This paper examines how different approaches in mathematics education conceptualise the relationship between school mathematics and university mathematics. The approaches considered here include: (a) Klein's elementary mathematics from a higher standpoint; (b) Shulman's transformation of disciplinary subject matter into subject matter for…

In this participatory research, two pre-service teachers (PSTs) and a mathematics teacher educator (MTE) collaboratively analyzed multiple voices that influence syllabi from elementary mathematics teaching methods courses. Findings suggest syllabi fall along a continuum from harmonious to dissonant orchestration of the voices of past and present…

The analysis of the content of school textbooks, particularly in a time of cross-cultural borrowing, is a growing field restricted by the tools currently available. In this paper, drawing on the analyses of three English year-one mathematics textbooks, we show how two approaches to the analysis of sequential data not only supplement conventional…

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

The multiplicative reasoning that students should develop in elementary school is a key area of research in contemporary mathematics education. Researchers employ various views including multiplication as arithmetic operation, multiplicative structures, and multiplicative relationships. They also propose various classifications of multiplicative…

This theoretical paper examines views about the role of language and mathematical discourse in learning mathematics. Current research is still addressing what constitutes a mathematical discourse. As new conceptions of the purpose of language use in mathematics are explored, and associated ontological and epistemic positions are revealed, one…

This article explores the potential of using children's literature in elementary mathematics classrooms as contexts for students to understand more fully the issues of equity, diversity, and inclusion. Informed by culturally responsive pedagogy, opportunities to link children's literature to mathematics education create cultural relevance for…

In this paper, we list some of the areas of the Australian curriculum that have links with the concept of infinity. We do this in order to promote a discussion about what aspects of infinity should become familiar to primary teachers. From our viewpoint, infinity has connections with Algebra, Art, Geometry and Measurement, Probability, Science and…

Many elementary education programs have only one mathematics methods course designed for preservice teachers (PTs). Such courses typically cover a range of content and present a challenge for mathematics teacher educators (MTEs) who strive to prepare their PTs to teach mathematics in equitable and humane ways. Due to the "stand-alone"…

One characteristic of high-quality mathematics teaching is supporting students in engaging in tasks of high cognitive demand. In this paper, we explore relationships between two elementary teachers' efforts to integrate computational thinking (CT) practices--abstraction, debugging, and decomposition--into their mathematics instruction and their…

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

In this article Dan Jazby also explores the issue of noticing, but this time from the teacher's perspective. Dan argues that teacher noticing is a purposeful activity that requires both the technical skills to recognise how students are thinking and the tactical skills to know when and where to look for particular cues.

Nat Banting, argues that the "invert and multiply" algorithm for division of fractions is, in fact, not an algorithm. He suggests that Liping Ma's (1999) algorithm, which involves writing the fractions with a common denominator and then dividing the numerator of the first fraction by the numerator of the second fraction, is better as it…