Mathematical self-efficacy and understanding: using geographic information systems to mediate urban high school students' real-world problem solving

• Main Author: DeBay, Dennis James
• Format: Others
• Language: English
• Published: Boston College 2013
• Subjects: geographic information systems; graphing; mathematical self-efficacy; mathematical understanding
• Online Access: http://hdl.handle.net/2345/3230

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.