Abstract by Leilani Fonbuena
Students\' visual reasoning of vectors, vector fields, and vector functions
Research has been done on graphing and visual reasoning for single variable functions but there is a lack of literature surrounding multivariable functions. Understanding vectors and their functions are notoriously difficult for students to understand. We will look at students’ understanding and visual reasoning of vectors, dot and cross products, vector functions, and vectors fields. To discover student thinking we will conduct interviews of students who are at the end of the multivariable calculus course as well as students who have completed multivariable calculus and some mathematics courses beyond it. The interview protocol includes general understanding of each of the four vector contexts, images associated with each. It also explores and challenges associated conventions. We will analyze the interview for student understanding, visual reasoning, conventions, and metaphors associated with vectors, vectors fields, and vector functions.