Leong Yew Hoong

In this paper we describe a problem solving course for first year undergraduate mathematics students who would be future school teachers.

The longstanding criticism against education research is: Has it made a difference to actual classroom practice? In this chapter, I present a case for the affirmative in the context of mathematics education research in Singapore – not merely by describing cases but also extracting common underlying features that contribute to impact. These examples include the now well-known ‘model method’, mathematics problem-solving and the concrete-pictorial-abstract instructional heuristic.

In redesigning a methods course for Singapore Secondary Mathematics prospective teachers, we leverage on video technology to help them learn about the instructional practice of going through textbook-type questions. We find that this innovation generates learning all round – both for the student teachers as well as teacher educators.

This article focuses on a challenging geometry problem that was originally posed to primary school students. Four solution approaches, ranging from elementary to advanced, are discussed. Reflections on these approaches and the problem solving processes are also shared.

In this symposium, we discuss some preliminary data collected from our problem solving project which uses a design experiment approach. Our approach to problem solving in the school curriculum is in tandem with what Schoenfeld (2007) claimed: “Crafting instruction that would make a wide range of problem-solving strategies accessible to students would be a very valuable contribution … This is an engineering task rather than a conceptual one” (p. 541). In the first paper, we look at how two teachers on this project taught problem solving. As good problems are key to the successful implementation of our project, in the second paper, we focus on some of the problems that were used in the project and discuss the views of the participating students on these problems. The third paper shows how an initially selected problem led to a substitute problem to meet our design criteria.

When mathematics teachers plan lessons, they interact with curriculum materials in various ways. In this paper, we draw on Brown’s (2009) Design Capacity for Enactment framework to explore the practice of adapting curriculum materials in the case of a Singapore secondary mathematics teacher. Problems from the textbook used and the worksheets she crafted were compared to determine how she adapted the content. Video-recordings of the lessons and post-lesson interviews were used to clarify how her personal teacher resources contributed to her design decisions. The findings suggest that her seemingly casual use of problems from the textbook are in fact unique variations of adapting curriculum materials.

In designing a set of instructional materials to use in his classroom, a teacher heavily offloaded items (e.g., worked examples, practice questions, exercises) from school-based materials and textbooks. At a cursory level, one may easily dismiss this as a thoughtless lifting of curricular materials. But upon careful analysis – as is detailed in this paper – a different picture emerges. In this paper, we describe and analyse how this teacher adapted one of many worked examples, beyond its typical use, during instruction to develop students’ conceptual understanding of proportionality. We argue that he noticed and harnessed multiple affordances in a single item that most teachers may overlook, without the need to modify the example, and propose a notion of “affordance space” as a lens to view teachers’ design of instructional materials.

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.

A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools, is a programmatic research project at the National Institute of Education (NIE) funded by the Ministry of Education (MOE) in Singapore through the Office of Education Research (OER) at NIE. The main goal of the project is to collect a set of data that would be used by two studies to research the enacted secondary school mathematics curriculum. The project aims to examine how competent experienced secondary school teachers implement the designated curriculum prescribed by the MOE in the 2013 revision of curriculum. It does this firstly by examining the video recordings of the classroom instruction and interactions between secondary school mathematics teachers and their students, as it is these interactions that fundamentally determine the nature of the actual mathematics learning and teaching that take place in the classroom. It also examines content through the instructional materials used – their preparation, use in classroom and as homework. The project comprises a video segment and a survey segment. Approximately 630 secondary mathematics teachers and 600 students are participating in the project. The data collection for the video segment of the project is guided by the renowned complementary accounts methodology while the survey segment adopts a self-report questionnaire approach. The findings of the project will serve several purposes. They will provide timely feedback to mathematics specialists in the MOE, inform pre-service and professional development programmes for mathematics teachers at the NIE and contribute towards articulation of “Mathematics pedagogy in Singapore secondary schools” that is evidence based.

Self-efficacy is a subject of ongoing intense research in cognitive psychology. Studies within this tradition are focused on how this agentic aspect of human functioning fits within and contributes to a network of other sociocognitive functionalities. From a mathematics education perspective, we seek a theoretical re-framing of self-efficacy that accounts for and advances thinking in students’ (lack of) learning of mathematics in the classroom. This study takes this perspective by starting with a student’s actual experiences in switches of self-efficacy states. Through a case study of a student who has a profile that matches one with low mathematics self-efficacy, I examine the contours of self-efficacy across nested mathematical domains. This nuanced view provides an alternative to static presumptions of self-efficacy models common in research reports in this area, and is in keeping with the dynamic ebb and flow of actual classroom experiences.