Toh Tin Lam
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- PublicationOpen AccessEnacting a problem-solving lesson using scaffolding to emphasize extending a problem(2021)
;Chor, Emily Wai SiIn this paper, we describe our conceptualization of teaching mathematical problem-solving at the upper primary level, emphasizing Polya’s Stage Four in extending a problem. Geometry is used as a context of the presentation. The objective is to engage pupils more metacognitively in their problem-solving process. By reviewing existing education literature, features that will support authentic problem solving were identified. The frameworks explored in this study include Polya’s 4-step problem-solving model, Schoenfeld’s framework, and the synthesis of the two frameworks through “Making Mathematics Practical” which utilize an extensive use of teacher scaffolding. The proposed scaffolding stresses pupils to problem solve beyond finding a solution as well as independently check and expand the given mathematics problem. 107 133
- PublicationOpen AccessComics for mathematics instruction for future-ready learnersIn this paper we present the views that the roles of comics for mathematics instruction extend beyond the role of addressing the affective needs of students, in particular the lower achieving students. We argue that within the broader framework of contextualization, comics have the potential to reach out to the entire spectrum of students to develop their higher order thinking skills and even raise their cognizance to environmental issues. Two exemplars based on the research carried out by us are presented.
- PublicationOpen AccessAn experienced and competent teacher's instructional practice for normal technical students: A case studyThis 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.
- PublicationRestrictedMathematical Problem Solving for Everyone (MProSE)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.
- PublicationOpen AccessA framework for designing comics-based mathematics instructional materials(2022)
;Cher, Zheng JiePurpose 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.
- PublicationOpen Access
- PublicationRestrictedMAthematics is Great: I Can And Like (MAGICAL)(Office of Education Research, National Institute of Education, Singapore, 2020)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
- PublicationOpen AccessMany pathways towards "excellence" in Singapore mathematics educationThis paper presents a snapshot of Singapore’s journey towards excellence in mathematics education by examining the role of the traditional notion of mathematics competition and other competitive activities. It could be seen using the context of mathematics competition that the notion of “excellence” has evolved over time. Excellence as a high standard for individuals to achieve or as a set of obstacles for individuals to pit against the norm has been gradually broadened to include excellence as an internal goal for an individual to achieve, and even excellence as a goal for the mathematics education landscape.