Although buoyed by the induction of a democratic government, and the high ideals of our constitution, the South African education system has in many ways not met the expectations of its people, in this case, the mathematics education community. With the birth of an expansive intended curriculum came the monitoring of the outcomes through systemic…

This research, which is the first part of a two-part study, was commissioned by the New Zealand Productivity Commission to inform their study of the future of work in New Zealand. The main research question asks, in essence: In what ways are secondary school subject-choice systems, and students' subject choices, positioned to respond to future of…

The concept of pattern recognition lies at the heart of numerous deliberations concerned with new mathematics curricula, because it is strongly linked to improved generalised thinking. However none of these discussions has made the deceptive nature of patterns an object of exploration and understanding. Yet there is evidence showing that pattern…

It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or…

Statistical association between two variables is one of the fundamental statistical ideas in school curricula. Reasoning about statistical association has been deemed one of the most important cognitive activities that humans perform. Students are typically introduced to statistical association through the study of the line of best fit because it…

Mathematical modeling is an open-ended research subject where no definite answers exist for any problem. Math modeling enables thinking outside the box to connect different fields of studies together including statistics, algebra, calculus, matrices, programming and scientific writing. As an integral part of society, it is the foundation for many…

The work described in this report is the first phase of a project to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low vision. This report describes the initial development, software implementation, and evaluation of the…

This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of…

The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.

In order to address concerns with the underrepresentation of spatial thinking in K-12 curricula, (National Research Council, 2006), Valentine and Kopcha (in press) designed and implemented a learning environment integrating cases as alternative perspective (Jonassen, 2011) in the context of eighth-grade mathematics. The design aimed to provide…

Through analysing a critical incident where a small group of pre-service secondary mathematics teachers work together on an annuities problem, we gain insight into the ways in which students make use of timelines and attend to time in their talk. Drawing on Lave and Wenger's notion of transparency, I argue that it was only when time became visible…

NCTM's Connections Standard recommends that students in grades 9-12 "develop an increased capacity to link mathematical ideas and a deeper understanding of how more than one approach to the same problem can lead to equivalent results, even though the approaches might look quite different" (NCTM 2000, p. 354). In this article, the authors…

The application of skills and knowledge to a "real world" context entails a greater set of competencies than just technical proficiency, for both the student who sits the problem and the teacher who sets it. These competencies require unpacking. A greater understanding of these competencies would enable teachers to create tasks that test…

In this article, we present a mathematical analysis that distinguishes two distinct quantitative perspectives on ratios and proportional relationships: variable number of fixed quantities and fixed numbers of variable parts. This parallels the distinction between measurement and partitive meanings for division and between two meanings for…

Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…