Yeo, Joseph Kai Kow

Mathematics 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.

Assessment is an essential part of the teaching and learning process. Since assessment plays such a significant part in the educational process, it is imperative that we examine closely the individual questions that make up the assessment paper. This paper is based on a preliminary investigation into about 30 sets of secondary one semestral examination papers. In this paper only a sample of problematic short-ended and structured / long-answer questions have been highlighted and discussed. From this sample, it could be seen that short-ended and structured / long-answer questions are challenging and demanding to design. The questions were scrutinized based on the following criteria involved in the designing of test/examination questions: (1) Questions with incorrect Mathematical Concept, (2) Questions which test trivial facts, (3) Questions with ambiguous verbal communication, (4) Questions with inconsistent symbols and notations, (5) Questions with misleading diagrams, (5) Questions with impracticality of scenarios, and (6) Questions with imbalanced learning objectives.

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.

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.

"This one-year project was an investigation into the ongoing implementation of recent policy initiatives that influence pedagogies, curriculum innovation, and instructional practices in primary education in Singapore. Investigation covered P1 and P2 in all core subjects: English, Mother Tongue (Chinese, Malay, Tamil) and mathematics. It included investigation of local contextual conditions which impact the work of policy developers and implementers at all levels within the system: class, school, zone, national. Our goal was to assist in developing a more complete understanding of the specific, local challenges of policy implementation." -- p. 2.

Teachers tend to design worksheets to assist their students to develop their spatial skills. Many secondary schools students may not have sufficient concrete experiences to tackle abstract reasoning in geometrical concepts competently. In addition, students who are nonvisual and spatial learners may have difficulties in learning geometrical topics. The aim of this study was to use the software, ProDesktop, to facilitate the teaching and learning of Plan and Elevation Geometry in a computer laboratory. A total of forty students from the Express stream of a neighborhood school in Singapore was selected to participate in the study. The results suggested that the use of ProDesktop had enhanced the learning of Plan and Elevation geometry both in terms of interest and proficiency of the topic.