Toh, Tin Lam

A research project on using comics for teaching mathematics was initiated in one Singapore primary school. One class of Grade 5 (students of age 11–12) students was exposed to comics for mathematics instruction. This paper reports a case study of seven students’ perception of the features of the comics instructional package and how these features impacted their learning of mathematics. The students’ responses in an interview with the researchers were analysed using Thematic Analysis and presented using the Singapore mathematics curriculum framework. Four main features of the comics instructional package: (1) humour; (2) story narrative; (3) scaffolding provided by the questions and (3) visuals and four main themes: Increase in (a) enjoyment; (b) understanding; (c) appreciation of real-world applications of mathematics and (d) participation during lessons; were uncovered. The use of comics could potentially impact positively on developing students’ Attitudes, Skills, Concepts and Processes of the Singapore mathematics curriculum framework in learning mathematics.

In Nov 2002, a research team in the National Institute of Education, NTU, launched a cross-discipline quasi-experimental study on “Positive Social Climate for Enhancing Students’ Math Self-concept”. Its main objective was to find the attributes (variables) in the social climate which are accountable for the increase of self-concept of Secondary Two students in the Math remedial classes in Singapore neighbourhood schools. Phase I of this study ( in 2003) was Instrumentation: validating the scales used in the measurement of treatment effect. H.W. Marsh’s Self-Description Questionnaire (SDQ-II, 1990), and B. Fraser’s “What Is Happening In This Class?” questionnaire (WIHIC) were validated together with the Motivational Orientation scale and Intellectual Achievement Responsibility (IAR) questionnaire. More than 700 Secondary Two students from four neighbourhood schools took part in this validating exercise. Phase II was Intervention`(in 2004): the teachers’ interactions with students, the enhancement of students’ capabilities and confidence. A training workshop for teachers in the experimental groups was conducted before the intervention. Two schools had the experimental groups and another two neighbourhood schools’ samples were held as the control groups of this study. Based on the results in Phase I, only two instruments: SDQII and WIHIC were selected to measure the effect of intervention. The total sample in this phase was close to 1000 Sec 2 students.

The dissertation English in Mathematics Discourse highlights for mathematics educators a body of practical knowledge about Junior College mathematics lecture discourse from the linguistic perspective. Although this dissertation is found among the collection of the dissertations done by postgraduate students of linguistic studies, it is of value to mathematics educators, particularly, mathematics teachers at the Junior College level.

It is easy to dismiss the work of “teaching students to apply formula” as a low-order priority and thus trivialises the professional knowledge associated with this practice. Our encounter with an experienced teacher—through the examination of her practices and elaborations—challenges this simplistic assumption. There are layers of complexities that are as yet under-discussed in the existing literature. This paper reports a case study of her practices that reflect a complex integration of relevant theories in task design. Through examining her praxis around the theme of “recognise the form”, we discuss theoretical ideas that can potentially advance principles in the sequencing of examples for the purpose of helping students develop proficiency in applying formula.

In this paper we elaborate on the ways for assessing problem solving that goes beyond the usual focus on the products of the problem solving process. We designed a ‘practical’ worksheet to guide the students through the problem solving process. The worksheet focuses the solver’s attention on the key stages in problem solving. To assess the students’ problem solving throughout the process, we developed a scoring rubric based on Polya’s model (1954) and Schoenfeld’s framework (1985). Student response to the practical worksheet is discussed.

The role of the teacher is central to the success of any curriculum innovation. Thus, teachers’ professional development has become an increasingly important subject of discussion in recent education literature. In the design and implementation of the project reported here, teachers’ preparation for the problem-solving curriculum featured prominently. This paper discusses the challenges of selecting a suitable problem and ways of using it productively within a professional development programme that the authors carried out for the teachers involved in the project.

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students’ reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students’ reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures.

In this chapter, we discuss the comics package we have developed to teach lower secondary school statistics of the mathematics curriculum. Most people would think that comics for classroom instruction can at most stop at arousing students’ interest in the subject, especially among the low-attaining students. However, we assert that using comics in teaching lower secondary statistics can introduce the students to much of the statistical processes within contexts that are meaningful to students, invite them to engage in higher order thinking tasks in order to develop their critical thinking ability. We also discuss snapshots of how one teacher enacted the statistics lessons based on our comics teaching package, and two teachers’ response to the comics package.