This article examines the mathematics learning experiences in proportional reasoning I created for pre-service teachers in my teacher education course in Canada. The approach aimed to enable pre-service teachers to work on and with their prior mathematics understandings, make connections that were particular to what emerged during group work, and…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This paper presents a mobile app, AlgeOps, created to assist students in understanding addition and subtraction of integers. The design of the app amalgamated the neutralization model (based on cancelling integers of opposite signs) and the number line model to offer a more holistic representation of integers. Furthermore, since AlgeOps presents…

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 article draws on some ideas explored during and after a writing workshop to develop classroom resources for the reSolve: Mathematics by Inquiry (www.resolve.edu.au) project. The project develops classroom and professional learning resources that will promote a spirit of inquiry in school mathematics from Foundation to year ten. The…

The relationships between three critical elements, and the associated mathematical language, to assist students to make the critical transition from additive to multiplicative thinking are examined in this article by Chris Hurst.

Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

This paper focuses on an implementation a sequence of instructional activities about addition of fractions that has been developed and implemented in grade four of primary school in Surabaya, Indonesia. The theory of Realistic Mathematics Education (RME) has been applied in the sequence, which aims to assist low attaining learners in supporting…

This article outlines how a Brisbane independent school, Clayfield College, improved the ability of its Year 3 students to solve addition and subtraction word problems by utilising a schematic approach. It was observed that while students could read the words in the text of a written problem, many had difficulty identifying the core information…

Ever since "mental arithmetic" was updated to "mental calculation," official documents have succeeded in perpetuating several basic misconceptions and misunderstandings about this topic. This situation does not augur well for the successful teaching of mental calculation strategies to young children. In this article, the author…

Direct instruction techniques were employed in a structured parental involvement program targeted toward improvement of basic arithmetic skills in six students ages 7-8. Among reported results was a statistically significant posttest improvement on an addition placement test compared to a control group performance without parental involvement. (JW)

A program for teaching "number sense" is suggested based on experiences in teaching numeracy to Papua New Guinean adults. Number sense starts out with some sort of "feel" about the size of a number and extends upwards to include any such mental arithmetical skills as can reasonably be incorporated in an appropriate program.…