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.

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.