Toh Tin Lam

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.

In this paper, we describe our conceptualization of teaching mathematical problem-solving at the upper primary level, emphasizing Polya’s Stage Four in extending a problem. Geometry is used as a context of the presentation. The objective is to engage pupils more metacognitively in their problem-solving process. By reviewing existing education literature, features that will support authentic problem solving were identified. The frameworks explored in this study include Polya’s 4-step problem-solving model, Schoenfeld’s framework, and the synthesis of the two frameworks through “Making Mathematics Practical” which utilize an extensive use of teacher scaffolding. The proposed scaffolding stresses pupils to problem solve beyond finding a solution as well as independently check and expand the given mathematics problem.

This paper reports a preliminary study on in-service Additional mathematics teachers' knowledge of kinematics concepts. A survey consisting of TRUE/FALSE questions was issued to the participating teachers. The questions were collations of the common misconceptions identified by some local Physics teachers among the local Physics students. The participants were asked to supply the answers to the questionnaire with their answers substantiated with reasons. In this paper, we discuss the results of the survey done on a group of twenty six in-service Additional mathematics teachers and classify the teachers' misconceptions of kinematics concepts. The finding of this initial survey could be useful to spur further research on Mathematics teachers' subject content knowledge on kinematics. Pragmatically it would also be useful for any agency which is planning for any content upgrading workshops for in-service teachers.

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.

It has been five years since the chapter on relative velocity was first introduced into the Singapore Additional Mathematics curriculum. This paper reports some general finding on the teaching of relative velocity in mathematics classrooms and the pupils' learning difficulties on relative velocity. Some implications to the teaching of this topic are also discussed.

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.

In this paper, we discuss the development of a very specific problem solving curriculum in an independent school in Singapore as part of the first phase of our research project. We are using a design research methodology to fine-tune the problem solving curriculum in which we are introducing the mathematics practical, an idea borrowed from science education.

In a design experiment, the feedback from the teacher-implementer is crucial to the success of the innovation simply because the teacher is finally the one that brings the innovation to life in front of the students. We describe in this paper the feedback made by the teacher-implementer after teaching one cycle of the problem solving module in a mainstream school, and the modifications the researchers and the teacher-implementer have made in our design of the module to fit into the requirement of the school.