Context Dependence of Student Responses and Explanations on Dot Product Magnitude Tasks

RUME 28

2026

Alexandria, Virginia

Context Dependence of Student Responses and Explanations on Dot Product Magnitude Tasks

Page: 1106

• Allison Molinari
• John R. Thompson

Preliminary findings from a study exploring student understanding of vector products are presented. We discuss multiple-choice and free-response data from 118 students who completed four dot product magnitude tasks across two semesters of introductory physics instruction. Each semester had a physics-free dot product along with a physics context relevant to the content of each course (mechanical work and electric flux). Performance ranged from 28% to 59% and students do not always answer consistently between pairs of tasks. Coding of explanations revealed four main computational strategies used by students along with two more conceptual reasoning categories. The most common strategy was students using a trigonometric definition of the dot product with varied results depending on the context.