Student Difficulties with Trigonometric Vector Components Persist in Multiple Student Populations

Abstract

Students in introductory physics courses sometimes struggle to correctly break down a single vector into its components when provided only with an arrow, a magnitude, a reference angle, and a coordinate system. Students struggle further when asked to break down a vector in an inclined coordinate system, such as the weight vector of a box on an inclined plane. Varying the placement of the angle consistently affects student error and response patterns across four physics student populations: algebra-based mechanics, algebra-based E&M, calculus-based mechanics, and calculusbased E&M. This suggests that student difficulties with trigonometric vector components are persistent and pervasive, even across different introductory physics courses, and are far below the requisite near-perfect accuracy needed for such fundamental skills. Student error and response patterns are discussed for both problem types.

Framework and implementation for improving physics essential skills via computer-based practice: Vector math

“…[1]), we find that a systematic characterization of specific student difficulties with an essential skill is useful for designing targeted, effective practice. In our experience [4,5,27,28], we have found that difficulties with skills in a given domain (such as reading logarithmic graphs) tend to be multidimensional and interrelated, even for relatively simple skills, and exploring each dimension can lead to a robust set of practice examples that "triangulate" the issue by addressing the difficulty from different perspectives, dimensions, and representations. Of course incorrect student answers also provide useful material for distractors on practice questions.…”

“…In our experience we have always found the difficulties with skills to be more complex than first expected. For example, in the case of vector math, we found that some vector math skills (such as addition) must be broken further into subskills (e.g., finding trigonometric components of vectors), and in this case an exploration of difficulties with these subskills is critical [27,28].…”

“…Specifically, the research literature contains a number of papers detailing student difficulties with various vector operations (e.g., Refs. [27,28,[48][49][50]), showing that typically-even postinstruction-only 50%-70% of calculus-based physics students can correctly perform these basic vector arithmetic operations. These student difficulties produce predictable and consistent wrong answers that can be used as realistic distractor options when designing training and test questions.…”

“…In some instances, it was necessary to collect our own data to better understand student difficulties and common errors with specific vector skills (e.g., Refs. [27,28]). …”

“…Note that the Test of Understanding Vectors [48] overlaps significantly with our vector skills assessment, but the former is aimed more at assessing conceptual understanding, and the latter is more aimed at assessing accuracy in vector math skills. Second, many of the items had also been pilot tested and refined through testing in our education research lab, including student interviews [3,27,28]. Third, pretest assessment scores were significantly correlated with grade in the course (r ¼ 0.36, 0.32; p 0 s < 0.001) for experiments 1 and 2, respectively.…”