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# Toh, Tin Lam

#### A framework for designing comics-based mathematics instructional materials

2022, Cher, Zheng Jie, Toh, Tin Lam

Purpose and Research Question - In this paper we propose a PATH framework for designing comicsbased
instructional material for classroom lesson enactment through conducting a literature review in mathematics education.

Methodology – Systematic review was made with a focus on the potential benefits of comics for education, in particular, on developing students’ motivation for learning and facilitating their knowledge retention.

Findings – We further demonstrate with an exemplar the use of the framework in designing one set of comics-based instructional material for lower secondary mathematics lessons on mensuration.

Significance and Contribution in Line with Philosophy of LSM Journal – An exemplar of a comics-based instructional material designed according to the PATH-CoHANa framework.

#### Pre-university students’ errors in integration of rational functions and implications for classroom teaching

2008, Ng, Kin Yee, Toh, Tin Lam

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.

#### Calculus for teaching and learning (CASTLE): An exploratory study

2022, Toh, Tin Lam, Toh, Pee Choon, Teo, Kok Ming, Zhu, Ying, Tan, Victor, Tang, Wee Kee

#### From the past to the future of technology in mathematics education in Singapore

2023, Toh, Tin Lam

This paper discusses the changes in classroom instructions due to technology over the years in mathematics education, and how these changes have impacted mathematics learning and teaching. The impact on learning can be seen over a few phases in Singapore: The use of scientific and graphing calculators has allowed the focus on the developing of higher order thinking skills, while at the same time de-emphasizing the routine computation. With the introduction of various computer softwares such as spreadsheets, mathematics teaching and learning has moved towards the next level of emphasis on coding and computational thinking. Technology can and has been harnassed by teachers to enhance student learning. These will be discussed in details in the talk, with particular reference to the Singapore education context.

#### A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools

2018, Kaur, Berinderjeet, Tay, Eng Guan, Toh, Tin Lam, Leong, Yew Hoong, Lee, Ngan Hoe

#### The Mathematician Educator special issue: Mathematics instruction for the future

2023, Toh, Pee Choon, Toh, Tin Lam

#### Mathematical Problem Solving for Everyone (MProSE)

2020, Toh, Tin Lam, Quek, Khiok Seng, Tay, Eng Guan, Leong, Yew Hoong, Dindyal, Jaguthsing

This 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.

#### Fine-tuning in a design experiment

2013, Ho, Foo Him, Toh, Pee Choon, Toh, Tin Lam

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.

#### The roles of mathematics competition in Singapore mathematics education

2015, Toh, Tin Lam

The roles of mathematics competitions in Singapore mathematics education have expanded beyond helping the country in identifying and supporting of mathematical talents. In this note, test items from the past years mathematics competition were examined. It was proposed that mathematics competitions can potentially play three important roles in Singapore mathematics education: to (1) stretch students to explore mathematics beyond the usual school curriculum; (2) set direction in higher order thinking skills could be infused into the usual classroom teaching; and (3) preserve the “elementary mathematics” within the constantly evolving national mathematics curriculum. This note further presents some episodes of students’ responses to some competition questions from previous years. It was found that some students developed incomplete or incorrect mathematical reasoning but gave the correct answers to these questions, which is contradictory to the intention of setters of the questions. Readers are cautioned to the existence of a mismatch between the intentions of these competition questions and the actual format and structure of the competitions.

#### Diffusion of the mathematics practical paradigm in the teaching of problem solving: Theory and praxis

2012, Quek, Khiok Seng, Leong, Yew Hoong, Tay, Eng Guan, Toh, Tin Lam, Dindyal, Jaguthsing

In 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.