Cheng, Lu Pien

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (i) several sets of comic strips expounding all related mathematical concepts in a lively way; (ii) tiered practice questions for learning reinforcement; and (iii) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and eleven students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.

Mathematics education in Singapore schools in the twenty-first century is still going through the period of change and innovation that began in the early 1990s: changes in emphasis from rote memorisation to meaningful understanding of concepts and problem-solving; from a dependence on paper and pencil and manipulative calculations and skills to mental computations and thinking strategies; and from teaching by telling to activity-based learning, group work, and communication in mathematics. This chapter makes an attempt to describe how the mathematics curriculum in Singapore has responded to such changes and innovations. At the same time, the chapter has chosen three out of many major innovations in Singapore mathematics education and discusses them in relation to school mathematics: problems in real-world contexts (PRWC), Learning Support for Mathematics (LSM), and Improving Confidence and Achievement in Numeracy (ICAN). These innovations are selected because the ways Singapore has approached them might be of theoretical and practical interest to international readers.

The aim of this study is to examine the effect of constructivist instruction on secondary school students’ learning engagement, measured as the psychological state of flow, in mathematics lessons. Ninth grade students (n = 144) from two Singapore secondary schools were assigned to receive either constructivist or traditional direct instruction for the learning of a unit on angle properties of circles. Mixed analyses of variance revealed that students who received constructivist instruction reported higher levels of engagement compared to their direct instruction counterparts. In addition, the results showed that students’ learning engagement decreased over the course of the instructional unit, and that constructivist instruction could potentially offset this negative trend. Overall, the findings suggest that instruction that is founded on constructivist principles may be promising in mitigating engagement issues, thus promoting the joy of learning mathematics among secondary school students.

As part of a mathematics teacher's skillset, knowing what kinds of assessment, when and how to assess, and for what purposes, are important. Although there have been frameworks outlining the various facets of teacher assessment literacy, recent literature suggest that gaps exists on the theoretical underpinnings as well as in psychometric claims of the measures. A framework of assessment literacy is proposed in this paper, informed by the mathematics education literature: (1) knowledge about assessment concepts; (2) skills in applying the knowledge in actual assessment practices; (3) communication and action in providing feedback or changing instructional practices based on assessment information; (4) attitudes and beliefs about assessment and its role in mathematics teaching and learning; and (5) meta-cognition and self-regulation of teachers' own assessment literacy.

The Concrete-Pictorial-Abstract (CPA) approach, based on Bruner’s conception of the enactive, iconic and symbolic modes of representation, is a well-known instructional heuristic advocated by the Singapore Ministry of Education since early 1980’s. Despite its ubiquity as a teaching strategy throughout the entire mathematics education community in Singapore, it is somewhat surprising to see a lack of an account of its theoretical roots. This paper is an attempt to contribute to this discussion on the CPA strategy and its potential role in continuing advancement of quality mathematics education.

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.