• Retangular fraction models.

      Kibler, Rachael H. (2015)
      The purpose of this mixed methods study was to explore how implementation of a new, researcher-developed simple improvised manipulative (SIM) impacted 5th graders in an urban, Common Core-aligned classroom. The Rectangular Fraction Model, a SIM created with two overlapping pieces of transparent plastic, was tested through performance of this experiment. This research sought to answer the following two central questions: How does implementation of a SIM, the Rectangular Fraction Model, impact 5th grade students’ math achievement in a mathematics class at an urban Chautauqua County elementary school in Western New York? How does use of a concrete representation affect students’ conceptual understanding of abstract material as taught through the Common-Core aligned EngageNY curriculum? The researcher was interested in two areas of possible impact on student learning; student achievement measured by a formal assessment and student understanding of abstract materials evaluated through use of an interview and questionnaire. Twelve students participated in the study; they were placed in heterogeneous control and experimental groups. The results indicate that although students in the experimental group scored better on the post test and appeared to have a better understanding of the concept taught, the difference between the control and the experimental group was not statistically significant. Thus, the use of SIM is not more effective than the traditional teaching approach. However, student responses indicate an interest in using this type of intervention material, and further research should be conducted on the impact of SIM in the mathematics classroom.
    • A study of college students' misconceptions about fractional expressions.

      Tydings, Shannon M. (2014)
      This study investigates the possible reasons why students struggle with the concept of fractions. During this study, college students from both a mathematics course required for their major and students in a basic core curriculum mathematics course completed a 10- problem test containing different types of problems involving fractions. These participants were not allowed to use a calculator. The number of correct responses for each problem was recorded. The scores were then compared to a survey that students answered, specifically looking at which problems they felt were the easiest/hardest to solve, and the method which they used to solve each problem. The results of this study indicated that all students struggled to solve word problems and had greater success with symbolic questions. The results indicated that there was an issue with conceptual and procedural knowledge levels. Also, the research showed that students resorted to traditional ways of solving problems. Additional results revealed that the students enrolled in the course required for their major were more successful than those in the core curriculum course. There was also no significant difference between performance on the test and gender.