Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

The main goal of this research was to assess the effect of a dynamic environment on relationships between the three geneses (figural, instrumental, and discursive) of Spaces for Geometric Work. More specifically, it was to determine whether the interactive geometry program GeoGebra could play a specific role in the geometric work of future…

Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…

The new representations enabled by the educational computer game the "Juggler" can place vectors in a central role both for controlling and measuring the behaviours of objects in a virtual environment simulating motion in three-dimensional spaces. The mathematical meanings constructed by 13 year-old students in relation to vectors as…