Auditing the Numeracy Demands of the Middle Years Curriculum

The National Numeracy Review Report recognized that numeracy development requires an across the curriculum commitment. To explore the nature of this commitment we conducted a numeracy audit of the South Australian Middle Years curriculum, using a numeracy model that incorporates mathematical knowledge, dispositions, tools, contexts, and a critical orientation. All learning areas in the published curriculum were found to have distinctive numeracy demands. The audit should encourage teachers to promote numeracy in even richer ways in the curriculum they enact with students

Changing classroom practice through a rich model of numeracy across the curriculum

This paper reports on a research and development project that helped teachers to plan and implement numeracy strategies across the school curriculum. It presents a rich model of numeracy whose elements comprise mathematical knowledge, dispositions, tools, contexts, and a critical orientation to the use of mathematics. This model is then applied to analyse changes in one teacher’s planning, classroom practice, and personal conceptions of numeracy

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods

USING DIGITAL PHOTOGRAPHY TO SUPPORT TEACHING AND LEARNING OF PROPORTIONAL REASONING CONCEPTS

Abstract Proportional reasoning entails multiplicative relationships in situations of comparison. Successful proportional reasoners can recognise a proportional situation as distinct from a non-proportional one; they have a sense of co-variation and they have a range of strategies for solving proportional problems. As educators we realise that teaching proportional reasoning cannot solely rely on asking students to complete symbolic and mechanical methods, such as the cross-product algorithm. To develop proportional reasoning, students must have regular opportunities to experience the underlying concepts. These concepts include foundational aspects of proportional reasoning, such as fractional thinking, multiplicative thinking (as opposed to additive), relative thinking (as opposed to absolute), as well as concepts of rate and scale. As part of a large multi-state project in Australia to enhance middle years students' numeracy through a focus on proportional reasoning, 120 teachers participated in a series of professional learning workshops. These teachers generally reported feeling confident teaching the algorithmic aspects of proportional reasoning but a number of them specifically asked for assistance with the conceptual development of their students' proportional reasoning. In response, the researchers developed a series of activities with the teachers, where digital cameras were used in the school environs to capture images that represented examples of proportional reasoning concepts. In small groups, the teachers moved around the school taking their photos and then reported back to the workshop, showing their images through a data projector while they explained the concepts they felt their images captured. This presentation articulates the ways that the digital cameras were used by the teachers to capture and report on the proportional reasoning concepts, and their thoughts and aspirations as to how they would use the cameras to develop the proportional reasoning of their students

Applying psychological learning theory to helping students overcome learned difficulties in mathematics: An alternative approach to intervention

The appearance of systematic errors in computation suggests relatively unlinked computational knowledge to conceptual knowledge, and hence difficulties with forward learning of mathematics. The provision of programs of good teaching, where concrete materials are used to exemplify and thus legitimize algorithmic processes, frequently are not effective for use with upper primary students: systematic errors often resurface. A novel and quite alternate approach to intervention is the Old Way/New Way (O/N) strategy (Lyndon, 1989) based on psychological principles of memory, forgetting and interference. In this article, issues associated with intervention, systematic errors and upper primary students are addressed through a discussion of results of previous research into seventh graders' subtraction knowledge development by overcoming error patterns in subtraction computation. By comparing re-teaching strategies and O/N, it is proposed that both good teaching and effective intervention strategies should be integral to the craft of teaching, particularly in the middle school

Investigating Textbook Presentations of Ratio and Proportion

Many topics within the middle school mathematics curriculum connect to the concept of proportion. Interpretation of proportion situations and understanding of methods for solving proportion problems provides a structure than can be applied to other related topics. As a major resource for secondary mathematics, the extent to which popular textbooks link proportion-related topics was the focus of this study. Our analysis revealed little connectivity of ideas, confusing definitions and frequently illogical calculations. Questions are raised as to the messages texts send to students

An analysis of middle-years school mathematics textbooks

Studies have shown that a set mathematics textbook chosen by teachers is the dominant resource in mathematics classrooms in Australia and many countries throughout the world. The textbook exerts a strong influence on both content and pedagogy. In this study, a method of analysing textbooks was developed and applied to three middle years mathematics textbook series. The method was based on two pedagogical principles related to deep understanding, namely connectedness and structure and context, and focused on mathematical ideas based on proportional reasoning. The study found that the textbooks provided little support for the pedagogical principles. In most cases, the textbooks presented a specific procedure for each problem type, with little or no recognition of similar structures in different problem contexts

Instruction to Support Mental Computation Development in Young Children of Diverse Ability

Fostering young children’s mental computation capacity is essential to support their numeracy development. Debate continues as to whether young children should be explicitly taught strategies for mental computation, or be afforded the freedom to develop their own. This paper reports on teaching experiments with two groups of students in their first year of schooling: those considered ‘at-risk’, and those deemed mathematically advanced. Both groups made considerable learning gains as a result of instruction. Importantly, the gains of the at-risk group are likely to renew both their own, and their teacher’s confidence in their ability to learn. In this paper, the instructional programs are documented, highlighting the influence of instruction upon the children’s development

The use of a new mathematics text book scheme- Support or impediment.

School mathematics textbooks are used in varying ways and to varying degrees by teachers and schools. The textbook materials of focus in this study were designed in accordance with current curriculum reform principles, advocating a student-centred approach that emphasises conceptual understanding and fostering of students’ thinking and mathematical communication. The purpose of this study was to investigate the impact of a new reform-based mathematics textbooks series on teachers’ classroom practices. Observations were conducted in six primary teachers’ mathematics classrooms as they implemented the new textbook series. The observations were combined with interview data to explore the impact of the textbook upon teachers’ classroom practice. Through combining interview data with classroom observations, this study provided a snapshot of various teachers’ use of new curriculum materials. It was apparent from this study that the materials were used to varying degrees of effectiveness by individual teachers. Results suggested that when the textbook was regarded as a resource, quality pedagogy was enacted. Conversely, if teachers felt challenged by the new reforms evidenced in the textbook they tended to follow the textbook in a prescriptive manner, resulting in teacher-directed pedagogy