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 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.

We have applied the ‘practical paradigm’ in teaching problem solving to secondary school students. The key feature of the practical paradigm is the use of a practical worksheet to guide the students’ processes in problem solving. In this paper, we report the diffusion of the practical paradigm to university level courses for prospective and practising teachers. The higher level of mathematics content would demand higher order thinking skills. Learners without a model of problem solving would often revert to solving by referring to many examples of the same ‘type’ of problem. Polya-type problem solving skills framed by the practical worksheet was used as an attempt to elicit more effective problem solving behaviour from them. Preliminary findings show that they were able to use the practical worksheet to model their solution of problems in the courses.

This paper outlines an analytical framework that was developed, to examine the mathematics in mathematics lessons of competent teachers in Singapore secondary schools. The framework is guided by Schoenfeld's Teaching for Robust Understanding (TR U) framework and also the field notes of the project - A study of the enacted school mathematics curriculum which is presently underway in Singapore. The framework was trialled and the indicators were suitable but may not be comprehensive. Therefore more trials and also more codes on how the teacher aided students in developing mathematical knowledge and student engagement with mathematical ideas are needed. In addition student perspectives of the lesson are also necessary to make any valid claims related to the quality of the lessons.

In this paper, we discuss the diffusion (of an innovation) and relate it to our attempt to spread our initial design of a mathematics practical paradigm in the teaching of problem solving.