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# 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.

#### MAthematics is Great: I Can And Like (MAGICAL)

2020, Toh, Tin Lam

This project is a cross-discipline mix-method study which aims to explore and develop a package of alternative approach to teach Lower Secondary Normal (Technical) mathematics using story-telling, comics, and other graphic stimulus in context. It will study the effect of this alternative approach on students' mathematical self-concept, motivation to learn mathematics and achievement in mathematics. As an outcome of this project, a package (MAGICAL) will be developed to teach three main topics in N(T) mathematics. The package will be presented in (i) print form; (ii) web-based material; and (iii) mobile apps for use by schools. For data collection, both qualitative and quantitative methods will be used. A series of professional development will be provided for participating teachers as an essential by product

#### Mathematical problem solving for everyone: Infusion and diffusion (MInD)

2020, Toh, Tin Lam, Tay, Eng Guan, Leong, Yew Hoong, Quek, Khiok Seng, Toh, Pee Choon, Dindyal, Jaguthsing, Ho, Foo Him

This research project is an attempt to realise the ideals of mathematical problem solving, which is at the heart of the Singapore mathematics curriculum in the daily practices of mainstream mathematics classrooms. This work builds on the foundation of M-ProSE (OER 32/08 TTL) to diffuse the findings to the mainstream school curriculum. Our work involves three steps: (1) initialisation of problem solving as an essential part of the mathematics curriculum in a school at the foundational year; (2) infusion of problem solving as an embedded regular curricular and pedagogical practice across all year levels in the school, and (3) diffusion of this innovation from this school to the full range of schools in Singapore. In each of the above steps, we take a complex systems approach and include curriculum, instructional practices, assessment and teacher professional development in our overall design research process. Our current project builds upon the initial foundation of MProSE to scale out (infuse) and scale up (diffuse) the innovation to mainstream schools in Singapore, hence the project is named MInD. With the experience and data collected from MProSE research school, the design needs to be re-adjusted in order for problem solving to be diffused throughout the mainstream schools. The importance and relevance of this research project to schools is readily observed by the schools' responses: To the researchers' pleasant surprise, four mainstream schools readily expressed their commitment to participate in this research as the school leaders see the relevance of this project to their school curriculum. Further, the Principal of MProSE research school expressed his interest to get his school involved for the infusion phase(step (2)) of the research. The research team of MInD consists of the original researchers from MProSE and two more new team members. The entire team consists of expertise from different fields: mathematicians, mathematics educator, educational psychologist, curriculum specialist, senior teacher, a school principal (who is also a mathematician), an expert of change management and leadership studies, a senior MOE curriculum specialist.

#### Enhancing the pedagogy of mathematics teachers to facilitate the development of 21st century competencies in their classrooms (EPMT-21st CC)

2023, Kaur, Berinderjeet, Toh, Tin Lam, Bhardwaj, Divya

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.

#### Scaling UP the education research: MAGICAL (SUPER-MAGICAL): Use of comics in teaching mathematics

2024, Toh, Tin Lam

This project is a continuation from the earlier research project MAGICAL on using comics for mathematics instruction for the low attaining students.