Cheng, Lu Pien

As teachers begin to construct an understanding of ‘inquiry’, and incorporate IBL into their classroom practice, they are challenged to be sensitive to the ‘constructivist’ nature of the CLD. This paper presents a reflection model structured to trigger thinking about beliefs in teaching and learning in order for teachers to re-examine their practice and adopt new pedagogies. The reflections by two secondary school mathematics teachers are presented as they experiment with inquiry-based learning in the CLD. The teachers showed awareness, monitoring and regulation of their teaching practices including new and existing beliefs.

The Riemann-integral of a function defined on [qb] is well known. It is also well known though not easily found in literature that the Riemann integral can be defined as the limit of Riemann sums using divisions as "directed sets". Many properties of the Riemann integral will then have straightforward proofs. We shall develop equi-Riemann convergence and D-onvergence using such an approach called the Moore-Smith limits or Generalised limits.

This paper documents how a team progressed through the five stages of team development as a result of a school-based professional development program using a laboratory class cycle. Six Grade two teachers and their administrator in a primary school in the south eastern United States participated in the study. All the teachers were interviewed at the end of each laboratory class cycle. Their administrator was interviewed after the program ended. A grounded theory approach and constant comparative method were used. The study revealed how the teachers' participation in the program progressed according to Tuckman and Jenson's (1997) model of team development in the laboratory class cycle. Establishment of trust among teachers and team support over an extended time were identified as important factors in shaping the team development.

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.

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 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.

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.

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.

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.