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On in-service mathematics teachers’ content knowledge of calculus and related concepts

2009, Toh, Tin Lam

Studies have shown that teachers do not have good understanding of calculus concepts. This paper reports a study of teachers' content knowledge of calculus, on 27 in-service mathematics teachers. A questionnaire dealing with the concept images and concept definitions of various calculus concepts was administered to the group of participating teachers. The responses to the questionnaire showed that most of the participants had not built up sufficiently rich and comprehensive concept images related to the various differential calculus concepts, and they generally turned to procedures in handling calculus tasks. This study sheds light on the type of calculus content needed by school teachers.

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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.

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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

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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.

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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.

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Using comics to contextualise the teaching of percentages: An adaptation of a comics-based teaching package for primary school mathematics classrooms

2022, Toh, Tin Lam, Cheng, Lu Pien

In this article, an adaptation of a secondary school mathematics comics-based instructional package for primary school mathematics classroom, and the teachers' and students' perceptions about the use of comics in the classroom are discussed. Further suggestions by the teachers on fine-tuning the package are also discussed.

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

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

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.

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School mathematics mastery test and preservice mathematics teachers' mathematics content knowledge

2007, Toh, Tin Lam, Chua, Boon Liang, Yap, Sook Fwe

As part of the effort to equip preservice mathematics teachers with the necessary secondary school mathematics content that they would need to deliver mathematics lessons, a School Mathematics Mastery Test was implemented for all preservice mathematics teachers in the Postgraduate Diploma in Education programme in the National Institute of Education. This paper describes the rationale and the different phases in the implementation of this test,sample test questions. and the performance of the preservice teachers in the different batches since its implementation. The implication of the implementation of this mathematics content test and the future direction of study on preservice teachers' mathematics content knowledge are also discussed.

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A framework to examine the mathematics in lessons of competent mathematics teachers in Singapore

2017-07, Kaur, Berinderjeet, Wong, Lai Fong, Toh, Tin Lam

This 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.

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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