Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra

Abstract

Mathematical reasoning with algebraic and geometric representations is essential for success in upper-division 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 several algebraic representations, we identified students’ facilities and difficulties with complex number algebra. Students were successful when they isolated approaches, which was characterized by students’ use of circle trigonometry, triangle trigonometry, the Pythagorean theorem, and the square of the norm approaches. When students were not successful, they inappropriately mixed approaches to the problem, including failing to distinguish between triangle and circle trigonometry.