Pre-university students’ errors in integration of rational functions and implications for classroom teaching
This paper reports on students’ errors in performing integration of rational functions, a topic of calculus in the pre-university mathematics classrooms. Generally the errors could be classified as those due to the students’ weak algebraic concepts and their lack of understanding of the concept of integration. With the students’ inability to link integration to differentiation, these errors could not be detected or rectified. From a deeper perspective, these errors were due to a lack of deep mathematical thinking when the students learnt calculus. This paper also presents the implications of the findings of this study in relation to the classroom teaching of mathematics. It is hoped that the articulation of students’ errors and the implications could provide guidance for classroom teachers and prompt further research into students’ errors and misconceptions in calculus concepts.
On in-service mathematics teachers’ content knowledge on kinematics
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.
Teacher preparation for a problem solving curriculum
The role of the teacher is central to the success of any curriculum innovation. Thus, teachers’ professional development has become an increasingly important subject of discussion in recent education literature. In the design and implementation of the project reported here, teachers’ preparation for the problem-solving curriculum featured prominently. This paper discusses the challenges of selecting a suitable problem and ways of using it productively within a professional development programme that the authors carried out for the teachers involved in the project.
Positive social climate for enhancing students' math self-concept: some research findings
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.
What is spoken in a junior college mathematics lecture?
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.
School mathematics mastery test and preservice mathematics teachers' mathematics content knowledge
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.
Assessment in a problem solving curriculum
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.
Reconceptualising problem solving in the school curriculum
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.
On in-service mathematics teachers’ content knowledge of calculus and related concepts
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.