Cheng, Lu Pien

Mathematical connections are true relationships and are important for deep mathematical understanding. Connections are also important components of successful problem solving. At the heart of effective teaching and learning of mathematics is task design. This chapter unpacks the different types of mathematical connections through concrete examples to address aspects of task design that draw attention to connections. The relationships between task design, anticipated pedagogies and student learning are also illustrated for teachers to make links and connections explicit in the primary mathematics classrooms.

In this paper the teachers’ learning journey on designing a mathematics problem that involves a real-life context is reported. This is part of a larger project undertaken in a primary school in Singapore where the teachers were engaged in planning, observing and critiquing mathematics lessons to investigate teaching and learning. These unique features from laboratory class cycles were used to facilitate the design and implementation of mathematics problems involving real-life context. Based on one cycle of a laboratory class of an authentic classroom lesson, the teachers’ construction of the mathematics problems embedded in real-life context is reported. The children’s solutions to one of the problems are also discussed in this paper.

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.

In 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.

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.

In this study, ways in which problem posing activities aid our understanding of children’s learning of addition of unlike fractions and product of proper fractions was examined. In particular, how a simple problem posing activity helps teacher take a second, deeper look at children’s understanding of fraction concepts will be discussed. The problems posed by the students were explored and insights into the students’ understanding of fractions were identified.