Brian Doig

The Critical Role of Task Development in Lesson Study

While many aspects of Lesson Study are characteristic of effective pedagogy, the task or problem is perhaps the least understood by non-Japanese adopters of Lesson Study. In this chapter we focus on the pivotal role played by the task in the Research Lessons of Lesson Study practice in Japanese primary school mathematics. The metaphor adopted is that tasks are akin to icebergs, where most of the support is hidden, and is used in order to raise awareness of the bases of effective tasks. Examples of such tasks are described as they were presented in classrooms in both Australia and Japan.

Large‐scale mathematics assessment: looking globally to act locally

In this paper, I will argue that it is possible to use data from large‐scale international and national mathematics assessment programmes, whose attention is on summative achievement, to provide formative information that informs teachers about the effects of their classroom practice. However, to have impact on, and be useful for, classroom practitioners, these achievement data need to be reworked and re‐presented in ways that are plausible, provide a basis for inferences about practice, and be appropriate for the intended audience. This paper examines achievement‐focused assessment programmes in terms of their aims and approaches, and develops the argument that formative assessment possibilities are present, within these programmes, although usually hidden. Examples are drawn from several sources to support this argument, and demonstrate a variety of approaches that have been taken in the past. Suggestions for further action are made.

Easier Analysis and Better Reporting: Modelling Ordinal Data in Mathematics Education Research.

This paper presents an examination of the use of Rasch modelling in a major research project,Improving Middle Years Mathematics and Science (IMYMS). The project has generated both qualitative and quantitative data, with much of the qualitative data being ordinal in nature. Reporting the results of analyses for a range of audiences necessitates careful, well-designed report formats. Some useful new report formats based on Rasch modelling—the Modified Variable Map, the Ordinal Map, the Threshold Map, and the Annotated Ordinal Map—are illustrated using data from the IMYMS project. The Rasch analysis and the derived reporting formats avoid the pitfalls that exist when working with ordinal data and provide insights into the respondents’ views about their experiences in schools unavailable by other approaches.

Developing Formal Mathematical Assessment for 4- to 8-Year-Olds

The assessment of children in their years before school and their first years of school has been, traditionally, informal. Further, assessment of children’s mathematical skills at this level has been infrequent compared to social, emotional and physical assessments. However, there are contexts where reliable, valid, standardised data from assessment in mathematics are required. This paper outlines the development of two assessment tools for mathematics that were originally developed for such contexts. Item Response Theory (IRT) analyses enabled the construction of assessment forms that address the range of abilities of 4- to 8-year-old children, and provided the scales used for constructing formative and summative reports of achievement. A description of the development of the assessment tools and the IRT analysis that provides the reporting formats are presented together with some research uses of the tools.

Broadening assessment, improving fairness? some examples from school science

Following a review of equity issues in testing, especially in relation to science, two assessment programmes in school science, each of which was designed both to probe a range of aspects of student performance and for use in a large-scale study, are discussed. Both have been developed and used in the 1990s, one in Australia only and the other in many countries. The programmes and the range of aspects they attempt to assess are described and results are cited for several groups of students. Issues of fairness through the broadening of large-scale assessments to include tasks requiring students to construct their answers or carry out investigations are addressed as the second focus of the paper.

Interdisciplinary Mathematics Education: A State of the Art

This book provides an introductory reading of the State of the Art on Interdisciplinary Mathematics Education. It begins with an outline of the relevant historical, conceptual and theoretical backgrounds to this topic, what ‘discipline’ means and how inter-, trans-, and meta-disciplinary activity might be understood. Key ideas in theory involve boundaries, discourses, identity, and the division of labour in practice. Second, it reviews empirical research findings of the extant literature. For example, we report that a common theme in studies in middle and high schools is the motivational benefits for the learner of the subsumption of disciplinary motives to extra-academic problem-solving activity; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. Finally, we offer some case studies of current R&D in practice.