This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

In many parts of the world, Pi Day is celebrated on March 14 (3.14), but because of the day-month ordering of dates in Australia, and because March is very close to the start of the academic year, Australians prefer to celebrate Pi (Approximation) Day on 22 July (22/7). Thirty-eight Year 8 students (aged 13-14 years) from two local high schools in…

In this article James Russo presents the Strategies, Understanding, Reading and Fast Facts Framework (SURF) for mental computation. He explains how this framework can be used to deepen mathematical understanding and build mental flexibility.

In this study it was aimed to determine pre-service primary teachers' knowledge structures of fraction through problem posing activities. A total of 90 pre-service primary teachers participated in this study. A problem posing test consisting of two questions was used and the participants were asked to generate as many as problems based on the…

"Mathematical modeling of the physical world should be the central theme of physics instruction" (Hestenes 1987). Science teachers know this, but because of standardized state testing, many math teachers and some science teachers feel the need to focus on memorizing facts that will be on a multiple-choice test (Volante 2004). As a…

This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in…

Students often experience difficulty with attaching meaning to mathematics symbols. Many students react to symbols, such as the equal sign, as a command to "do something" or "write an answer" without reflecting upon the proper relational meaning of the equal sign. One method for assessing equal-sign understanding is through…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

The research relates to undergraduate students' understanding of mathematical concepts that relate to the conceptualisation of the continuous such as the notion of limit. The cognitive difficulties that accompany the learning of these concepts at the different stages of the mathematics education are well reported in the literature. I analyse the…

This study reports on an intervention that was aimed at improving the content knowledge of first-year intermediate-phase education students at a South African university. The study gives some insight into preservice teachers' perceptions of an online programme for the development of mathematics common content knowledge for teachers of mathematics…

Supporting students to build robust fraction schemes and operations is an enduring challenge in mathematics education. Recent research has explored a developmental trajectory of fractions schemes and operations constructed by upper-elementary and middle school students in an effort to support student learning. This study broadened the existing…

This study examines the extent to which deeper learning is expected to be present in the new college and career ready (CCR) standards. This is done by examining the distribution of items and tasks at high levels of cognitive demand (DOK3 and DOK4) in the summative test blueprints developed by the Partnership for Assessment of Readiness for College…

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal's analysis of the fraction concept, we regard "comparing," rather than "fracturing," as the primary activity from which students are…

The research presented in this paper focuses on the cognitive diagnostic strategies that prospective elementary mathematics teachers (PTs) use in their reflections of one-on-one diagnostic interviews with children in grade one. Thereby, it responds to the detected lack of knowledge regarding qualitative facets of diagnostic proceeding in interview…