Tay, Eng Guan

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.

This paper examines the calculus curriculum in the current Singapore secondary and pre-university levels. Two concepts, (1) increasing and decreasing functions and their derivatives, and (2) the second derivative test for the nature of stationary points, are elaborated. An example of an incorrect calculus item in a national examination is brought up in relation to conditional reasoning involving calculus concepts. We reckon that the current emphasis on procedural knowledge in calculus is useful. However, we argue that formal conditional reasoning should not be introduced prematurely for school students.

Given a connected and bridgeless graph G, let D(G) be the family of strong orientations of G. The orientation number of G is defined to be đ(G) := min{d(D) | D ∈ D(G)}, where ,d(D) is the diameter of the digraph D. In this paper, we focus on the orientation number of complete tripartite graphs. We prove a conjecture raised by Rajasekaran and Sampathkumar. Specifically, for q ≥ p ≥ 3, if đ(K(2, p, q)) = 2, then q ≤ (^p_└p/2┘). We also present some sufficient conditions on p and q for đ(K(p, p, q)) = 2.

The quality of any education system is signifi cantly dependent on the quality of teachers in that system. A 21st century teacher professionalism requiring specialist knowledge and skills is essential for ensuring the quality of teachers. This paper will describe the key features of the teacher education model used in Singapore. In addition, the paper will discuss some key challenges for the teaching profession in the 21st century and possible ways to prepare teachers for the 21st century. Since its establishment as the Teacher Training College in 1950, the National Institute of Education (NIE) has served as the national teacher education institute in Singapore. NIE provides all levels of teacher education, from initial teacher education programmes to professional development programmes as well as higher degree programmes. The NIE’s Teacher Education Model for the 21st Century (TE21) and how this model addresses several key challenges for teacher education are explained in this paper. NIE’s TE21 Model revolves around the Values, Skill and Knowledge (V3SK) model which focus on three value paradigms: Learner-centredness, Teacher Identity, and Service to the profession and community. Finally, the paper will outline some possible issues relevant for the improvement of teacher education.

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.

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 article, we confront the (hardly acknowledged) issue of uneven learning among members of Lesson Study teams. The site of research is a Singapore secondary school where the mathematics department had been involved in a number of Lesson Study projects over a five-year period. Based on interviews with two mathematics teachers who had different backgrounds and histories of participation in these projects, we examine the trajectories of their learning in a most recent Lesson Study on Number Patterns. We conjecture lessons for teacher development in relation to the framing concept of “standpoints”.