In this article we consider, via a specific modelling example, the educational benefits to be gained from running mathematical activities with our sixth-form and undergraduate students that, in modern parlance, might be termed "rich tasks". The idea for this modelling activity arose while the author was reading a popular-science book on cosmology…

Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…

The main objective of this paper is to apply the onto-semiotic approach to analyze the mathematical concept of different coordinate systems, as well as some situations and university students' actions related to these coordinate systems. The identification of objects that emerge from the mathematical activity and a first intent to describe an…

Problem Statement: Preservice teachers acquire the knowledge and skills needed for elementary mathematics education by themselves obtaining quality university educations and by being actively involved in mathematics. Thus, it is essential to make room in teacher education for student-centered projects and activities. Purpose of Study: This study…

Students' lack of understanding about the relationships between geometry in two and three dimensions led the author to a surprising source of inspiration--the ancient philosopher and geometer Plato. From a theoretical perspective, the author's approach embodies the four instructional strategies that Eggen and Kauchak (2001) suggest for engaging…

This article takes another look at the sliding ladder problem that students meet in the study of related rates in calculus. Physically realistic situations with both constrained and understrained ladders are explored.

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

Linton Waters and Jayne Kranat ran a session on the Nuffield "Applying Mathematical Processes" (AMP) activities at BCME7 in Manchester in April this year. These 1-2 hour activities are revamps of some of the Graded Assessment in Mathematics (GAIM) resources, developed in the 1980s, and are freely available via the Nuffield website and…

The "Let's Count" pilot early mathematics program was implemented in five early childhood educational contexts across Australia during 2011. The program used specifically formulated materials and workshops to enlist the assistance of early childhood educators to work with parents and other family members of children in their settings to…

Recognizing meaning in students' mathematical ideas is challenging, especially when such ideas are different from standard mathematics. This study examined, through a teaching-scenario task, the reasoning and responses of prospective elementary and secondary teachers to a student's non-traditional strategy for dividing fractions. Six categories of…

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in…

The purpose of this research has been to generate learning environments that surrounded second and third grade students with bi-directional counting experiences, leading them to discover and come to an understanding of opposite numbers. While engaged in games and bi-directional activities, these young students eagerly counted, by jumping frogs…

This article reports on the findings of a research project whose aim was to support and enhance the teaching of risk at Key Stage 4. An innovative and cross-curricular approach has been used, based on modelling socio-scientific issues using new technological tools, designed specifically to enable the consideration of ethical and social issues,…

Constructivism has constituted a predominant philosophical trend in mathematics education, but its implementation in the classroom has proven to be "far more difficult than the reform community acknowledges". This difficulty may be due in part to administrative cultures that might insist on more procedural types of instruction aimed at testing, in…