Alternative learning trajectories

Lesson planning usually involves the generation of a hypothetical learning trajectory. This paper illustrates a teaching strategy that is one focus of a major research project. Alternative learning trajectories with different entry level prompts were used to enable students to access the concepts and procedures necessary for their joining the main learning trajectory. The strategy is being trialled in primary classrooms that have a large proportion of lower SES students, with the aim of maximising success in mathematics for all students.<br />

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.<br />

Open ended tasks and barriers to learning : teachers' perspectives

Examines barriers to learning mathematics when using an open-ended task teaching strategy. Features of an open-ended task; Benefits of an open-ended task; Problems concerning multiplicity of responses and contexts in an open-ended task.<br /><br />

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.<br />

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. <br />

Increasing access to mathematical thinking

This article is a contribution to understanding of teacher actions that can contribute to a successful mathematics learning experience, defined as one that engages all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. We offer an example of a task that can form the basis of such a learning experience. The key elements are that the task is open-ended, that the teacher offers specific pedagogical prompts to support student leaning, that the teacher builds a sense of community by ensuring that there are some common experiences, and the teacher prepare prompts that can be used to support students who are experiencing difficulty, or to extend those students who complete the<br />basic task readily.<br />

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&ndash;12) class.<br />

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.<br /><br />