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Vectors  (7 resources)
This annotated collection provides links to publications by the PER community (Physics Education Research) on the topic of student understanding of vector concepts. Most were published in recent Physics Education Research Conference Proceedings and are available for free download. The purpose of the proceedings is to provide a written record of the scholarly work undertaken by PER researchers. The conference publishes final results but also welcomes submission of preliminary research results and discussions of works in progress.
Testing Students’ Understanding of Vector Concepts
If your time's very limited, make this the article you read. It discusses results of a large scale 4-year project involving 2,000+ students at Monterrey University. The researchers used a 20-question concept test to gauge the understanding of students in a variety of vector concepts.
Students’ Understanding of the Concepts of Vector Components and Vector Products
In this paper, researchers look at misconceptions in the vector component concept and difficulties with dot product and cross product operations. A key finding: "One of the most important findings of this study is that students finishing the introductory physics courses still have difficulties calculating products, related in some part to their problems with components."
Students’ Responses to Different Representations of a Vector Addition Question
This is a condensed summary of research involving four graphical vector addition questions administered to students in algebra-based college physics courses after 6 weeks of study. Each question has the same two vectors being added, but different graphical representations and features provided. Results? Not surprising -- students preferred to use tip-to-tail over bisector method, and surprising result -- the use of components method was not affected by the presence of coordinate grids.
Students' difficulties with unit vectors and scalar multiplication of a vector
This study was conducted on students who completed a calculus-based physics course, but has implications for all teachers of introductory physics. It documents serious student difficulty in conceptual understanding of unit vectors and negative scalar multiplication of a vector. The difficulties persisted even among students who had completed a course in Electricity and Magnetism.
Student Difficulties with Trigonometric Vector Components Persist in Multiple Student Populations
This study was designed to explore the effects of angle placement on student aptitude with trigonometric vector components. The field of 638 students consisted of four groups: algebra-based mechanics enrolees, algebra-based E&M enrolees, calculus-based mechanics students, and calculus-based E&M students. The findings: "even post instruction, student performance is nowhere near the 90-100% accuracy needed for the essential skill of applying trigonometric
functions to vector decomposition."  The implication: "Students need more practice on a variety of angle configurations."
Students’ Consistency of Graphical Vector Addition Method on 2-D Vector Addition Tasks
This study was based on in-depth interviews with 8 students enrolled in either a calculus-based physics course or the second semester of algebra-based physics. The questions were designed to trigger different problem-solving strategies among the students. Although the field is small, the results are worthy of pondering. All but one student stuck to a single method of solving vector addition tasks for the entire interview, even when changing conditions favored a different method. Implications: consider exposing students to multiple representations of vector addition and promote using a variety of solution strategies.
Vector Addition: Effect of the Context and Position of the Vectors
This study investigated the effect of context and position of the vector on 2D vector addition tasks. It was performed on 512 students who had completed a calculus-based college physics course. The results indicate that the context helps most of the students build a mental model and then solve the problem with their own sketches. "One can argue the need to teach vectors using a context; however, students should be able to transfer knowledge among different contexts, and that probably is better achieved with a context-free approach."