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Hilton, Annette; Hilton, Geoff – Australian Primary Mathematics Classroom, 2018

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

Descriptors: Mathematics Education, Mathematics Instruction, Abstract Reasoning, Mathematical Logic

West, John – Australian Primary Mathematics Classroom, 2018

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

Descriptors: Mathematics Instruction, Mathematical Logic, Problem Solving, Fractions

Hurst, Chris – Australian Primary Mathematics Classroom, 2018

Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

Descriptors: Mathematics Instruction, Mathematical Logic, Multiplication, Teaching Methods

Bragg, Leicha A.; Herbert, Sandra – Australian Primary Mathematics Classroom, 2017

Mathematical reasoning is one of the four proficiencies in the Australian Curriculum: Mathematics (AC:M) where it is described as: "[the] capacity for logical thought and actions, such as analysing, proving, evaluating, explaining, inferring, justifying and generalising" (Australian Curriculum, Assessment and Reporting Authority [ACARA],…

Descriptors: Foreign Countries, Mathematics Instruction, Mathematics Skills, Mathematical Logic

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E. – Australian Primary Mathematics Classroom, 2017

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

Descriptors: Mathematics Instruction, Educational Games, Mathematical Logic, Access to Education

Vale, Colleen; Bragg, Leicha A.; Widjaja, Wanty; Herbert, Sandra; Loong, Esther Yook-Kin – Australian Primary Mathematics Classroom, 2017

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

Descriptors: Elementary School Students, Elementary School Teachers, Mathematical Logic, Creative Thinking

Otten, Mara; van den Heuvel-Panhuizen, Marja; Veldhuis, Michiel; Heinze, Aiso; Goldenberg, Paul – Australian Primary Mathematics Classroom, 2017

The importance of laying a foundation for algebraic reasoning at a young age is increasingly being emphasized. In this article, the authors report on an activity that elicits in a natural way algebraic strategies that in a later stage of learning algebra are crucial for solving equations. The activity brings about the students' spontaneous use of…

Descriptors: Mathematics Instruction, Algebra, Teaching Methods, Concept Formation

Fuentes, Sarah Quebec; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline – Australian Primary Mathematics Classroom, 2017

All students should have opportunities to develop their ability to reason mathematically. Gersten and Chard (1999) support this stance with respect to students with learning disabilities: "Even if students are not automatic with basic facts, they still should be engaged in activities that promote the development of number sense and…

Descriptors: Teaching Models, Mathematics Instruction, Mathematical Logic, Comparative Analysis

Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2017

A journey into multiplicative thinking by three teachers in a primary school is reported. A description of how the teachers learned to identify gaps in student knowledge is described along with how the teachers assisted students to connect multiplicative ideas in ways that make sense.

Descriptors: Elementary School Teachers, Elementary School Mathematics, Mathematics Instruction, Multiplication

Hurst, Chris; Hurrell, Derek – Australian Primary Mathematics Classroom, 2016

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

Descriptors: Multiplication, Mathematics Instruction, Algebra, Mathematical Logic

Taylor, Merilyn; Hawera, Ngarewa – Australian Primary Mathematics Classroom, 2016

Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

Descriptors: Probability, Educational Games, Mathematics, Mathematics Education

Russo, James – Australian Primary Mathematics Classroom, 2016

This article describes activities in which students deepen their relational understanding of the equals sign through exploring inequalities in a competitive dice game, built around the familiar fairy-tale "The Three Little Pigs" and "The Big Bad Wolf." The activity can be adapted to different abilities by choosing more or less…

Descriptors: Picture Books, Teaching Methods, Class Activities, Mathematics Education

Russo, James – Australian Primary Mathematics Classroom, 2016

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging task in Year 2.

Descriptors: Mathematics Instruction, Elementary School Mathematics, Teaching Methods, Mathematical Concepts

Russo, James – Australian Primary Mathematics Classroom, 2016

The Smarties-Box Challenge encourages students to apply several different mathematical capabilities and concepts--such as, estimation, multiplication, and the notion of being systematic--to solve a complex, multistep problem. To effectively engage in the Smarties-Box Challenge, students are required to demonstrate aspects of all four proficiency…

Descriptors: Problem Solving, Mathematics, Mathematical Concepts, Mathematics Instruction

Ramful, Ajay; Ho, Siew Yin – Australian Primary Mathematics Classroom, 2015

In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.

Descriptors: Mathematics Instruction, Problem Solving, Statistical Analysis, Mathematical Logic