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# Toh, Tin Lam

- PublicationOpen AccessMathematical Problem Solving for Everyone (MProSE)(Office of Education Research, National Institute of Education, Singapore, 2020)
; ;Quek, Khiok Seng; ; 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.141 28 - PublicationOpen AccessLearning from the implementers in a design experiment(2013)
; ;Dindyal, JaguthsingIn a design experiment, the feedback from the teacher-implementer is crucial to the success of the innovation simply because the teacher is finally the one that brings the innovation to life in front of the students. We describe in this paper the feedback made by the teacher-implementer after teaching one cycle of the problem solving module in a mainstream school, and the modifications the researchers and the teacher-implementer have made in our design of the module to fit into the requirement of the school.123 94 - PublicationOpen AccessFallacies about the derivative of the trigonometric sine function(2021)
; ; Tong, Cherng LuenIn this paper, several fallacies about the extension of the formula \frac{d}{dx} (\sin x) = \cos x to the erroneous formula \frac{d}{dx} (\sin x^\circ) = \cos x^\circ are discussed. In a Commognitive Theory Framework, misconceptions by ‘newcomers’ can be traced to the use of the word “unit”.89 173 - PublicationOpen AccessInfusing problem solving into mathematics content course for pre-service secondary school mathematics teachers(2013)
; ;Quek, Khiok Seng; ; ; ;Ho, Foo HimDindyal, JaguthsingThis paper presents a re-design of an undergraduate mathematics content course on Introductory Differential Equations for pre-service secondary school mathematics teachers. Based on the science practical paradigm, mathematics practical lessons emphasizing problem-solving processes via the undergraduate content knowledge were embedded within the curriculum delivered through the traditional lecture-tutorial system. The pre-service teachers' performance in six mathematics practical lessons and the mathematics practical test was examined. They were able to respond to the requirements of the mathematics practical to go through the entire process of problem solving and to carry out "Look Back" at their solution: checking the correctness of their solution, offering alternative solutions, and expanding on the given problem. The use of Mathematics Practical has altered the pre-service teachers’ approach in tackling mathematics problems in a positive direction.219 495 - PublicationOpen AccessMathematics education in Singapore(2015)
; ;Wong, Khoon Yoong; ; ; ;Ng, Swee Fong ;Dindyal, Jaguthsing ;Yen, Yeen Peng ;Loh, Mei Yoke ;Tan, June Hwee ChiatTan, Lay ChinMathematics education in Singapore is a shared responsibility of the Ministry of Education (MOE) and the National Institute of Education (NIE) . The MOE overseas the intended, implemented and attained curriculum in all schools while the NIE is involved in teacher preparation and development and also research in mathematics education. Therefore this report has two sections respectively , the first describes the education system and school mathematics curricula while the second briefly provides relevant information on teacher preparation and development and mathematics education research in Singapore.508 586 - PublicationOpen AccessReconceptualising problem solving in the school curriculum(2009-07)
;Dindyal, Jaguthsing; ;Quek, Khiok Seng; 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.95 136 - PublicationOpen AccessMathematical problem solving for everyone: Infusion and diffusion (MinD)(2016)
; ; ; ;Quek, Khiok Seng; ;Dindyal, Jaguthsing ;Ho, Foo Him ;Hang, Kim HooYen, Yeen Peng239 199 - PublicationOpen AccessDiffusion of the mathematics practical paradigm in the teaching of problem solving: Theory and praxis(2012)
;Quek, Khiok Seng; ; ; Dindyal, JaguthsingIn this paper, we discuss the diffusion (of an innovation) and relate it to our attempt to spread our initial design of a mathematics practical paradigm in the teaching of problem solving.251 176 - PublicationOpen AccessTeaching undergraduate mathematics: A problem solving course for first year(2022)
; ; ; ; ; ;Quek, Khiok SengIn this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.50 81 - 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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