Thesis advisor: Lillie R. Albert / To explore student mathematical self-efficacy and understanding of graphical data, this dissertation examines students solving real-world problems in their neighborhood, mediated by professional urban planning technologies. As states and schools are working on the alignment of the Common Core State Standards for Mathematics (CCSSM), traditional approaches to mathematics education that involves learning specific skills devoid of context will be challenged. For a student to be considered mathematically proficient according to the CCSSM, they must be able to understand mathematical models of real-world data, be proficient problem solvers and use appropriate technologies (tools) to be successful. This has proven to be difficult for all students--specifically for underrepresented students who have fallen behind in many of the Science, Technology, Engineering and Mathematics (STEM) fields. This mixed-method design involved survey and case-study research to collect and examine data over a two-year period. During the first year of this study, pre- and post-surveys using Likert-scale questions to all students in the urban planning project (n=62). During the two years, ten high school students' mathematical experiences while investigating urban planning projects in their own neighborhoods were explored through interviews, observations, and an examination of artifacts (eg. presentations and worksheets) in order to develop the case studies. Findings indicate that real-world mathematical tasks that are mediated by professional technologies influence both students' mathematical self-efficacy and understanding. Student self-efficacy was impacted by causing a shift in students beliefs about their own mathematical ability by having students interest increase through solving mathematical tasks that are rooted in meaningful, real-world contexts; students' belief that they can succeed in real-world mathematical tasks; and a shift in students' beliefs regarding the definition of `doing mathematics'. Results in light of mathematical understanding demonstrate that students' increased understanding was influenced by the ability to use multiple representations of data, making connections between the data and the physical site that was studied and the ability to communicate their findings to others. Implications for informal and formal learning, use of GIS in mathematics classrooms, and future research are discussed. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Lynch School of Education. / Discipline: Teacher Education, Special Education, Curriculum and Instruction.

The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four sources of mathematical self-efficacy of 102 college freshmen attending three small, private, liberal arts institutions. Even though this study found no interaction effects between the student characteristics, the four sources of mathematical self-efficacy, or the three subcategories of the vicarious experience construct, this study did find statistically significant results for several independent variables: gender, hometown environment, and the letter grade received in the mathematics course the preceding semester at the Bonferroni correction rate of .025. Additionally, small p-values for race and hometown environments warrant further investigation with a larger sample size.

In today’s educational landscape, digitalization, driven by economic interests, has become increasingly prominent. This development has sparked interest in understanding how high school students’ technical capital and mathematical self-efficacy influence their outcomes. To deepen the understanding of this interplay, this study integrates Selwyn’s Bourdieusian capital theory on technical capital with Bandura’s theories on mathematical self-efficacy. Empirical data were collected through a survey administered to 208 high school students across three schools in Sweden, ensuring anonymity and integrity. Linear regression was employed, controlling for gender, academic program, socioeconomic factors, and completed coursework. The results demonstrate that technical capital significantly predicts mathematical self-efficacy, with a predictive capacity of up to 59.6%. Moreover, tolerance for deviation in the model increased the predictive capacity to 94.2%. No significant differences in predictability were observed based on gender or academic program dependencies. However, gender differences revealed a more linear relationship between technical capital and digital/technical competence among women compared to men. Additionally, both genders displayed equivalent performance in knowledge-based questions. This suggests that men tend to overestimate their digital competence relative to their technical self-efficacy, while women do not exhibit the same tendency toward overconfidence. In conclusion, this study offers insights into how technical capital and self-efficacy in mathematics shape students’ educational outcomes.