Ng, Dawn Kit Ee

In this paper, I present the Constructivist Learning Design (CLD) as an instructional design for teaching through problem solving and describe how differentiated instruction complements CLD to engage diverse learners in the mathematisation process for construction of knowledge towards mathematical literacy. An example of a CLD task implemented with Secondary Two students (aged 13-14) in Singapore schools as part of a research study is discussed in view of the mathematisation process elicited through use of differentiated instruction. We argue that CLD has the potential to support teachers in planning for deep learning.

The Singapore mathematics curriculum framework emphasises sense-making, requiring teachers to use varied methods to develop students' understanding of mathematical concepts so as to make sense of ideas, connections, and applications. Mathematical reasoning, which refers to the ability to analyse mathematical situations and construct logical arguments, is also one of the key focuses in the Singapore mathematics syllabus. Research in Singapore on reasoning and sense making during the negotiation of meaning in group collaborative problem solving involving real-world mathematical tasks is limited albeit the importance of such tasks in engaging the learner. This paper compares and contrasts key features of the reasoning and sense making journeys of two case study groups as they participated in a real-world design-based mathematical project. It was discovered that the two groups had contrasting reasoning and sense making processes related to the reasonableness of measurements within their interpretations of the real-world constraints of the project. This was mainly due to group dynamics and their members' ability to communicate their mathematical arguments effectively during group discussions.

Research has indicated that for teachers to facilitate mathematical modelling activities in the mathematics classroom, they need to be familiar with the process of mathematical modelling. As such, it is imperative that teachers experience the whole mathematical modelling process. This paper reports on a Multi-tiered Teaching Experiment designed to help a teacher develop his capacity in the domain of mathematical modelling. Drawing on part of a larger case-based study conducted using Design Research phases situated within the Multi-tiered Teaching Experiment framework, the purpose of the paper is to exemplify how the research design fostered growth in teacher capacity through the natural development of critical moments of learning by the teacher during interactions between the researchers and the teacher-modeller himself. The potentials of the Multi-tiered Teaching Experiment as a useful non-prescriptive teacher development approach building upon the existing repertoire of individual teachers will be discussed.

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes and competencies needed to develop in their students during mathematical modelling. This paper reports on the assessment of two groups of Primary 5 students’ (aged 11) mathematical modelling competencies in their first attempt in completing a modelling task. The students’ competencies are assessed to be at levels 1 and 2 of a researcher-designed rubric. Findings appear to suggest that students faced particular challenges in formulating a mathematical problem from the real-world problem through making assumptions. Implications on teacher education on the facilitation of problem formulation and mathematisation during mathematical modelling at the primary level are drawn.

The quality of any education system is significantly dependent on the quality of teachers in that system (Barber, Mourshed, How the World’s Best-Performing School Systems Come out on Top. McKinsey & Company, New York, 2007). A twenty-first century teacher professionalism requiring specialist knowledge and skills is essential for ensuring the quality of teachers (Darling-Hammond, Journal of Teacher Education 6:35–47, 2010). This chapter presents a multi-faceted and multi-dimensional framework which synergises a teacher education institute, the Ministry of Education, and professional teacher organisations in providing teacher education for a twenty-first century mathematics teacher in Singapore from pre-service through life-long professional development. Singapore’s pragmatic approach in preparing teachers who can adapt to the constantly changing education landscape will be discussed. Directions for future developments towards life-long, life-wide, life-deep, and life-wise Singapore teacher education will be outlined.