Semester

Fall

Date of Graduation

2021

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Marjorie Darrah

Committee Member

Nicole Engelke Infante

Committee Member

Michael Mays

Committee Member

Michelle Richards-Babb

Committee Member

Vicki Sealey

Abstract

Spatial reasoning is required for many topics in undergraduate mathematics as well as other STEM fields. In calculus specifically, there are few interventions that assess students’ spatial skills and provide remediation. Haptic technology is a novel approach to spatial skills remediation due to its unfamiliarity to students and its flexibility with regard to models. The purpose of this dissertation is two-fold: first, to determine what level of spatial abilities students possess upon entering an undergraduate calculus course, and second, to determine whether haptic feedback will enhance an intervention for improving spatial skills.

The dissertation research was a mixed-methods study using the combination of a quantitative spatial reasoning test, semi-structured interviews, and student activities. The design of the study was pre-test – post-test matched subject, using the quantitative spatial reasoning test – the Santa Barbara Solids Test (SBST) – and other demographic information to match students of similar spatial reasoning abilities and backgrounds for the qualitative part of the study. In all, 306 students completed both the SBST pre-test and post-test. Ten of these students were selected as matched pairs, of which nine completed the pre-interview, intervention activities, and post-interview, leaving eight students in four matched pairs for the qualitative analyses.

Analysis of the pre-test and post-test scores showed that the students who completed the intervention activities performed significantly better on the SBST post-test than on the pre-test. Furthermore, these students improved their scores more than the students who did not complete the intervention activities, and the difference between these groups was significant. While some differences were noted between the students who completed the intervention activities with haptic feedback and those who completed them without, there were not significant differences in performance on the post-test, nor the improvement from the pre-test to the post-test.

The pre-interviews and post-interviews were coded using the spatial skills framework created by Engelke et al. (2016). Examination of the codes applied to each set of interviews showed a similar ratio of codes in each set. Both interviews contained an overwhelming majority of visualization language over orientation language. The most prominent subcategory displayed was representing objects, followed by structuring, mathematical properties, and finally measurement. The students who completed the intervention activities with haptic feedback and those who completed them without showed similar changes in their spatial language between the pre-interview and post-interview. Analysis of the scores of the interview questions did not show a significant difference between the pre-interviews and post-interviews, nor did it show a significant difference between the students who completed the intervention activities with haptic feedback and those who completed them without.

These findings indicate that students entering calculus have strong visualization and representing objects spatial skills, but lack orientation and structuring spatial skills. They also show that putting students through a short remediation, even without feedback on their performance, can improve spatial skills. Although significant differences could not be found between the students who received haptic feedback in the intervention activities and those who did not, this could be due to the small number of matched pairs, and does not rule out the potential for haptic feedback use in spatial reasoning training.

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