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Toh, Tin Lam
- PublicationMetadata onlyMovie clips in the enactment of problem solving in the mathematics classroom within the framework of communication model
In this chapter, we propose that the teaching of mathematical problem solving can be understood through a classical model of communication. The use of movie clips for the teaching of mathematical problem solving can be seen as a communication process. The role of the movie clips, serving in addition to being a narrative hook, presents the mathematical problem in a way understandable and relatable to students through its appropriate contextualization of the mathematical problem. The chapter further discusses the characteristics of two movie clips that can be used for teaching mathematical problem solving.
18 - PublicationMetadata onlyProblem posing and problem solving in mathematics education: International research and practice trends(Springer, 2024)
; This book presents both theoretical and empirical contributions from a global perspective on problem solving and posing (PS/PP) and their application, in relation to the teaching and learning of mathematics in schools. The chapters are derived from selected presentations in the PS/PP Topical Study Group in ICME14. Although mathematical problem posing is a much younger field of inquiry in mathematics education, this topic has grown rapidly. The mathematics curriculum frameworks in many parts of the world have incorporated problem posing as an instructional focus, building on problem solving as its foundation. The juxtaposition of problem solving and problem posing in mathematics presented in this book addresses the needs of the mathematics education research and practice communities at the present day. In particular, this book aims to address the three key points: to present an overview of research and development regarding students’ mathematical problem solving and posing; to discuss new trends and developments in research and practice on these topics; and to provide insight into the future trends of mathematical problem solving and posing.
32 - PublicationOpen AccessMathematical Problem Solving for Everyone (MProSE)(Office of Education Research, National Institute of Education, Singapore, 2020)
; ; ; Dindyal, JaguthsingThis project involves the development and implementation of a problem solving package (M-ProSE) in the secondary school mathematics curriculum. It aims to induct secondary school mathematics students into the discipline of mathematics via a programme that turns well established theories of mathematical problem solving into praxis. In contrast with conventional training for mathematics competitions which tend to be restricted to a small number, M-ProSE is designed for all mathematics students Development of the project: In a pilot study conducted over two years in an Integrated Programme of a junior college, the research team observed that students were generally resistant to following the stages of Polya's model. In an attempt to 'make' the students follow the Polya model, especially when they were clearly struggling with the problem, we decided to construct a worksheet like that used in science practical lessons and told the students to treat the problem solving class as a mathematics 'practical' lesson. In this way, we hoped to achieve a paradigm shift in the way students looked at these 'difficult, unrelated' problems which had to be done in this 'special' class. Practical work to achieve the learning of the scientific processes has a long history of at least a hundred years. It is certainly conceivable that similar specialised lessons and materials for mathematics may be necessary to teach the mathematical processes, including and via problem solving. Implementation of the project: M-ProSE is an attempt to teach problem solving in 'practical' setup. Students will be taught Polya's model and problem solving in general in two or three dedicated lectures. The main mode of learning is then through a series of 'mathematics practical' lessons. Students work on usually one or at most two problems which have to be worked out on a special worksheet which requires the student to systematically and metacognitively go through the Polya model. M-ProSe is to be implemented as part of the mathematics curriculum and will be assessed. In order to implement M-ProSE, we need to build the teachers' capacity first to solve non-routine mathematics problems and thereafter to teach problem solving to their students. This involves the researchers conducting a series of workshops for the school teachers to widen their repertoire of problem solving resources. Next, we will develop with the teachers the instructional strategies to teach problem solving to their students, by means of a lesson study approach. Some of the researchers will initially teach some student classes as a model for the teachers before they take over entirely. To contribute to the understanding of teaching mathematical problem solving in general, the researchers will collect data over some cohorts which will enable them to further improve the package and make the package useful to other schools. The evidence collected will provide the basis for pedagogical practices in the mathematics classrooms.161 154 - PublicationOpen AccessA note on Kurzweil-Henstock's anticipating non-stochastic integralMotivated by the study of anticipating stochastic integrals using Kurzweil-Henstock approach, we use anticipating interval-point pairs (with the tag as the right-end point of the interval) in studying non-stochastic integral, which we call the Kurzweil-Henstock anticipating non-stochastic integral. We prove the integration-by-parts and integration-by-substitution results, the convergence theorems using our new setting. Using the convergence theorems, we show that the Kurzweil-Henstock's anticipating non-stochastic integral is equivalent to the Lebesgue integral.
20 322 - PublicationOpen AccessInfusing problem solving into mathematics content course for pre-service secondary school mathematics teachers(Association of Mathematics Educators, 2013)
; ; ; ; 237 601 - PublicationOpen AccessA survey on the teaching of relative velocity and pupils’ learning difficultiesIt 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.
149 426 - PublicationMetadata onlyThe evolution of mathematics education research in Singapore
Up until 1990, the Institute of Education in Singapore was primarily a teaching institute involved in training teachers for Singapore schools. Since the inception of the National Institute of Education (NIE) in 1990, as an institute of the Nanyang Technological University, the focus of the institute has been enlarged to include research in education. This chapter examines, through a documentary analysis, how a research culture specifically in mathematics education at the National Institute of Education was nurtured, developed and supported from 1990 onwards. Development of the culture for Mathematics Education Research (MER) has been in tandem with all other areas of research at the NIE. Both top-down and bottom-up approaches have been adopted to support research as part of an academic’s work at the institute. Policies related to recruitment and promotion of academics were developed to ensure that emphasis was on both teaching and research. Development of research, from individually led bite-sized grains to team-based project with coherent themes, was supported. The setting up of the Centre for Research in Pedagogy and Practice in 2004 and dedicated funding from the Ministry of Education Singapore for research of the Singapore education system heralded an era of MER that has made significant contributions both nationally and internationally. This chapter will also illuminate the four main areas of focus and sources on MER through examples of studies carried out in Singapore since 2000. In addition, it briefly outlines the contribution of MER in ASEAN countries.
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18 - PublicationMetadata onlyThe instructional core that drives the enactment of the school mathematics curriculum in Singapore secondary schools(Springer, 2021)
; ; ; Quek, Khiok Seng12 - PublicationMetadata onlySchool calculus curriculum and the Singapore mathematics curriculum frameworkIn this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students’ performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students’ procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.
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