This article describes some of the essential mathematics that underpins the use of algorithms through a series of learning pathways. To begin, a graphic depicting the mathematical ideas and concepts that underpin the learning of algorithms for multiplication and division is provided. The understanding and use of algorithms is informed by two…

This article describes Ulrich Kortenkamp's Place Value Chart app and the accompanying teacher guide developed by the members of an international research team led by regular contributor Kevin Larkin.

We are pleased to bring you this follow-up to Mairéad Hourigan and Aisling Leavy's article [EJ1289314] that was published in issue 1 this year. In this contribution, they demonstrate that embedding mathematics within a rich context and learning sequence assists with the consolidation of student understanding and makes more effective use of teacher…

Differentiating instruction can be difficult, however, when higher performing students yearn to be stretched and lower performing students benefit from scaffolded support. One way to meet these students' learning needs and everyone in-between is to embrace the notion of novel exploration in support of critical school mathematics concepts. Novelty…

It is frequently surprising to new teachers (and even those with experience) when they find that not only do some children need to recount the group they have just counted to be assured of the total but also that this need seems to be resistant to intervention. Although moving from "counting-all" to "count-on" is sometimes…

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.

In this article Jessica Hunt explores the use of clinical interviews to gain a deep understanding of students' knowledge. Examples of clinical interviews are provided and advice for planning, giving and interpreting the results of interviews is also included.

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

This article outlines the author's efforts to build her knowledge of students' understandings of mathematics whilst catering for different abilities within a Year 1 classroom, using the freely available "Assessment for Common Misunderstandings tools." "The Assessment for Common Misunderstandings" materials have been…

Lorna Quinnell and Merrilyn Carter examine the use of symbols in teaching mathematics and outline the difficulties students experience in "reading symbols and abbreviations." We are sure teachers will appreciate the way the authors have examined the use of symbols and abbreviations in NAPLAN testing and organized them into five distinct…

Decipipes are a representational model that can be used to help students develop conceptual understanding of decimal place value. They provide a non-standard tool for representing length, which in turn can be represented using conventional decimal notation. They are conceptually identical to Linear Arithmetic Blocks. This article reviews theory…

Place value underpins much of what people do in number. In this article, the author describes some simple tasks that may be used to assess students' understanding of place value. This set of tasks, the Six Tasks of Place Value (SToPV), takes five minutes to administer and can give direct insight into a student's understanding of the number system…

In 2008, the authors worked with a range of schools to trial ideas that assisted young Indigenous students to engage with mathematics as they enter the school environment. This article highlights some key pedagogical strategies that assisted classroom teachers to improve Indigenous students' understanding of mathematics, particularly in the area…

Children are often intrigued by number patterns and games and so it makes sense for teachers to include them in their mathematics lessons. Puzzles encourage the use of critical thinking skills and provide practice in important skills areas. The use of games fosters mathematical learning and encourages the mathematical processes that children use.…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…