This research aimed to find out the differences in how students (with a baseline knowledge of calculus from school) understand and approach calculus depending on whether or not they have studied preliminary courses in Analysis and Calculus.
In this seminar, I focus on the use of cognitive interviews to assess students’ understanding of calculus-related keywords, but also how they approach some calculus problems. In the first, I sought to establish what they think of when they hear/read the keywords and what they relate to in their minds, and for the second I wanted to see what tools they have to tackle calculus problems and what their thought process is. This approach combines a set of fixed questions, prompts, and clarifications to try and obtain as detailed responses as possible, drawing on ideas from think-aloud interview techniques. The calculus context raises a particular challenge for the use of cognitive interviews as this mathematics is more easily communicated through symbols, and thinking aloud processes are generally combined with written notes that do not have a linear form (cannot be read from left to right) and can appear messy and chaotic to others.
As a student who is blind, I worked with a support worker to carry out these interviews and some of the analysis, this included developing gestures to communicate participant activity in the interviews, developing ways to make the written data accessible for analysis, supporting with transcription of data, and practical assistance with use of analysis software.
I will also present some of my findings arising from the Thematic Analysis, as described by Braun & Clarke, of the accessible forms of the data from my interviews and draw conclusions of an overall picture and a comparison of students with different levels of calculus education.
