In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…

This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…

Developing and supporting understanding of the meaning of multiplication and multiplicative relationships in students with mathematics learning disabilities requires carefully designed instruction that emphasizes strategic representation use. This article discusses three ways in which teachers can incorporate multiple representations within…

This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

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.…

Research has shown that many primary students experience transition barriers between additive and multiplicative thinking. This paper analysed responses from 253 Years 3 to 6 students to a diagnostic assessment which consists of whole number multiplication and division problems involving equal groups, arrays, multiplicative comparison and…

This study sought to use indigenous ("Adinkra") artefacts to present "Concreteness Fading" in multiplication of one-digit and one-digit numbers. The researcher used simple random sampling technique to select 51 participants from 300 student teachers. Two sets of tests were used to collect the data. The results were equally…

In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic…

How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

This study used a constructivism theoretical framework to focus on a group of elementary mathematics teachers and their lived experiences after the introduction of new mathematical content standards through the lens of the Mathematical Teacher's Specialized Knowledge Model. After the introduction of new mathematics content standards, many…

When teaching the multiplicative domain in New Zealand primary schools, teachers tend to spend a greater proportion of time on the meaning and processes of multiplication, to the detriment of a specific focus on understanding the concept of division. When division is taught, it tends to be by reversing the context and turning the division…

Representations are used throughout school mathematics for students to both think through a problem and communicate their ideas. Students also often come to mathematics class with a repertoire of representations. This article presents the ideas of different and multiple representations with conceptual connections as their underlying distinguishing…

Developing and supporting understanding of the meaning of multiplication and multiplicative relationships in students with mathematics learning disabilities requires carefully designed instruction that emphasizes strategic representation use. This article discusses three ways in which teachers can incorporate multiple representations within…

This study examined a cohort of middle school pre-service mathematics teachers' understanding of the rate of change as they engaged in a model development sequence. By adopting a design-based research perspective, a model development sequence on the concept of rate of change has been designed and implemented as part of a mathematical modeling…