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Problem solving in the school curriculum from a design perspective

2010-07, Toh, Tin Lam, Leong, Yew Hoong, Dindyal, Jaguthsing, Quek, Khiok Seng

In this symposium, we discuss some preliminary data collected from our problem solving project which uses a design experiment approach. Our approach to problem solving in the school Curriculum is in tandem with what Schoenfeld (2007) claimed: “Crafting instruction that would make a wide range of problem-solving strategies accessible to students would be a very valuable contribution … This is an engineering task rather than a conceptual one” (p. 541). In the first paper, we look at how two teachers on this project taught problem solving. As good problems are key to the successful implementation of our project, in the second paper, we focus on some of the problems that were used in the project and discuss the views of the participating students on these problems. The third paper shows how an initially selected problem led to a substitute problem to meet our design criteria.

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Mathematical problem solving for everyone: A new beginning

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

Mathematical problem solving has been at the core of the Singapore mathematics curriculum framework since the 1990s. We report here the features of the Mathematical Problem Solving for Everyone (M-ProSE) project which was carried out in a Singapore school to realise the learning of mathematical problem solving and as described by Pólya and Schoenfeld. A mathematics problem solving package comprising “mathematics practical” lessons and assessment rubric was trialled in the school for Grade 8 in 2009. Responses from three students show mixed perceptions to the module, but an end-of-module assessment shows that the students were able to present their solutions along Pólya’s four stages. We also describe teacher preparation for teaching the module. After the trial period, the school adopted the module as part of the curriculum and it is now a compulsory course for all Grade 8 students in that school.

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Mathematical problem solving for everyone: Infusion and diffusion (MinD)

2016, Toh, Tin Lam, Tay, Eng Guan, Leong, Yew Hoong, Quek, Khiok Seng, Toh, Pee Choon, Dindyal, Jaguthsing, Ho, Foo Him, Hang, Kim Hoo, Yen, Yeen Peng

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Instructional coaching and learning of instructional practices: A study of the perceptions of coaches and teachers

2024, Leong Yew Hoong, Tay Eng Guan, Ho, Foo Him

As it has been established that quality instruction improves student learning (Barber & Mourshed, 2007; Darling-Hammond, 2000), efforts to improve student learning have largely focused on improving instructional practices (Gallucci, Van Lare, Yoon, & Boatright, 2010). It was widely agreed that the most effective effort is one that is collaborative, sustained, embedded in real-life learning contexts, and supported by specialists and peers (P Cordingley, Bell, Rundell, & Evans, 2003; Elmore, 2002). In addition, it is one that encourages observation and engagement in professional dialogue and reflection (Darling-Hammond & Richardson, 2009; Supovitz, 2001). Therefore, there has been a growing interest in coaching, “a form of inquiry-based learning characterised by collaboration between individual, or groups of, teachers and more accomplished peers” (Poglinco et al., 2003, p. 1), which “involves professional, ongoing classroom modelling, supportive critiques of practice, and specific observations” (Poglinco et al., 2003, p.1).

Out of the several approaches to coaching—peer coaching, cognitive coaching, instructional coaching—instructional coaching, in particular, is invaluable in assisting teachers translate best practices into improved classroom instruction and improving student learning (Knight, 2006; Reddell, 2004). Knight (2008) defined instructional coaching as more of a partnership between coaches and teachers whereby they are committed to (a) equality in the relationship, (b) teacher choice in the content and process in learning, (c) empowerment and respect for varying perspectives, (d) authentic dialogue (e) reflection (f) praxis, that is, applying their learning to their real-life practice as they are learning (g) reciprocity of learning between coaches and teachers. This study adopts Knight’s comprehensive definition emphasizing collaboration, as the researchers investigate the perception, reception and impact of instructional coaching on teachers in the Singapore mathematics classroom.

