In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas.…

The authors define two mathematical cognitive verbs which are fundamental to the development of mathematical thinking and reasoning. They distinguish between 'describing' and 'explaining' in relation to doing mathematics, rather than using them interchangeably.

Teacher knowledge is one of the main factors in the quality of mathematics learning. Many mathematics teachers have difficulty using proportional reasoning. Proportional reasoning is one of the essential aspects of the middle school mathematics curriculum to develop students' mathematical thinking. Teachers should realize that developing…

This paper describes results from a case study about how a primary pre-service teacher (PST) used curriculum materials (CMs) when planning for a mathematics lesson during her final practicum. The data is drawn from a doctoral study (in progress) and results show how the PST initiated an active process of searching for and sifting through CMs on a…

The importance of multiplicative thinking in supporting students' learning of key topics and success in further mathematics is widely and clearly stated in mathematics education literature. However, multiplicative thinking is not clearly stated in curriculum documents of many countries including Australia. In the "Australian Curriculum:…

This article considers the development of synthetic landscapes of multiplicative reasoning constructed by student teachers (pre-service teachers). It explores the implications of working in a way that integrates literature from Maths Recovery, Cognitively Guided Instruction and Realistic Mathematics Education approaches. The aim is to better…

This qualitative descriptive study was designed to address the deficiency in early math literacy skills, specifically those related to multiplication fact fluency, in early elementary students. More specifically, this study was designed to gather research and data to provide understanding of the mathematical curriculum instruction used in…

This paper deals with the nature of teaching mathematical thinking and presents a case study of a single Japanese lesson where the characteristics of mathematical thinking and the teaching thereof are identified in relation to multiplication. The raison d'être for this teaching is questioned and investigated by looking at how multiplication is…

The movie "Frozen" took the world by storm and this global popularity of the movie and its music can be harnessed by teachers of mathematics. This article builds on the "frozen fractal" lyric from "Let It Go" to incorporate fractal geometry into primary mathematics classrooms.

This article explores how a focus on understanding divisibility rules can be used to help deepen students' understanding of multiplication and division with whole numbers. It is based on research with seven Year 7-8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a…

Of the "big four", division is likely to regarded by many learners as "the odd one out", "the difficult one", "the one that is complicated", or "the scary one". It seems to have been that way "for ever", in the perception of many who have trodden the learning pathways through the world of…

This study examined the impact of a commercially available math fluency intervention program on the basic multiplication fluency of three classrooms of fifth grade students. Baseline assessment and progress monitoring of thirty-three regular- and eleven special education students occurred over nine weeks. Within-group analyses revealed significant…

The multiplication and division algorithms that are taught in German schools are presented. It is suggested that these algorithms may be better than standard algorithms in terms of development of useful concepts and processes. (MK)

Developed by the Initial Learning in Mainstreaming Project, the manual presents an instructional program to teach mainstreamed handicapped elementary school students multiplication with multipliers of up to three digits. In addition to detailed teaching instructions and text of tape recordings for students, the manual includes tests, worksheets,…

Discussed is the topic of least common multiple (LCM), a rationale for its importance, and suggestions for when and how to teach it. (RH)