In high school geometry, proving theorems and applying them to geometry problems is an expectation for students. An essential part of most geometry proofs is the diagram because it not only helps encapsulate the claim being proved but can also be a tool in reasoning or communicating an argument. This interview-based study investigated how high…

Structure sense can be interpreted as an intuitive ability towards symbolic expressions, including skills to perceive, to interpret, and to manipulate symbols in different roles. This ability shows student algebraic proficiency in dealing with various symbolic expressions and is considered important to be mastered by secondary school students for…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…