Reliable and validated assessments of introductory physics have been instrumental in driving curricular and pedagogical reforms that lead to improved student learning. As part of an effort to systematically improve our sophomore-level Classical Mechanics and Math Methods course (CM 1) at CU Boulder, we have developed a tool to assess student learning of CM 1 concepts in the upper-division. The Colorado Classical Mechanics/Math Methods Instrument (CCMI) builds on faculty consensus learning goals and systematic observations of student difficulties. The result is a 9-question open-ended post-test that probes student learning in the first half of a two-semester classical mechanics / math methods sequence. In this paper, we describe the design and development of this instrument, its validation, and measurements made in classes at CU Boulder and elsewhere.

Vector decomposition is a skill required across physics contexts and levels. In this paper, we present our analysis of 463 student responses to an item on the Colorado Classical Mechanics/Math Methods Instrument that assesses student proficiency with vector decomposition in multiple coordinate systems. We offer separate categorizations for students' final expressions and their approaches to determining those expressions. The intersection between approaches and final expressions suggests that certain approaches are more productive. We discuss these intersections and the differences between students' responses in Cartesian and polar coordinate systems.