I\u27m proud to be a toy teacher: Using CRA to become an even more effective teacher

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

Measurement: Five considerations to add even more impact to your program

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

Assessing children\u27s multiplicative thinking

Multiplicative thinking is a \u27big idea\u27 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\u27s 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

Process over product: It\u27s more than an equation

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

Investigating children\u27s multiplicative thinking

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 used to inform teaching

The shape of reasoning: Using geometry to promote the reasoning proficiency

Derek Hurrell shares a number of geometry tasks designed to tease out students\u27 reasoning. Concrete materials are used to initiate discussions and develop a culture of reasoning in the mathematics classroom

Australian curriculum linked lessons

In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, in this issue we focus on the Statistics and Probability strand

Conceptual knowledge OR Procedural knowledge OR Conceptual knowledge AND Procedural knowledge:Why the conjunction is important for teachers

: The terms conceptual knowledge and procedural knowledge are often used by teachers and never more so than when discussing how teachers teach, and children learn mathematics. This paper will look at literature regarding conceptual and procedural knowledge and their place in the classroom, to offer teachers and teacher educators’ advice on some of the more pressing issues and understandings around them. A thorough synthesis of extant and seminal literature will provide advice to teachers and teacher educators on how a deeper insight into conceptual and procedural knowledge could improve the quality of mathematics teaching

Sliding into multiplicative thinking: the power of the ‘marvellous multiplier

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\u27 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 this may be possible through the use of a device called \u27The Marvellous Multiplier\u27