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…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

This article provides a classroom resource for identifying, assessing and promoting one aspect of reasoning--analysing--through the Assessing Mathematical Reasoning Rubric. Practical examples of student work and rubric levels are offered.

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…

The importance and usefulness of building on perceptual subitising and the development of conceptual subitising is explained. A guide on how to continue to develop numerical ideas based on subitising is shared.

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…

This paper was originally presented at the 25th Biennial Conference of AAMT, 'Capital Maths', and published in the Conference Proceedings. The author discusses the development and beginning implementation of a detailed sequence of concepts, with the intention of supporting teachers to support students to understand place value.

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

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.

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.