Digital Commons Network^™

Process Over Product: It's More Than An Equation, Lorraine Day, Derek Hurrell

Derek Hurrell

Developing number and algebra together provide opportunities for searching for patterns, conjecturing, justifying, and generalising mathematical relationships. It allows the focus to be on the process of mathematics and noticing the structure of arithmetic, rather than the product of arriving at a correct answer. Two of the big ideas in mathematics are multiplicative thinking and algebraic reasoning. By noticing the structure of multiplicative situations, students will be in a position to reason algebraically, and the process of reasoning algebraically will allow students to appreciate the value of thinking multiplicatively rather than additively.

Assessing Children's Multiplicative Thinking, Chris Hurst, Derek Hurrell

Derek Hurrell

Multiplicative thinking is a 'big idea' of mathematics that underpins much of the mathematics learned beyond the early primary school years. This paper reports on a current study that utilises an interview tool and a written quiz to gather data about children's multiplicative thinking. The development of the tools and some of the research findings are described here. Findings suggest that middle and upper primary aged children often have a procedural level of understanding of aspects of multiplicative thinking and that various aspects of multiplicative thinking are partially known, and known in different ways by different children.

Sliding Into Multiplicative Thinking: The Power Of The ‘Marvellous Multiplier, Chris Hurst, Derek Hurrell

Derek Hurrell

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times relationship between places in the number system and what happens when numbers are multiplied or divided by powers of ten. Evidence from the research project discussed here suggests that many students have a procedural view of these ideas, and that a conceptual understanding needs to be developed. It is suggested that …

I'M Proud To Be A Toy Teacher: Using Cra To Become An Even More Effective Teacher, Derek Hurrell

Derek Hurrell

The role of manipulative materials in mathematics can be a contentious one. It seems that in the mind of some teachers, manipulatives are fine in the early years but have no place in a rigorous maths classroom as the students get older. It is a topic worth our consideration.

Effectiveness Of Teacher Professional Learning : Enhancing The Teaching Of Fractions In Primary Schools, Derek Hurrell

Derek Hurrell

This study was motivated by the need to develop professional learning for primary school teachers that would support them to more effectively teach the mathematics topic of fractions. What seemed evident, was that previous professional learning attended by teachers had not adequately met their needs.

The aim of this study was to investigate whether professional learning, with a focus on subject content knowledge, pedagogical knowledge and reflective practice could enhance primary school teachers’ PCK for teaching fractions and make them more confident teachers of fractions. Demonstrating this to be the case would have wide implications for the development of professional …

A Case Study Of Effective Practice In Mathematics Teaching And Learning Informed By Valsiner's Zone Theory, Vince Geiger, Vince Geiger, Judy Anderson, Judy Anderson, Derek Hurrell

Derek Hurrell

The characteristics that typify an effective teacher of mathematics and the environments that support effective teaching practices have been a long-term focus of educational research. In this article we report on an aspect of a larger study that investigated ‘best practice’ in mathematics teaching and learning across all Australian states and territories. A case study from one Australian state was developed from data collected via classroom observations and semi-structured interviews with school leaders and teachers and analysed using Valsiner’s zone theory. A finding of the study is that ‘successful’ practice is strongly tied to school context and the cultural practices …