Ng, Dawn Kit Ee

Mathematical modelling as use of mathematics to solve or deepen understanding of real-world problems is an inherent part of mathematics, and education research in this field is increasingly important. This chapter critically reviews mathematics education research, from the early years through to tertiary education, and related curricula documents published by Australasians or with particular relevance to Australasia. Contributions to the field are organised in six broad areas: (i) developments in curricula on the teaching of mathematical modelling intended to promote mathematical thinking and ways of working, (ii) practices of mathematics and practices of mathematical modelling, (iii) teacher preparation and professional learning, (iv) assessment of mathematical modelling, (v) interdisciplinarity and connections with data modelling, and (vi) research as design: honouring the mathematics in mathematical modelling.

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.

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.

As part of a mathematics teacher's skillset, knowing what kinds of assessment, when and how to assess, and for what purposes, are important. Although there have been frameworks outlining the various facets of teacher assessment literacy, recent literature suggest that gaps exists on the theoretical underpinnings as well as in psychometric claims of the measures. A framework of assessment literacy is proposed in this paper, informed by the mathematics education literature: (1) knowledge about assessment concepts; (2) skills in applying the knowledge in actual assessment practices; (3) communication and action in providing feedback or changing instructional practices based on assessment information; (4) attitudes and beliefs about assessment and its role in mathematics teaching and learning; and (5) meta-cognition and self-regulation of teachers' own assessment literacy.

The introduction of Project Work (PW) to schools in 1999 could be seen as an attempt to prepare students for the challenges posed by a knowledge-based economy. This paper hopes to present the background of PW and share some concerns related to the implementation of PW in schools. It also hopes to suggest potential areas of educational research into PW.

This paper reports mathematical and real world knowledge application by lower secondary students (aged 13-14 years) in a design-based interdisciplinary project with mathematics, science, and geography as anchor subjects implemented in Singapore1. Key findings from two mathematical tasks attempted by 10 case-study groups during the project reveal that whilst students displayed taught knowledge and skill, they lacked in-depth understanding of the use and purpose of scale drawings. There was also limited activation of real-world knowledge during mathematical decision making and little monitoring of accuracy and reasonableness of mathematical results.