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Effects of geometer's sketchpad on spatial ability and achievement in transformation geometry among secondary two students in Singapore

2003, Leong, Yew Hoong, Lim-Teo, Suat Khoh

Does the use of a common construction programme - the Geometer's Sketchpad - in different pedagogical settings have an impact spatial ability and achievement scores of students within concepts in transformation geometry? The subjects were 13 to 14 year-old students from a school with above-average ranking among Singapore schools. The software was employed differently in the three classes: In Class A, the approach adopted by the teacher was that of guided-inquiry where students explored concepts and made conjectures with extensive hands-on experience with the software; in Class C, the teacher's predominant role was that of an expositor and the students' role that of knowledge-recipients, and the software was used as a teacher's tool to demonstrate dynamicallv the properties of transformations; in Class B , the 'in between' class, the pedagogy of guided-inquiry in whole-class discourses was adopted but with the teacher manipulating objects on the projected screen as directed by the students. The results showed that spatial ability improved for all three classes with no significant difference between the classes although classes A and B performed significantly better than Class C in the transformation geometry achievement test.

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NA: Improvement of Learning, Innovations in Teaching (NA:ILIT)

2024, Leong Yew Hoong, Tay Eng Guan, Quek, Khiok Seng, Yap, Sook Fwe, Toh, Karen Wei Yeng

Although there is an acknowledged need to attend to the learning needs of low achievers in mathematics, there is relatively scant research in this area locally. This proposed project aims to contribute to this sub-field within mathematics education. In particular, this study will focus on helping Normal Academic (NA) students make improvements in their learning of Mathematics.

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Singapore mathematics teachers' design of instructional materials

2021, Leong, Yew Hoong, Cheng, Lu Pien

This paper focuses on one major component of the project which examined the enactment of the Singapore mathematics curriculum in the Secondary Schools: the design and use of instructional materials by the teachers. We define instructional materials to be classroom-ready materials that teachers incorporate into their lessons for students’ direct access for their learning. We make a distinction between instructional materials (IM) and reference materials (RM). The latter are resources (including textbooks) which teachers refer to while planning for lessons; the former are the actual materials that are brought into their classrooms for use in their mathematics instruction. For most teachers which were the subjects of our study, their instructional materials differ substantially from their reference materials – it is this ‘transformational space’ that is an area of interest to us. For the rest of this paper, we will briefly describe a few such transformational moves as illustrated by some teachers in our study and their underlying intentions.

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An insight into the ‘balancing act’ of teaching

2006, Leong, Yew Hoong, Chick, Helen L.

This paper examines some of the complexities involved in the actual work of classroom instruction by examining interactions among the goals of teaching. The research is part of a case study of teaching a Year 7 Singapore class comprising students of average mathematical ability. Among the complexities of teaching analysed here are the problems associated with trying to fulfil the multiple goals of teaching and the conflict experienced by the teacher as he attempts to carry out these goals. This provides insight into how a teacher performs the act of balancing different goals while carrying out instruction in class. The implications of these insights into teaching practice for the wider education community are also discussed.

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Four solutions of a geometry problem

2020, Toh, Pee Choon, Ho, Weng Kin, Leong, Yew Hoong, Tay, Eng Guan, Tong, Cherng Luen

This article focuses on a challenging geometry problem that was originally posed to primary school students. Four solution approaches, ranging from elementary to advanced, are discussed. Reflections on these approaches and the problem solving processes are also shared.

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Passing a proof message: Student-teacher communication through a commognitive lens

2019, Ho, Weng Kin, Lim, Seo Hong, Tay, Eng Guan, Leong, Yew Hoong, Teo, Kok Ming

This study employs Sfard’s (2008) socio-cultural theory of Commognition to analyse student teachers’ thinking and communicating practices. Specifically, we investigate the effectiveness of the student teachers’ communication of a particular mathematical proof with reference of the four features of the commognitive framework, i.e., word use, visual mediators, narrative and routines. In this paper, we can report on the routine of the discourse to analyse the quality of mathematical discourse in two situations of “Expert-to-Novice” and “Novice-to-Novice”.