Listening to children's explanations of fraction pair tasks: When more than an answer and an initial explanation are needed

Research has shown that children can offer the right answer but have mathematically incorrect reasoning (Clements & Ellerton, 2005). One-to-one task-based interviews enabled the researchers to engage in observational listening (Empson & Jacobs, 2008) and uncover the mathematical strategies used by Grade 6 students in fraction pair tasks. Some students’ answers and initial explanations were similar, but different strategies were revealed by further questioning: the correct strategy of benchmarking or the misconception of gap thinking

An empirically based practical learning progression for generalisation, an essential element of algebraic reasoning

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic Reasoning (LPAR). Our learning progression in generalisation is more specific than the LPAR, more coherent regarding algebraic generalisation, and enabling teachers to locate students’ performances within the progression and to target their teaching. In addition, a selection of appropriate teaching resources and marking rubrics used in the RMFII project is provided for each level of the learning progression

Showcasing recent Australian research in gender and mathematics

In this paper findings from a recent review of Australian research on gender issues in mathematics education (Vale, Forgasz & Horne, 2004) are presented

Working with practitioners and learning trajectories: Sharpening the focus on mathematical reasoning in grades 5-9

This paper will report on the role of practitioners in a recent Australian study that developed empirically based learning and assessment frameworks (i.e. learning trajectories) for algebraic, geometrical, and statistical reasoning in the middle years of schooling. To understand the nature of the teachers’ role, the paper begins with a description of what is meant by ‘curriculum’ in Australia and the implications of this for teacher decision making and planning. We then provide a rationale for the study and a brief description of the methodology before illustrating how teachers were involved in the iterative research design through task development and the trial and refinement of partial credit scoring rubrics. The paper concludes by describing the development of targeted teaching advice and considering some of the challenges involved in dissemination

From research to practice: The case of mathematical reasoning

Mathematical proficiency is a key goal of the Australian Mathematics curriculum. However, international assessments of mathematical literacy suggest that mathematical reasoning and problem solving are areas of difficulty for Australian students. Given the efficacy of teaching informed by quality assessment data, a recent study focused on the development of evidence-based Learning Progressions for Algebraic, Spatial and Statistical Reasoning that can be used to identify where students are in their learning and where they need to go to next. Importantly, they can also be used to generate targeted teaching advice and activities to help teachers progress student learning. This paper explores the processes involved in taking the research to practice

A step in the development of an evidence based learning progression for geometric reasoning: focus on shape and angle

International audienceThe Reframing Mathematical Futures II Project set out to develop an evidence-based learning progression for mathematical reasoning in years 7-10 of schooling. This paper reports part of the process and findings particularly around student reasoning about shape and angle as part of the development of a progression for geometrical reasoning. Concerns are raised about the low level of understanding and reasoning in these areas and the need for further research in the study of the development of the concept of angle

A step in the development of an evidence based learning progression for geometric reasoning: focus on shape and angle

International audienceThe Reframing Mathematical Futures II Project set out to develop an evidence-based learning progression for mathematical reasoning in years 7-10 of schooling. This paper reports part of the process and findings particularly around student reasoning about shape and angle as part of the development of a progression for geometrical reasoning. Concerns are raised about the low level of understanding and reasoning in these areas and the need for further research in the study of the development of the concept of angle