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.

Thinking teaching: seeing mathematics teachers as active decision makers

Many teachers are now incorporating a broader range of strategies into their teaching, including problem solving, investigations and open-ended questions. Among other things, such teaching requires teachers to talk less but to make more decisions. The acknowledgment of this complexity and the centrality of active decision making have implications for teacher education and teacher development, and for the strategies and resources used.

The stereotyping of mathematics: gender and cultural factors

The Who and mathematics instrument is used to measure the extent to which mathematics is considered a male, female or gender-neutral domain. Data from students in grades 7-10 in Australia and Greece were compared to explore the impact of the cultural environment. The data were also examined for within country gender differences and possible differences among males and among females across the two countries. An additional perspective on the influence of prevailing cultural norms - Greek ethnic home background and the broader Australian milieu - was provided by the findings from a small sample of Australian students who attended a school with a strong Greek affiliation and who completed a trial version of the Who and mathematics instrument.

The contexts of mathematics tasks and the context of the classroom: are we including all students?

Mathematics teachers are encouraged to use realistic contexts in order to make mathematics more meaningful and accessible for all students. However, the focus group research reported in this article shows that decisions on the suitability of contexts are complex and multidimensional. Similarly, the way the task contexts are presented, and the way the tasks are incorporated into classroom routines have potential to alienate some groups of students. We suggest that teachers and researchers should be sensitive to difficulties that students might experience as a result of both the task and classroom contexts, and take specific steps to avoid or overcome the difficulties.

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 actions to maximize mathematics learning opportunities in heterogeneous classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.

Primary mathematics practice : the Victorian position

In order to establish what constitutes current primary practice in Victoria, video and other data were collected from a stratified random sample of ten year 3 and 4 classrooms in Victoria. Three video vignettes, representing the contrasting pedagogical flows captured on the videotapes, were produced to stimulate discussion in three separate Focus Groups of randomly selected teachers, principals, and mathematics teacher educators and consultants. This paper reports on their views of what constitutes current Victorian practice in primary mathematics

Being explicit about aspects of mathematics pedagogy

It is conventional wisdom that contextualising mathematics tasks can make them more meaningful for students, and that open-ended questions create opportunities for student engagement. Yet concerns are emerging that strategies such as these may exacerbate the disadvantage of some. We report data from a project that seeks to address such concerns by encouraging teachers to be explicit about aspects of their pedagogy. Men teachers were explicit about aspects of the pedagogy, the students responded in the direction intended.

Describing elements of mathematics lessons that accommodate diversity in student background

We are researching actions that teachers can take to improve mathematics learning for all students. Structural elements of the lessons being trialled include making aspects of pedagogy explicit to seek to overcome differences in familiarity with schooling processes, and sequencing tasks with the potential to engage students. This article reports research on teachers building learning communities by preparing variations to set tasks in order to address differences in students’ backgrounds.

Using word problems in Malaysian mathematics education: looking beneath the surface

This paper reports on aspects of a project that investigated the influence of Chinese Malaysian students’ schooling in a tradition of abstract, technical mathematics and rote learning on ways that they responded to mathematical word problems. Data from an action research project are reported. Supposedly “shallow” and “ deep” learning are shown to be interlinked, and assumptions frequently made by Western educators about modelling and practice are questioned.

Planning and teaching mathematics lessons as a dynamic, interactive process

We are researching actions that teachers can take to improve mathematics learning for all students, with particular attention to specific groups of students who might experience difficulty. After identifying possible barriers to learning, we offered teachers mathematics lessons structured in a particular way. Teachers’ use of the model outlined in this paper seemed productive and their resulting planning and teaching proved to be dynamic and interactive. This paper uses excerpts from a conversation between two teachers to illustrate specific aspects of the model.

Developing guidelines for teachers helping students experiencing difficulty in learning mathematics

As part of an ongoing project, we have developed a model of planning and teaching that is designed to assist teachers to help students overcome barriers they might experience in learning mathematics. The following is a discussion of one aspect of the model that we term “enabling prompts”. These refer to the directions, invitations, or questions that a teacher offers when interacting one-on-one with students experiencing difficulties. We argue that teachers should plan to pose subsidiary questions in the first instance, rather than, for example, offering further explanations. We outline our overall planning and teaching model, we present some examples of enabling prompts used by our project teachers, and we propose some considerations for teachers when structuring their own enabling prompts.

Sociocultural research on mathematics education : an international perspective

This volume--the first to bring together research on sociocultural aspects of mathematics education--presents contemporary and international perspectives on social justice and equity issues that impact mathematics education. In particular, it highlights the importance of three interacting and powerful factors--gender, social, and cultural dimensions. Sociocultural Research on Mathematics Education: An International Perspective is distinguished in several ways:

* It is research based. Chapters report on significant research projects; present a comprehensive and critical summary of the research findings; and offer a critical discussion of research methods and theoretical perspectives undertaken in the area.
* It is future oriented, presenting recommendations for practice and policy and identifying areas for further research.
* It deals with all aspects of formal and informal mathematics education and applications and all levels of formal schooling.

As the context of mathematics education rapidly changes-- with an increased demand for mathematically literate citizenship; an increased awareness of issues of equity, inclusivity, and accountability; and increased efforts for globalization of curriculum development and research-- questions are being raised more than ever before about the problems of teaching and learning mathematics from a non-cognitive science perspective. This book contributes significantly to addressing such issues and answering such questions. It is especially relevant for researchers, graduate students, and policymakers in the field of mathematics education.