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.

Reason for hope : primary students' mathematics learning environment

This paper reports the results of a student survey of perceptions of classroom learning environment conducted as part of a major investigation into effective pedagogical practices in mathematics and science. All primary school project participants were surveyed, The 36 Likert-type items were subjected to a Partial Credit Model analysis, and response categories subjected to statistical requirements. The results are presented graphically, their meanings examined, and the implications of the findings for both researchers and practitioners are discussed.

Students` impressions of the value of games for the learning of mathematics

The use of mathematical games in primary classrooms is commonplace in Australia. This paper reports on key findings from a larger investigation exploring the impact of games on mathematical learning, student attitudes, and behaviours. 222 Grade 5 and 6 children were taught multiplication and division of decimal numbers using calculator games. This paper raises questions about the students’ attitudes towards games as a vehicle for learning mathematics. One aspect reported in this paper is an apparent difference between students’ attitudes to games usage when data were
collected quantitatively compared with qualitatively.

Generic versus subject specific pedagogy - should mathematics be in the centre?

Research into pedagogy and school change is a high priority in Australia and many other countries. This paper, which includes some preliminary findings from the Improving Middle Years Mathematics and Science: The role of subject cultures in school and teacher change (IMYMS) project, argues that, while there are key features that are common to quality learning environments across all subject areas, generic formulations of pedagogy fail to take account of the extent to which the disciplines being taught shape pedagogy or the contribution of Pedagogical Content Knowledge (PCK) to effective teaching - i.e. that there really is a need to put "mathematics in the centre ".

Students' conflicting attitudes towards games as a vehicle for learning mathematics : a methodological dilemma

Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students' attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children's attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This article reports on the methodological dilemma of resultant conflicting attitudinal data related to game- playing. Concerns arising from the divergence in the results are raised in this article. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.

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.

Fun or profit : primary students' perceptions of mathematics and science

As the number of students pursuing mathematics and science in higher education decline, it becomes imperative· that we look for the causes of the decline. As part of the Australian Improving Middle Years Mathematics and Science (IMYMS) project, students were asked to rate their perceptions of classroom practice in mathematics and science and their attitudes to these subjects. Results of this survey reveal little difference in perceptions of classroom practice, but significant differences in students' attitudes between mathematics and science. Differences were particularly evident for items relating to the usefulness of mathematics and science (mathematics was more useful) and enjoyment of the subjects (science is more fun). If teachers are aware of such perspectives, it may be possible to change students' attitudes.

Effective student engagement depends on students enjoying their studies in mathematics and science, being confident in their ability and recognising the relevance of these subjects to everyday life, now and in the future.
(Education Training Committee, 2006, p. xvii)

Science and technology are the widely acknowledged foundation of Australia's future development. Underpinning these are the key learning areas of mathematics and science. However, Australia is experiencing a decline in numbers of mathematics and science students in higher education. Moreover, studies over the last two decades have shown a general decline in Australian students' interest and enjoyment of science across the compulsory secondary school years, with a particularly sharp decline across the primary to secondary school transition (e.g. Adams, Doig, & Rosier 1991; Goodrum, Hackling, & Rennie, 200 I) and a decline in the numbers of students studying' advanced mathematical courses in upper secondary school (Thomas, 2000).

Improving teaching and learning in the middle years of schooling (Years 5 to 9) is receiving particular attention because of the coincidence of the disengagement of students with the significance of these years for the preparation of students for their future role in society. Thus the Improving Middle Years Mathematics and Science: The role of subject cultures in school and teacher change (IMYMS) project, which is the source of data for this paper, is investigating the role of mathematics and science' knowledge and subject cultures in mediating change processes in the middle years of schooling.

Mathematics and science are sometimes seen as "love-hate" subjects, rating highest for subjects disliked, but also rating relatively highly among preferred subjects (Hendley & Stables, 1996). Students, even primary aged students, can often shed light on what constitutes good practice (see, for example, 'van den Heuvel-Panhuizen, 2005). Students' attitudes towards mathematics and science and their perceptions of what they regard as positive aspects of classroom practice have been shown to decline from the primary years to junior secondary (Race, 2000). The decline in interest in science in the early years of secondary school is of particular concern, since it is in these years that attitudes to the pursuit of science subjects and careers are formed (Speering & Rennie, 1996). Students' negative attitude towards the relevance of science ,content for their lives was a strong theme in the report by Goodrum, Hackling, & Rennie (2001) on the status and quality of teaching and learning of science.

As part of the IMYMS project, the IMYMS Student Survey was administered to all students in 2004 and 2005. The survey included a 36 item section on students' perceptions of classroom practice and attitudes towards mathematics and science, and a 24 item section on students' learning preferences. Students completed separate, parallel surveys for mathematics and science.

This paper focuses on students' perceptions and attitudes. It explores the differences in 700 Year 5 and 6 students' perceptions of their learning environment and their attitudes to mathematics and science during 2005, the second (and final) year of schools , involvement in the IMYMS project.