• College Students' Performance on Isomorphic Visual vs Non-Visual Regents Level Geometry Problems

      Leitner, Dylan (State University of New York at Fredonia, 2017-09)
      This study explores students' misconceptions regarding pictorial geometry problems. Specifically, to investigate misunderstandings students experience when solving visual and nonvisual geometry problems. During this study, college students completed two identical 6-problem assessments on the topics of area, volume, and surface area. The instrument was administered several weeks apart and directly generated from past state tests: New York State Geometry Regents and Mathematics A Exams. It was hypothesized that given an assessment composed of visual and non-visual isomorphic geometry problems college students would score lower on non-visual problems. Furthermore, students would struggle most to complete volume problems compared to area and surface area problems. After analyzing the data the hypothesis was partially confirmed. The scores were compared to a survey students completed following each assessment recording their confidence on the overall exam and each problem. The results of this study indicated there was no significant difference on student scores when comparing visual and non-visual Regents geometry problems. Additional results revealed the topic that students struggled with most was volume.
    • Compose Yourself: It's Just a Function!

      Cole, Madison (State University of New York at Fredonia, 2016-07)
      This research examines students’ understanding and ability to work with composition functions in different representations. Its underlying purpose is to analyze students’ level of procedural knowledge and conceptual understanding of composite functions and to identify common errors and misconceptions associated with these functions. It was hypothesized that college students would incorrectly substitute one function into another when evaluating at a variable. Furthermore, it was hypothesized that evaluating a function value at a constant would produce better results as well as working with visual representations, such as tables and graphs. The results of this study indicate that non-mathematics major college students have neither strong conceptual understanding nor adequate procedural fluency in terms of composition functions. However, there was no significant difference between evaluating constants versus variables in the functions. Additional results revealed that while visual and algebraic representations produced no significant differences in their means (p-value = 0.545), algebraic notation negatively influenced students’ solving capabilities (p-value = 0.000).