In this paper we report our development of instruments to measure Big Ideas in school mathematics. In tackling the issue of assessment fatigue among students, we present an aggregated approach to measure students' knowledge of Big Ideas.

Big Ideas in school mathematics can be seen as overarching concepts that occur in various mathematical topics in a syllabus. For teachers, this knowledge can be used to help students develop a better understanding of mathematics by making visible the central ideas, and connection across topics and across levels. For students, this knowledge can…

In sharing solutions of mathematical tasks, students may use various modes of representation such as: language (oral/written), numerical and symbolic, or drawings (pictures, diagrams or markings). In this paper we explore the potential of student drawings to provide evidence of mathematical fluency. Examples of young students' (5-8 years old)…

Following the teaching of a unit on mass measurement to 274 children (6 to 8 years of age), each of 13 classroom teachers administered an open-ended assessment task. Children represented their perceived knowledge of mass measurement in response to an "Impress Me" prompt. Drawn and written recordings were complex and multi-dimensional,…

Teachers' conceptions play an important role in their instructional practices. In this study, the researcher explored a small sample of Fijian secondary school mathematics teachers' conceptions of assessment. Thirteen mathematics teachers from two case study schools took part in this study that utilised one-to-one interviews to gain insights into…

Multiple-choice items are used in large-scale assessments of mathematical achievement for secondary students in many countries. Research findings can be implemented to improve the quality of the items and hence increase the amount of information gathered about student learning from each item. One way to achieve this is to create items for which…

We assume many things when considering our practice, but our assumptions limit what we do. In this theoretical/philosophical paper I consider some assumptions that relate to our work. My purpose is to stimulate a debate, a search for alternatives, and to help us improve mathematics education by influencing our future curriculum documents and…

There is an identified and growing need for a levelled diagnostic basic facts assessment tool that provides teachers with formative information about students' mastery of a broad range of basic fact sets. The Individual Basic Facts Assessment tool has been iteratively and cumulatively developed, trialled, and refined with input from teachers and…

In early childhood settings narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool. However, in the New Zealand context there is increasing concern that learning stories currently downplay domain knowledge. Data from teacher interviews and samples of learning stories…

On-line quizzes are used to help first year University Mathematics students identify weaknesses in their basic skills and improve them. Quizzes developed as a formative tool have been utilised at JCU [James Cook University] for eight years. However, before this research no-one has questioned the effectiveness of quizzes for this task. We present a…

This paper reports the results of a pencil-and-paper test developed to assess young children's understanding of mass measurement. The innovative element of the test was its use of photographs. We found many children of the 295 6-8 year-old children tested could "read" the photographs and diagrams and recognise the images as…

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

Mathematics educators and mathematics standards of curriculum have emphasised the importance of constructing the interconnectedness among mathematic concepts ("conceptual understanding") instead of only the ability to carry out standard procedures in an isolated fashion. Researchers have attempted to assess the knowledge networks in…

Teacher mobility is often viewed as a limitation of longitudinal analyses of teacher learning in communities, in which membership changes. I introduce an analytical tool developed to address the continuation of the learning of such communities across changes in membership. In the case analysis, I examine whether changes in membership should be…

This is a record of the proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia (MERGA). The theme of the conference is "Mathematics: Essential research, essential practice." The theme draws attention to the importance of developing and maintaining links between research and practice and…