In this article, the history of the golden ratio is discussed to demonstrate how exploring this ratio would be of value in a secondary mathematics classroom. Following this, a mathematical activity related to the golden ratio that is suitable for students from Year 7 to Year 12 is outlined.

In this article we address the 'educationalization' of authentic marine navigation tasks for upper secondary mathematics classrooms and their potential for students' learning. Our approach is based on boundary crossing and as well as on the distinction between realistic tasks (targeting students' familiarization with the marine navigation…

When deciding what constitutes students' "on task" or "off task" mathematical communication, teachers and researchers are also making judgements about what is, and what is not, mathematics. In this paper, we question our ability to separate the mathematical from the nonmathematical. We explore intersecting storylines in Grade…

This study explores the relationships among students' perceived learning opportunities in school mathematics, their perceptions of self in mathematics, and their desire to learn more mathematics in the future. Data included student survey responses from eighth and tenth grade students from a state in the Southeast region of the United States.…

To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical…

In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

This paper presents a series of illustrative LEGO Mindstorms-based science and math activities, developed under an NSF GK-12 Fellows project, for elementary, middle, and high school grades. The activities, developed by engineering and science graduate Fellows in partnership with K-12 teachers, are grade appropriate, address pertinent learning…

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

Students must be encouraged to think for themselves by tapping into their imaginations. Only when mathematical concepts are presented in an imaginative way will students fully benefit from their experience. Both teachers and students must engage themselves in this creative realm of thinking, where imagination plays a vital part in learning and…

In this paper, we describe the skeleton of two teaching units, based on a Model for teaching mathematics, Context Orientated Teaching (COT). The first teaching unit concerns the proof of a mathematical proposition, while the second one concerns the solution of an open problem. Both are taught in the 10th grade, under the specific conditions of the…

The purpose of this paper is to contribute to the debate about how to tackle the issue of "the teacher in the teaching/learning process", and to propose a methodology for analysing the teacher's activity in the classroom, based on concepts used in the fields of the didactics of mathematics as well as in cognitive ergonomics. This…