Easier analysis and better reporting : modelling ordinal data in mathematics education research

This article presents an examination of the use of Rasch modelling in a major research project, 'Improving Middle Years Mathematics and Science' (IMYMS). It is unarguable that it is important to take students' perceptions, or views, into account when planning learning and teaching for them. The IMYMS student perceptions survey is an attempt to make visible these student viewpoints, and report them in a way that is accessible to teachers and researchers involved in the project. The project involves four clusters of schools from urban and regions of Victoria to investigate the role of mathematics and science knowledge and subject cultures in mediating change processes in the middle years of schooling. There are five secondary and twenty-eight primary schools. 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 modeling -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.

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.

Assessing effects of technology usage on mathematics learning

Computer-based technologies are now commonplace in classrooms, and the integration of these media into the teaching and learning of mathematics is supported by government policy in most developed countries. However, many questions about the impact of computer-based technologies on classroom mathematics learning remain unanswered, and debates about when and how they ought to be used continue. An increasing number of studies seek to identify the effects of technology usage on classroom learning, and at a time when governments are calling for 'evidence-based' policy development, many studies applying quasi- scientific methodologies to this field of practice are emerging. By analysing a series of conceptual frameworks for assessing the use of computer-based technologies to support school learning, this article emphasises the value of research into the relationship between technical and conceptual aspects of technology use in mathematics education and beyond, and challenges the usefulness of large-scale, quasi-scientific studies that focus on educational inputs and outputs.

Australian and US preservice teachers' perceptions of the gender stereotyping of mathematics

Historically mathematics was considered a pursuit more suited to males than females. Using a new instrument, contemporary high school students' beliefs about the gender stereotyping of mathematics have been measured and an apparent change in beliefs reported. The same instrument was administered to preservice teachers in Australia and the USA. These countries share common social and cultural characteristics and both were active in addressing identified female disadvantage in mathematics education outcomes. The preservice teachers were asked to respond to the survey items as they believed high school students would answer. The Australian and US preservice teachers' responses were compared. The results are reported and discussed in this paper.

The positioning of mathematics in an environmental thematic curriculum

With a crowded curriculum, many primary schools attempt to integrate their key learning areas. One primary school in a large regional city has taken this a step further. Using the ’environment’ as the overarching theme, the key learning areas are interwoven into the teaching of the environment. This has presented some issues when attempting to teach English and Mathematics. These issues and the way the school and teachers solve them are documented in this case-study.

Children's perspectives on mathematics and game playing

This paper reports on data collected from a larger study investigating the effect of game playing on students' mathematical learning and motivation. The study was conducted in three schools with 240 students participating in four different treatment groups. This paper reports some of the results of interviews with students to gather data on their attitudes towards mathematics and game playing. The interview data collected from a sample of students in the· three game playing groups pertaining to attitudes are presented and discussed below.

Progressive discourse in mathematics classes - the task of the teacher

This paper uses data from two mathematics lessons to explore the nature of progressive discourse and examine critical features of teacher actions that contribute to mathematics classrooms functioning as communities of inquiry. Features found to promote progressive discourse include a focus on the conceptual elements of the curriculum and the use of complex, challenging tasks that problematised the curriculum; the orchestration of student reporting to allow all students to contribute to progress towards the community's solution to the problem; and a focus on seeking, recognizing, and drawing attention to mathematical reasoning and justification, and using this as a basis for learning.

What does mathematics understanding look like?

The concept of mathematical understanding is central to curriculum development, classroom interaction, and the training of mathematics teachers In this paper, some models of the growth of understanding that the literature presents are outlined Some results of a study that documented four primary teachers’ mental models of, and beliefs about, different forms of understanding are reported It is proposed that linear models may restrict ways that these teachers plan lessons Questions for further research are raised

Primary and secondary mathematics practice: how different is it?

This paper describes the practices of ninety-nine teachers at the beginning of their involvement in a large-scale project investigating the influence of subject cultures on school and teacher change. Data collected from these teachers, using the IMYMS. Components of effective teaching and Learning mapping procedure, were analysed to investigate similarities and differences in primary and secondary teachers’ perceptions of their practice in mathematics. Results of the analysis show different patterns across a range of components of effective teaching and learning.

A first priority when working with teachers is to help them become aware of and make problematic aspects of their current practice …. Only then would they have reason to attempt to reform their instructional practices when working with us. (Yackel, 1994, p. 386)

Effective mathematics learning environments : primary teachers' beliefs and practices

A first priority for changing teaching practice is to make problematic for teachers aspects of their current practice. As part of a project on improving mathematics and science teaching in the middle years of schooling, teachers were asked to rate their practice against components of effective teaching and learning and to rate each of these according to their perceived importance. Findings suggest that primary teachers endorsed the components as representing effective practice, scoring most components higher than their actual practice. Gaps were particularly evident for items relating to challenging students conceptually and higher-order thinking, with these becoming the basis for some of the action planning for change.