Ng, Dawn Kit Ee

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.

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.

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 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.

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.

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.