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# Toh, Tin Lam

- PublicationOpen AccessWhat 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.
320 182 - PublicationMetadata onlyMathematics education for excellence(2021)This chapter discusses how Singapore strives for excellence in mathematics education in various ways. The chapter begins with the importance that Singapore has placed in identifying and developing its mathematically talented students for the prestigious mathematics competitions. Simultaneously, local mathematics community attempt to popularise mathematics competition among more interested student population and even attempt to align mathematics competition with the school curriculum, so as to benefit more student population in a variety of ways. The chapter continues to discuss the notion of mathematics competitive activities to include mathematics research and real-world problem-solving in order to identify and nurture a much wider group of mathematics talents among the Singapore students. At the systemic level, various attempts to develop and stretch our talents are emplaced, such as the Gifted Education Programme and the Integrated Programme. Within the curriculum structure, much has been done to provide differentiated instructions for students from primary to preuniversity education. This will culminate in the imminent subject-based banding, which will be implemented in full scale in the near future.
28 - PublicationOpen AccessAn experienced and competent teacher's instructional practice for normal technical students: A case study(2021)This paper presents a case study of an experienced and competent mathematics teacher’s classroom instructional practice in a Normal Technical Mathematics course. The topic that was observed was Volume and Surface Area of a Pyramid, a subtopic within the mensuration topic in Secondary Two syllabus. The teacher used a video clip on the Egyptian Pyramids to integrate students’ prior knowledge on pyramids, which raised their attention on the topic. This was followed by engaging the students in hands-on activity to understand the formulae.
55 96 - PublicationOpen AccessA framework to examine the mathematics in lessons of competent mathematics teachers in Singapore(2017-07)
; ;Wong, Lai FongThis paper outlines an analytical framework that was developed, to examine the mathematics in mathematics lessons of competent teachers in Singapore secondary schools. The framework is guided by Schoenfeld's Teaching for Robust Understanding (TR U) framework and also the field notes of the project - A study of the enacted school mathematics curriculum which is presently underway in Singapore. The framework was trialled and the indicators were suitable but may not be comprehensive. Therefore more trials and also more codes on how the teacher aided students in developing mathematical knowledge and student engagement with mathematical ideas are needed. In addition student perspectives of the lesson are also necessary to make any valid claims related to the quality of the lessons. - PublicationUnknownA 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.
- PublicationUnknownMathematical problem solving for integrated programme students(2006-05)
; ;Quek, Khiok Seng; ;Lee, Tuo Yeong ;Lim-Teo, Suat Khoh; Ho, Foo Him - PublicationUnknownMathematical 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. - PublicationRestrictedEnhancing the pedagogy of mathematics teachers to facilitate the development of 21st century competencies in their classrooms (EPMT-21st CC)(Office of Education Research, National Institute of Education, Singapore, 2023)
; ; The results of both PISA (2009, 2012) and TIMSS (2011, 2007) for Singapore show us that majority of our students are very good in applying their knowledge in routine situations and this is definitely a consequence of what teachers do and use during their mathematics lessons. For our students to scale greater heights we need our teachers to nurture metacognitive learners who are active and confident in constructing mathematical knowledge.

A significant finding from the CORE 2 research at NIE led by Professor David Hogan is that amongst the secondary three and primary five mathematics lessons that were studied teachers appeared to engage students in doing performative tasks (77.3% for secondary 3 and 63.7% for primary 5) more often than knowledge building tasks (22.7% for secondary 3 and 36.3 % for primary 5) (Hogan et al, 2013). A performative task mainly entails the use of lower order thinking skills such as recall, comprehension and application of knowledge while a knowledge building task calls for higher order thinking skills such as synthesis, evaluation and creation of knowledge.

Hattie (2009), drawing on 50,000 research articles and related achievement of 240 million students, notes that the greatest source of variance in the learning equation comes from teachers. Therefore as we are desirous of improving student learning, in our mathematics classrooms, it is critical that we engage our teachers in specific and targeted professional development.

21 9 - PublicationOpen AccessFine-tuning in a design experiment(2013)
;Ho, Foo Him; Quek, Tay, Toh, Leong, and Dindyal (2011) proposed that a design-theory-practice troika should always be considered for a designed package to be acceptable to the research users who, in this case, are teachers and schools. This paper describes the fine-tuning to the MProSE problem-solving design made by the teachers in the school after first round of teaching. This process involved teacher input from their experience, and detailed time-consuming discussions and learning between the researcher-designers and the teacher-implementers.112 154