Toh Tin Lam

This paper reports a preliminary study on in-service Additional mathematics teachers' knowledge of kinematics concepts. A survey consisting of TRUE/FALSE questions was issued to the participating teachers. The questions were collations of the common misconceptions identified by some local Physics teachers among the local Physics students. The participants were asked to supply the answers to the questionnaire with their answers substantiated with reasons. In this paper, we discuss the results of the survey done on a group of twenty six in-service Additional mathematics teachers and classify the teachers' misconceptions of kinematics concepts. The finding of this initial survey could be useful to spur further research on Mathematics teachers' subject content knowledge on kinematics. Pragmatically it would also be useful for any agency which is planning for any content upgrading workshops for in-service teachers.

In this paper we elaborate on the ways for assessing problem solving that goes beyond the usual focus on the products of the problem solving process. We designed a ‘practical’ worksheet to guide the students through the problem solving process. The worksheet focuses the solver’s attention on the key stages in problem solving. To assess the students’ problem solving throughout the process, we developed a scoring rubric based on Polya’s model (1954) and Schoenfeld’s framework (1985). Student response to the practical worksheet is discussed.

It has been five years since the chapter on relative velocity was first introduced into the Singapore Additional Mathematics curriculum. This paper reports some general finding on the teaching of relative velocity in mathematics classrooms and the pupils' learning difficulties on relative velocity. Some implications to the teaching of this topic are also discussed.

In this paper, we discuss the development of a very specific problem solving curriculum in an independent school in Singapore as part of the first phase of our research project. We are using a design research methodology to fine-tune the problem solving curriculum in which we are introducing the mathematics practical, an idea borrowed from science education.

In Nov 2002, a research team in the National Institute of Education, NTU, launched a cross-discipline quasi-experimental study on “Positive Social Climate for Enhancing Students’ Math Self-concept”. Its main objective is to find the attributes (variables) in the social climate which are accountable for the increase of self-concept of Secondary Two students in the Math remedial classes in Singapore neighbourhood schools. Phase One of this study is Instrumentation: validating the scales used in the measurement of treatment effect. Phase Two is Intervention: the teachers’ / tutors’ interactions with students, the enhancement of students’ capabilities and confidence. These teachers / tutors will attend workshops conducted before the intervention in Phrase Two. The Pretest results will help identify students with high or low Math Self-concept. And the Posttest will help measure the effect of invention on these students’ Math Self-concept. Factors contributed to the significant changes will also be explored. H.W. Marsh’s Self-Description Questionnaire (SDQ-II, 1990) and B. Fraser’s “What is happening in this Class?” questionnaire were validated together with the Motivational Orientation scale and Intellectual Achievement Responsibility (IAR) questionnaire in Phase One. More than 700 Secondary Two students from four neighbourhood schools took part in the survey. Some preliminary findings in Phase One of this study will be presented in this paper. Gender and course differences in Math Self-concept and other variables will also be discussed.

As part of the effort to equip preservice mathematics teachers with the necessary secondary school mathematics content that they would need to deliver mathematics lessons, a School Mathematics Mastery Test was implemented for all preservice mathematics teachers in the Postgraduate Diploma in Education programme in the National Institute of Education. This paper describes the rationale and the different phases in the implementation of this test,sample test questions. and the performance of the preservice teachers in the different batches since its implementation. The implication of the implementation of this mathematics content test and the future direction of study on preservice teachers' mathematics content knowledge are also discussed.

In Nov 2002, a research team in the National Institute of Education, NTU, launched a cross-discipline quasi-experimental study on “Positive Social Climate for Enhancing Students’ Math Self-concept”. Its main objective was to find the attributes (variables) in the social climate which are accountable for the increase of self-concept of Secondary Two students in the Math remedial classes in Singapore neighbourhood schools. Phase I of this study ( in 2003) was Instrumentation: validating the scales used in the measurement of treatment effect. H.W. Marsh’s Self-Description Questionnaire (SDQ-II, 1990), and B. Fraser’s “What Is Happening In This Class?” questionnaire (WIHIC) were validated together with the Motivational Orientation scale and Intellectual Achievement Responsibility (IAR) questionnaire. More than 700 Secondary Two students from four neighbourhood schools took part in this validating exercise. Phase II was Intervention`(in 2004): the teachers’ interactions with students, the enhancement of students’ capabilities and confidence. A training workshop for teachers in the experimental groups was conducted before the intervention. Two schools had the experimental groups and another two neighbourhood schools’ samples were held as the control groups of this study. Based on the results in Phase I, only two instruments: SDQII and WIHIC were selected to measure the effect of intervention. The total sample in this phase was close to 1000 Sec 2 students.

Studies have shown that teachers do not have good understanding of calculus concepts. This paper reports a study of teachers' content knowledge of calculus, on 27 in-service mathematics teachers. A questionnaire dealing with the concept images and concept definitions of various calculus concepts was administered to the group of participating teachers. The responses to the questionnaire showed that most of the participants had not built up sufficiently rich and comprehensive concept images related to the various differential calculus concepts, and they generally turned to procedures in handling calculus tasks. This study sheds light on the type of calculus content needed by school teachers.

The dissertation English in Mathematics Discourse highlights for mathematics educators a body of practical knowledge about Junior College mathematics lecture discourse from the linguistic perspective. Although this dissertation is found among the collection of the dissertations done by postgraduate students of linguistic studies, it is of value to mathematics educators, particularly, mathematics teachers at the Junior College level.