Janette Bobis

Supporting Teachers in the Development of Young Children's Mathematical Thinking: Three Large Scale Cases.

Recognition of the importance of the early childhood years in the development of numeracy is a significant characteristic of the New Zealand Numeracy Development Project, the Victorian Early Numeracy Research Project and the Count Me In Too program in New South Wales, Australia. This article outlines the background, key components and major impacts of these three innovative and successful professional development and research initiatives. Juxtaposing the three projects highlights important commonalities—research-based frameworks, diagnostic interviews, and whole-school approaches to professional development. Each program has been significant in rethinking what mathematics and how mathematics is taught to young children.

Cognitive Load Effects in a Primary-School Geometry Task.

Abstract Cognitive load theory suggests that some instructional procedures are ineffective because they require students to engage in superfluous cognitive activities purely because of the manner in which the material is presented rather than because of its intrinsic nature. When students are forced to process redundant material or split their attention between multiple sources of information, an extraneous cognitive load may be imposed. Four experiments were designed to investigate the redundancy and split-attention effects using a primary-school paper-folding activity. Experiment 1 indicated that instructional presentations with extraneous information eliminated were superior to formats containing redundant material. Experiment 2 indicated that the redundancy effect could be increased if more elaborated text was included in the redundant format of the instructional material. The aim of Experiment 3 was to test the prediction that the redundancy effect could also be generated by the inclusion of extraneous diagrams. It was found that redundant instructional material could increase cognitive processing load even when all redundant information is conveyed diagrammatically. Experiment 4 indicated that a format in which instructions were embedded in materials that required manipulation could facilitate learning by reducing redundant information and removing the need to split attention between physically separated materials. It was concluded that the usefulness of additional information must outweigh the consequences of having to process that information.

Exploring the Ups and Downs of Mathematics Engagement in the Middle Years of School

This study of 1,601 students in the middle years of schooling (Grades 5-8, each student measured twice, 1 year apart) from 200 classrooms in 44 schools sought to identify factors explaining gains and declines in mathematics engagement at key transition points. In multilevel regression modeling, findings showed that compared with Grade 6 students (upper elementary; the reference category), students in Grades 7 (typically the first secondary school year) and 8 have significantly declined in mathematics engagement from their previous year. Notably, in further analyses, these declines were found to be related to student (particularly mathematics self-efficacy and valuing), home (parent valuing of mathematics and availability of a computer for mathematics), classroom (class-average achievement and perceived climate), and school (socio-economic status and ethnic composition) factors. Implications for research and practice are discussed.

PROFESSIONAL KNOWLEDGE OF PRACTISING TEACHERS OF MATHEMATICS

Teachers’ knowledge of mathematics has become a central focus of educational researchers and policy makers with conceptions of teacher knowledge continuously being transformed. Intuitively, we have known for some time what research now provides an evidence base for—that “teacher knowledge matters” (Sullivan, 2008b, p. 2). But exactly what knowledge matters more, and why, are more significant and vexing questions for researchers and educators to address. Consequently, attention has moved beyond looking solely at what knowledge teachers possess to why different types of knowledge are important and how that knowledge is acquired, studied and impacts on the quality of instruction.

THE EFFECT OF INSTRUCTION ON THE DEVELOPMENT OF COMPUTATIONAL ESTIMATION STRATEGIES

The purpose of this research was (a) to investigate the effect of instruction on the development of computational estimation strategies, (b) to conduct exploratory investigations into the types of errors made after instruction, and (c) to investigate the degree of success in determining a close estimate after instruction. The research sample consisted of 101 fifth grade hoys from two schools in the same local region. Two tests were used. An Initial Evaluation Test (IET) was used at the pre- and post-test stages to assess children’s performance on estimation prerequisite skills such as place-value, rounding and skills pertaining to basic facts. A Computational Estimation Test (CET) was developed to assess the estimation ability of subjects at the pre- and post-test stages. Prior to post-testing the experimental group underwent fifteen weeks of instruction in computational estimation thinking strategies. IET post-tests revealed that both groups improved upon their prerequisite skills of estimation, but that the experimental group’s performance was significantly better than the control group’s. CET post-test results indicated a significant improvement on the performance of the experimental group and no significant improvement by the control group. Interviews revealed that most students successfully adopted the estimation strategies taught to them as well as indicating the areas where errors were made most frequently.

Teaching Mathematics Thematically: Teachers' Perspectives

Teaching mathematics through themes has been praised for relating mathematics to real-life situations. However, research shows that the implementation of teaching mathematics thematically has not been widely adopted. In the present study, instructional, curricula and organisational factors that teachers perceive as obstacles to the implementation of a thematic approach to teaching mathematics were explored. Findings from interviews with 10 secondary mathematics teachers who were implementing a curriculum requiring a thematic instructional approach are reported. The findings of the study extend the literature concerning teachers’ beliefs and practices in the teaching of mathematics, and broaden understandings of the issues surrounding the implementation of a thematically taught mathematics curriculum.

Researching Curriculum, Policy and Leadership in Mathematics Education

This chapter reviews research regarding the official mathematics curriculum and its enactment, the educational leadership to support this enactment, and the associated influential policy, such as national testing. It explores the interrelationships between inherent issues such as the potential influence of textbooks, curriculum equity, and the complexities of implementing numeracy across disciplines. Substantial research has led to the development of robust theoretical models to inform both future research and practical developments across a range of aspects of curriculum, policy and leadership. However, the seemingly diverse research perspectives are all drawn towards the teacher in the classroom as the critical context for further research.

Building Connections Between Children’s Representations and Their Conceptual Development in Mathematics

Young children’s representations of their mathematical experiences occur as a natural part of their everyday lives. They can occur in a variety of forms, including their drawings, play, writing, gesturing, and more recently, digital productions. These representations are an essential part of young children’s general cognitive, social, and emotional development. During the early years of schooling, children are expected to formalize their representations through increased use of symbols, conventional structures, and mathematical language. Supporting children to make explicit connections between their representations and mathematical concepts is an essential activity for early childhood teachers. Both researchers and teachers need to understand the nature of representations and the role they play in young children’s mathematics learning. In this chapter, we focus on the mathematical representations produced by children in their first two years of school (five- to six-year-olds). We revisit data from our previous research to generate new interpretations and propose new lines of inquiry that aim to extend our understanding of student-generated representations. In doing so, we also highlight the important role early-year teachers play in helping to build connections between young children’s representations and their conceptual development in mathematics.

Transforming Educational Practice Through Action Research: Three Australian Examples

Action research has played a major role in the history of educational inquiry in Australia. Recognition of its potential transformative powers has resulted in action research often being the preferred inquiry approach across a wide variety of educational contexts. In this chapter, we provide a succinct historical overview of some important education action research programs in Australia before critically examining three contemporary examples of Australian initiatives in our attempt to explore whether action research can bring about transformations of educational practice. We make a distinction between solely technical aspects of schooling and the more far-reaching improvements to teaching and learning facilitated through action research. In so doing, we highlight some compelling issues confronting the future of educational action research in Australia.