Remediation of Spatial Skills in First Semester Calculus Using Haptics-Based Applications

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

Experiences of Middle School Students With Visual Impairments Accessing Technologies In Inclusive Classrooms

As the educational environment is moving more towards a technology-rich system, students with visual impairments (VI) educated in general education classrooms must be guaranteed equitable access to content curricula. The purpose of this study was to understand the experiences of middle school students with VI when accessing and using technologies in general education classrooms. In this multiple case study, three middle school students with VI were observed in general education settings for two school days. In addition to the students, general education teachers and teachers of students with VI (TVI) also participated in the study to understand how best they support access to technologies for students with VI in their classrooms. The theoretical framework that guided this study was Piaget’s cognitive development theory, and the learning model was Universal Design for Learning. Data were collected through multiple instruments: observations, interviews, and educational documents. Students, their general education teachers, and TVIs were interviewed about their experiences with the use of technologies in classrooms. After data collection, the analysis was completed using within-case and cross-case analysis. The within-case analysis revealed the experiences of using technologies in general education classrooms for each student in the form of a narrative story. Each student’s story included the components: (a) how did they see their world?, (b) how did they experience their school day?, and (c) how did their ideal world compare to their real world? The cross-case analysis was conducted by comparing participants’ experiences with technologies in general education classrooms. Four broad themes emerged from the cross-case analysis: (a) technology is imperative in general education classrooms; (b) frustrations with accessibility issues in general education classrooms; (c) for general education teachers, it has been a learning curve; and (d) for TVIs, the buck stops with them when it comes to access technology. Within the above four broad themes, some emerged findings were intriguing. General education teachers were open to training on technologies that are more engaging for students, as opposed to technologies that were universally accessible. Inaccessible technologies used in classrooms were not only the ones adopted by the school or district, but they included programs that were created and shared by other teachers through learning communities. While the students, general education teachers, and TVIs in this study understood the legal mandates of IDEA and an IEP, they did not know any other accessibility laws related to technologies that Kindergarten-Grade 12 schools should abide by. Conceptually, some sub-themes found in this study were: (a) the majority of educators were differentiating the curricula to meet the needs of students through constant adaptation as opposed to using tools that account for learner variability at the outset, and (b) student choice and advocacy played a big role in the experiences of students with VI in general education classrooms. Based on the findings, implications for practice and future research directions are discussed in this study