Mathematical reasoning with algebraic and geometric representations is essential for success in upperdivision and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to…

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student…

Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…

Develops formulas for the number of bounces of a ball on a billiard table given an original path-angle. (MM)

Provides an activity for determining the relationship between the displacement of light rays passing through a plate of transparent material and the angle of refraction for the material. Describes related concepts and skills, prerequisites, objectives, rationale, content background, lesson outline, worksheet, evaluation, teacher notes, and…

Utilizes vector mathematics to explain the reflective properties of a corner cube retroreflector, consisting of three plane mirrors assembled at right angles with a common vertex. Analyzes the useful property that an incident beam of light at any point in this reflector will return on a parallel path. (MDH)