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.

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.

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.

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 Nov 2002, a research team in the National Institute of Education, NTU, launched a cross-discipline quasi-experimental study on “Positive Social Climate for Enhancing Students’ Math Self-concept”. Its main objective was to find the attributes (variables) in the social climate which are accountable for the increase of self-concept of Secondary Two students in the Math remedial classes in Singapore neighbourhood schools. Phase I of this study ( in 2003) was Instrumentation: validating the scales used in the measurement of treatment effect. H.W. Marsh’s Self-Description Questionnaire (SDQ-II, 1990), and B. Fraser’s “What Is Happening In This Class?” questionnaire (WIHIC) were validated together with the Motivational Orientation scale and Intellectual Achievement Responsibility (IAR) questionnaire. More than 700 Secondary Two students from four neighbourhood schools took part in this validating exercise. Phase II was Intervention`(in 2004): the teachers’ interactions with students, the enhancement of students’ capabilities and confidence. A training workshop for teachers in the experimental groups was conducted before the intervention. Two schools had the experimental groups and another two neighbourhood schools’ samples were held as the control groups of this study. Based on the results in Phase I, only two instruments: SDQII and WIHIC were selected to measure the effect of intervention. The total sample in this phase was close to 1000 Sec 2 students.

In Nov 2002, a research team in the National Institute of Education, NTU, launched a cross-discipline quasi-experimental study on “Positive Social Climate for Enhancing Students’ Math Self-concept”. Its main objective is to find the attributes (variables) in the social climate which are accountable for the increase of self-concept of Secondary Two students in the Math remedial classes in Singapore neighbourhood schools. Phase One of this study is Instrumentation: validating the scales used in the measurement of treatment effect. Phase Two is Intervention: the teachers’ / tutors’ interactions with students, the enhancement of students’ capabilities and confidence. These teachers / tutors will attend workshops conducted before the intervention in Phrase Two. The Pretest results will help identify students with high or low Math Self-concept. And the Posttest will help measure the effect of invention on these students’ Math Self-concept. Factors contributed to the significant changes will also be explored. H.W. Marsh’s Self-Description Questionnaire (SDQ-II, 1990) and B. Fraser’s “What is happening in this Class?” questionnaire were validated together with the Motivational Orientation scale and Intellectual Achievement Responsibility (IAR) questionnaire in Phase One. More than 700 Secondary Two students from four neighbourhood schools took part in the survey. Some preliminary findings in Phase One of this study will be presented in this paper. Gender and course differences in Math Self-concept and other variables will also be discussed.

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.