quadratic curves among the secondary two students. The two modes of instruction are Computer-Assisted Instruction (CAI) and Traditional Approach (TA). These two approaches were examined in terms of their effects on achievement and attitudes, both toward the topic and the subject. A total of 192 students from the Express stream of an independent school in Singapore participated in the study. Six intact classes were chosen. Two high, two medium and two low ability classes were selected. One of each of the ability group was randomly assigned as experimental group (CAI) and the other as the control group (TA). All the six groups were taught by the same teacher and used the same amount of time to learn the same concepts, with similar assignments set as homework. The experiment was conducted over a period of two weeks with a total of 10 periods each for the six groups. The duration of each period was 35 minutes.
In the CAI group, a specially designed program on Quadratic Curves was written to meet the specific instructional objectives of the topics. Worksheets were constructed to supplement the software.
Before the main study was conducted, a Quadratic Curves Achievement Test (QC1) was administrated to the six groups of students at the end of April 1993. This was to determine if the students in each ability group differed in terms of their achievement in Mathematics. Similarly, the Attitudes toward Mathematics Questionnaire (MA1) was also given to the students to respond. This was to find out if the six groups differed in their attitudes toward Mathematics prior to the treatments.
At the end of the experiment, a 40-item objective type Quadratic Curves Achievement Test (QC) was given to six groups to confirm the effects of both modes of instruction. The Attitudes toward Mathematics Questionnaire (MA2) was also administered as a posttest to determine if there were any changes in attitudes toward Mathematics for the six groups. In addition, a specially designed Attitudes toward Quadratic Curves Questionnaire was also given to the six groups to determine if the different groups differed in their attitudes toward the content topic covered.
The independent t-test was used to compare the means of pretest, QC scores, QCA scores, mean gain scores of QC1 and QC2 for the different ability group and mean gain scores of MA1 and MA2. An one way analysis of variance was also used to compare the means of gain scores of QC1 and QC2 and gain scores of MA1 and MA2 for the three different groups.
The main findings of the study were:
The analysis of Quadratic Curves Achievement pretest indicated that there were no significant differences in mathematical background before treatment between students in the CAI and TA groups. Analysis of posttest data on achievement (QC) test showed that medium ability CAI group seemed to perform significantly better than the medium ability TA group. However, The high and low ability CAI group did not differed significantly from the high and low ability TA group. When the results were further examined between the three CAI groups, the mean gain scores indicated that the three CAI groups differed in their quadratic curves achievement after the treatment. Similarly, the three TA groups mean gain scores also showed that the three TA groups differed in their quadratic curves achievement.
In terms of attitudes toward Mathematics as measured by the MA, the analysis of the pretest indicated that there were no significant difference in their attitudes toward Mathematics before treatment between students in the CAI and TA groups. On the other hand, analysis of mean gain scores showed that the high, medium and low ability students in the CAI group had more positive attitudes than the high, medium and low ability TA groups after the treatment.
In the attitudes toward the particular topic, the three CAI groups had significantly more positive attitudes than the three TA groups.
- PublicationOpen AccessDilemmas in English teaching and learning: Singaporean primary classrooms booklet 2
- PublicationOpen Access