Purpose: This paper compared the treatment of whole number multiplication and division in syllabi and textbooks from Zambia, South Africa and Japan. Design/methodology/approach: In-depth topic trace mapping was applied to determine when whole number multiplication and division were taught in the syllabi and textbooks. Vertical analysis involved…

True belonging requires more than welcome. Discover concrete strategies to create mathematics classrooms where students' thinking and identities are valued. This article explores how teachers can intentionally design for belonging in mathematics classrooms by integrating two powerful frameworks: Design for Belonging (Wise, 2022) and Complex…

This article examines how teachers with 'ability' grouped (set/streamed/tracked) classes describe their students' learning and behaviour, and how they teach such classes. We draw on teacher and student interviews and classroom observations from a study of about 450 Year Nine students (age 13-14) and their 16 mathematics teachers in three secondary…

Realistic Mathematics Education (RME) relies on the pedagogy of guided reinvention, in which opportunities for learning are created through the teacher's orchestration of whole-class mathematical discussion towards a specific goal. However, introducing an RME approach to students who are accustomed to traditional teaching requires a substantial…

The goal of this study is to identify the multiple ways in which instructors take advantage of a feature designed into university textbooks that seeks to invite students to get acquainted with the content prior to attending the class in which such content will be discussed. We present an analysis of teacher instrumentation of this feature, which…

Background: Many students solving quantitative problems in science struggle to apply mathematical instruction they have received to novel problems. The few students who succeed often draw on both their mathematical understanding of the equation and their scientific understanding of the phenomenon. Understanding the sensemaking opportunities…

The paper presents analyses of multivariable calculus learning-teaching phenomena through the lenses of DNR-based instruction, focusing on several foundational calculus concepts, including "cross product," "linearization," "total derivative," "Chain Rule," and "implicit differentiation." The…

Several new approaches to calculus in the U.S. have been studied recently that are grounded in infinitesimals or differentials rather than limits. These approaches seek to restore to differential notation the direct referential power it had during the first century after calculus was developed. In these approaches, a differential equation like dy…

In this article we consider two triangles: one inscribed in another. We prove that the area of the central triangle is at least the harmonic mean of the areas of corner triangles. We give two proofs of this theorem. One is based on Rigby inequality and the other is based on the known algebraic inequality, to which we bring a new, geometric, proof.…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

This paper conceptualizes children's mathematical thinking from a materialist perspective on language and mathematics. This perspective considers human and non-human bodies as ontologically equivalent; that is, as both being agentive, vibrant, and animated, thus resisting static representations. This conceptualization is an alternative to the…

Natural language helps express mathematical thinking and contexts. Conventional mathematical notation (CMN) best suits expressions and equations. Each is essential; each also has limitations, especially for learners. Our research studies how programming can be a advantageous third language that can also help restore mathematical connections that…

With mathematics education dominated by practices of standardized test alignment, the quest for mathematical understanding is adrift despite so much talk about the importance of STEM subject matters. To add to the confusion there has long been worries among educators about any curricular programs or instructional practices that can be labeled…

This is the fifth in a series of statistical articles for mathematics teachers. In this article the authors discuss graphs for exploring relationships between one categorical variable and one numerical variable using stemplots and boxplots and between two numerical variables, using scatterplots and time series plots. [For "The Data Files 4:…

Parents and caregivers can use the activities in this report to help youth learn to solve algebra problems using different strategies. Knowing different strategies for solving algebra problems may help your child approach algebra problems with confidence. Children could apply the most appropriate strategy for a particular problem or could try a…