Education Commons^™

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 …

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

Derek Hurrell

No abstract provided.

Tasks And Resources For Developing Children's Multiplicative Thinking, Derek Hurrell, Chris Hurst

Derek Hurrell

The development of multiplicative thinking determines largely the extent of the mathematics that a person learns beyond middle primary school. Our current research project has so far revealed that many primary children have a procedural view of aspects of multiplicative thinking that we believe inhibits their progress. This workshop focuses on some of the teaching resources and tasks that have been developed from our research. The purpose of these tasks is to promote the development of conceptual understanding of 'the multiplicative situation' and the many connections within it and with other big ideas such as proportional reasoning and algebraic thinking.

An Explanation For The Use Of Arrays To Promote The Understanding Of Mental Strategies For Multiplication, Lorraine Day, Derek Hurrell

Derek Hurrell

This article provides a convincing argument for using arrays to promote students’ understandings of mental computation strategies for multiplication. Also a range of different examples that illustrate the benefits of arrays in the primary classroom are provided.

Developing Proportional Reasoning, Derek Hurrell, Lorraine Day

Derek Hurrell

Proportional reasoning is one of the big mathematical ideas students will encounter. It applies to a wide range of contexts across all of the content strands and is considered a critical concept for success in secondary mathematics. It requires an ability to think multiplicatively and relationally, and is often problematic for students.

The Importance Of Fractions In Being A Successful Mathematics Student, Derek Hurrell, Lorraine Day

Derek Hurrell

Research and experience tells us that fractions are not easy to teach and learn and that a solid conceptual understanding of fractions has far reaching ramifications in the secondary mathematics classroom. A failure to acknowledge and remediate 'inherited' challenges to this understanding may result in the further success of students being severely impeded.

The Reasoning Proficiency, Lorraine Day, Derek Hurrell

Derek Hurrell

If students are to reason mathematically, they need to be engaged in mathematically rich, investigative tasks that allow them to explain their thinking, justify the strategies they use and the conclusions they reach, and adapt the known to the unknown. 1he importance of contextualised Learning should be highlighted so students may be encouraged to transfer their learning from one context to another, explain their choices within a context, and compare and contrast related ideas. 1he reasoning proficiency naturally interrelates with the understanding, problem solving and fluency proficiencies.v

Measurement: Five Considerations To Add Even More Impact To Your Program, Derek Hurrell

Derek Hurrell

The potential of using Measurement as a way of “tuning students into mathematics” is demonstrated. Five ideas that can form the basis of focusing on measurement to access other strands of the mathematics curriculum are examined.

Learning Environments That Support The Development Of Multiplicative Thinking, Derek Hurrell, Lorraine Day

Derek Hurrell

Given the right learning environment primary aged children can and do develop the capacity to think multiplicatively. Through vignettes taken from interviews with a Year 5 class during a research project, the optimal conditions for the conceptual development underpinning multiplicative thinking is examined.

Developing The Big Ideas Of Number, Chris Hurst, Derek Hurrell

Derek Hurrell

The mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) of primary and elementary teachers at all levels of experience is under scrutiny. This article suggests that content knowledge and the way in which it is linked to effective pedagogies would be greatly enhanced by viewing mathematical content from the perspective of the ‘big ideas’ of mathematics, especially of number. This would enable teachers to make use of the many connections and links within and between such ‘big ideas’ and to make them explicit to children. Many teachers view the content they have to teach in terms of what curriculum …

Investigating 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. The conference presentation reports on a recent study that utilised an interview tool to gather data about children’s multiplicative thinking. Using a workshop format, we present some of the interview tool and some of the findings, as well as demonstrate how the tool can be used for planning, teaching and assessment. The session also emphasises the importance of developing deep conceptual understanding as opposed to the teaching of procedures. This paper considers how evidence from the interview can be …