In this study, using ADDIE instructional design model, it is aimed to prepare English language educational material for 4th grade primary students to teach them numbers. At the same time, ARCS model of motivation's attention, relevance and satisfaction phases are also taken into consideration. This study also comprises of Design Based Research…

There is a general perception that the South African curriculum statements for mathematics create polarity between the 'old' and the 'new', which does not benefit both the teachers and the learners. The new curricula demand a radical shift from the traditional teacher-led approaches that teachers are familiar with, yet does not provide a model of…

This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concrete learning…

Teachers and researchers have known for decades that the use of storybooks can have a positive impact on students' experiences with mathematics. This article describes how first graders in an urban public school actively engage with mathematics by using the story "Bean Thirteen" as a context for developing number sense. This…

In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…

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…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…

One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

It is important to avoid ambiguity with numbers because unfortunate choices of numbers can inadvertently make it possible for students to form misconceptions or make it difficult for teachers to tell if students obtained the right answer for the right reason. Therefore, it is important to make sure when introducing basic summary statistics that…

Many students experience great difficulty understanding the meaning of fractions. For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is…