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.

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 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…

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, "Everyday Mathematics" (EM) and "Connected Mathematics 3" (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems…

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…

In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: "Everyday Mathematics" (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that…

The aim of the present study was to develop an on-line assessment system with constructed response items in the context of elementary mathematics curriculum. The system recorded the problem solving process of constructed response items and transfered the process to response codes for further analyses. An inference mechanism based on artificial…

This submission contains the Proceedings of the 2013 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Brock University in St. Catharines, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This guide is a collection of ideas for mathematics activities which were assembled and tested by primary teachers. The activities supplement the teaching of basic numeracy and include topics such as algorithms, pyramids, magic squares, multiples, and number values. The guide is organized into four sections: (1) addition and subtraction; (2)…

This study focused on the way mathematics was taught in selected primary school classrooms. The study involved the observation of 21 fourth-grade classes in eight schools over a two-week period. Results indicated a hiatus between what was taught and what should be taught and between how mathematics is taught and how it should be taught.…

These conference proceedings include two invited lectures, three working group reports, three topic group reports, two Ad Hoc group reports, a round table report, a list of participants, and a list of previous proceedings. The invited lectures were: "Values in Mathematics Education" (Ubiratan D'Ambrosio) and "Remarks on…