This study explores contradictions that emerge when utilizing a flipped classroom approach to university mathematics education. The work uses Activity Theory and its principle of dialectical contradiction as a theoretical framework to identify and analyse contradictions that arise in flipped mathematics classrooms for engineering students. Data…

This study aims to investigate the non-algebraic solution strategies that prospective mathematics teachers use to solve word problems and their thought process while they were solving the problems. A total of 76 prospective mathematics teachers were asked to solve two word problems without using algebraic solutions and, then, clinical interviews…

While the culture of many mathematics departments inflects strongly towards STEM, most mathematics departments also offer a significant number of introductory courses intended for both STEM and non-STEM majors. We are a group of mathematicians who, in this work, examine the intent and goals of a university mathematics education for the non-STEM…

It is generally agreed that good subject knowledge is an important prerequisite for successful teaching. However, what constitutes good subject knowledge is debated, with multiple perspectives taken by policymakers, researchers and schools. This article reports on research into interpretations of 'understanding mathematics in depth' (UMID) of…

Several teaching moves have been suggested to support young children's simple addition and subtraction performance, including use of a number path, directly modeling addition and subtraction, using mathematical symbols, and modifying problem difficulty. In the present study, teacher-researchers implemented an early arithmetic activity, "Big…

Much like one's experiences with the wonders of the world, concrete and multiperspective representations of mathematical concepts are key to understanding. Ideally, "learning environments should give students the opportunity to get to know different representations of a mathematical object in order for them to develop an appropriate…

The transition to tertiary mathematics requires students to use definitions of mathematical objects instead of intuitions. However, routines of defining and of proving with definitions are difficult to engage in, as they are not familiar to students who come from secondary school mathematics. Defining is highly complex because of its underlying…

Increasingly, digital technologies are being utilised to provide opportunities for teacher professional learning (PL) in fully online, blended and face-to-face environments. Videos have been used extensively across the three modes of delivery but there appears little research on the conceptual framing underpinning their development. This article…

Potential benefits of providing elementary school students experiences with coding robots are well-documented. These include building skill sets related to logical thinking, problem solving, persistence, collaboration, and communication (Harrell 2015). The authors embrace the value of coding in helping elementary school students develop these…

Folk wisdom of the state of Montana asserts that Flathead Lake, located in the state's northwest corner, is the largest natural freshwater lake west of the Mississippi. But what does it mean to be the "largest?" And, how does one respond to Californians' claims that Lake Tahoe, located on the California-Nevada border, is the rightful…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman's New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by…

Academic vocabulary networks were examined in 3 elementary grades textbook programs (first through fifth grade) in 3 domains--science, mathematics, and social studies. Within each program, a given network consisted of a focal domain-specific academic word and the collection of words from all grades that overlapped in meaning with the focal word.…

South African Universities are exploring pedagogic strategies that inspire and engage students with module content. One such strategy is the use of technology-based tools such as smartphones within Higher Education. The purpose of this study was to explore pre-service teachers' use of WhatsApp instant messaging when learning mathematics. To…

We examined asynchronous online discussion boards, specifically those that are unmediated by teacher figures, to identify characteristics of these spaces that support or constrain students as they seek help in mathematics. We analyzed 86 questions and 114 associated responses posted to two Khan Academy discussion boards centered around two related…