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.

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.

Teaching square roots: conceptual complexity in mathematics language

The article presents strategies for communicating the concept of square roots to limited English-proficient students. Instead of using mathematical terminology, mathematics teachers could communicate the concept of square roots by integrating the literal concept of square to the actual meaning of a square root. Such approach addresses the learning difficulty experienced by limited English proficient students who tend to associate square roots to geometric concepts. Several strategies for illustrating the concept of a square root using square figures are presented.

Conceptual complexity and apparent contradictions in mathematics language

The article explores the conceptual complexity and apparent contradictions in the language of mathematics and suggests ways to handle these problems. Mathematics, as described the author, is a formal, artificially constructed language. One problem arises from the changes of gradient and rates of change of gradient, continuous functions. Conceptual conflicts also arise when least upperbounds and greatest lower-bounds in discussing sequences and series, convergence and limits are considered.

Listening to students' voices in mathematics education

In many tertiary institutions, mathematics education staff teach courses from early childhood education through to professional development courses at Masters level. Similarly, research into teacher education processes spans these contexts. Common principles that underpin this work include staff willingness to be responsive to students’ needs. This symposium focuses on the importance of listening to students’ voices in mathematics teaching and research – no matter how old students are.

The answer is correct but can I explain it? Student explanations in mathematics

This paper explores an aspect of mathematics that has been overlooked often - student explanation, or communication. The data used is derived from a large-scale project in Victoria. Australia, the Improving Middle Years Mathematics and Science (IMYMS) project. Primary student explanations on two open-response items are examined to illustrate the bene tits of incorporating this type of item in mathematical assessments. Techniques for analysing the data and displaying the results of the analysis are presented. The analysis shows clearly how more sophisticated thinking and explanations develop - information of benefit to teachers of these students.

Making the pedagogic relay inclusive for indigenous Australian students in mathematics classrooms

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics.

Teacher professional growth : a study of primary teachers involved in mathematics professional development

The overall purpose of this study was to examine whether professional development programs can act as appropriate vehicles for the professional growth of teachers of primary mathematics. A longitudinal study was conducted of primary teachers involved in a Victorian mathematics professional development program — Exploring Mathematics In Classrooms (EMIC). The professional growth of six teacher participants in one EMIC course was examined over a period of 18 months. The teachers selected were from four different schools located in the southern metropolitan region of Melbourne. The central interest of this study was in teacher professional growth and accordingly the perspective sought was predominantly that of the teacher. A case study research approach was adopted and data were gathered through observations, interviews, questionnaire, and the collection of teacher work documents. A theoretical model of teacher professional growth was used to represent the teachers' growth. The study generated data on the nature of teacher professional growth and the features of professional development programs likely to influence teacher professional growth. All of the teachers reported and demonstrated growth with respect to their mathematics teaching, in areas associated with their: Classroom Practice, Knowledge and Beliefs, and Professional Attributes. The teachers' growth was highly individualistic, with no two teachers demonstrating exactly the same professional growth outcomes, or the same growth processes. The data provided evidence to confirm that teacher growth is a complex and gradual learning process. For each of the teachers several different routes to change and growth were evident, drawing attention to the non-linear nature of growth. The teachers' responses to the professional development program were influenced by various contextual and personal factors. The data provided evidence of a strong link between the content and outcomes of professional development programs — the outcomes reported and demonstrated by the teachers reflected the content of the EMIC program. Key factors associated with mathematics professional development programs perceived as influencing growth were: program content; program structure; and program presentation. A significant finding was the strong influence on teacher growth of the presenters of professional development programs—some data suggested that the 'quality' of the program presenter is fundamental to the success of any professional development program. The study provided insight into the processes involved in teacher professional growth and factors associated with the way in which professional development programs influence growth. The theoretical model of teacher professional growth used in this study has been elaborated and recommendations which might inform the design and implementation of future professional development programs have been made.

Construction of social difference in mathematics education

This study investigated the social context in which the learning of mathematics occured. It examined the practices of schools and mathematics in order to identify the ways in which they contributed to the construction of social difference. Accordingly, this study was concerned with how schools and mathematics classrooms contribute to working-class students lack of success in mathematics. The differences that occurred in these practices could be seen to contribute to the different outcomes likely to occur in the later years of schooling. It was argued that these differences mean that students from middle-classes would be more likely to undertake and be successful in the study of mathematics than their working-class peers.

How different is it really? – rural and urban primary students’ use of ICT in mathematics

Information and Communication Technology (ICT) offers the potential for changing mathematics education for both teachers and students. However, how ICT is used, and by whom, is critical to realizing this potential. This paper reports on an investigation of the use of ICT in the learning and teaching of mathematics in rural and urban primary schools in Victoria, Australia. Thirty-six teachers and almost 700 students were surveyed regarding their use of ICT for mathematics at home and at school, with a small number of selected teachers and students taking part in interviews. This paper focuses on students’ perceptions of ICT use. A comparison of rural and urban students’ responses shows little difference across most aspects of ICT use, and where there was a difference, the frequency of rural use almost always exceeded that in urban schools.