Ng, Dawn Kit Ee

Mathematical modelling is one of the current focuses in the Singapore Mathematics Curriculum Framework. A multi-tiered teaching experiment using design research methodology was conducted to build teachers' capacity in designing, facilitating, and evaluating learning during mathematical modelling tasks for Primary 5 students (aged 10-11). This paper illustrates the use of the retrospective analysis phase within design research cycles to activate a critical moment of teacher learning involving the interplay between questioning and listening during her first attempt at facilitating a mathematical modelling task. The teacher affirmed her deliberate focuses in the use of questions to (a) refine students' models, (b) encourage articulation of student ideas in self-evaluation of the models, and (c) clarify and understand student reasoning. However, she also discovered the importance of interpretative listening in conjunction with questioning to promote more sophisticated mathematisation processes in model development. Implications from the use of the retrospective analysis phase on activating critical moments of learning during teacher education 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.

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.

Limited Singapore research indicated a lack of exposure of modelling tasks at primary levels. Teacher reflection is used as a tool in design research cycles exploring the potentials of modelling tasks in a Singapore primary five classroom. Findings reveal that the teacher identified three potentials of a modelling task on children’s mathematisation process: the task provided a platform for children to (a) identify variables and form relationships between them, (b) relate school-based math learning to real-world experiences, and (c) justify their mathematical models. Implications on the promotion of modelling tasks at primary schools as well as teacher education are drawn.

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.

This paper reports on the investigation of pre-service trainee teachers’ perception of the use of the Geometer’s Sketchpad (GSP) for the teaching and learning of geometry. Findings from the survey design suggested that 80% of trainee teachers perceived GSP as a good teaching and learning tool, indicating that GSP has advantageous features that enhance teaching and learning, and GSP can be used as an alternative mode to traditional methods of teaching. Moreover, a large majority of trainee teachers commented positively on the framework for planning GSP tasks, describing it as a ‘helpful’ guide to lesson planning.

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.