Browsing by Subject "Fractions"
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Item Evidence-Based Instructional Principles and Sequences for Effective Fraction Instruction(2021-07) Running, KristinFraction proficiency is a critical milestone for students to reach, as fraction knowledge strongly predicts later math achievement. However, fractions are notoriously difficult for students to learn. The first study in this dissertation reviewed commonly used math curricula to determine if their fraction lessons used evidence-based instructional strategies. The results showed several strengths of the curricula, including sufficient prerequisite skill practice, instructional examples of fraction concepts, and practice opportunities. However, the curricula also needed more explicit instruction of fraction concepts and procedures. In addition to using evidence-based instructional principles, the order of conceptual and procedural instruction may also affect students’ learning and generalization of fraction skills. The second study in this dissertation compared the effect of two instruction sequences, concepts-first and iterative, on fraction performance during a classwide intervention. Fourth-grade students (N=114) were randomly assigned to the concepts-first, iterative, or control group. The primary conceptual assessment showed that the iterative and concepts-first groups performed similarly, demonstrating medium effect sizes compared to control. The primary procedural assessment again demonstrated that both intervention groups outperformed the control, this time with large to very large effects. Additionally, the iterative group outscored the concepts-first group with a medium effect size, though it was not statistically significant. Generalization assessments measuring skill transfer found no differential effects. Overall, iterative instruction was at least as effective as a concepts-first sequence during a fraction intervention. The implications of these findings for fraction instruction and the sequencing of conceptual and procedural instruction more generally are discussed.Item Preservice Elementary Teachers’ Understandings of the Connections Among Decimals, Fractions, and the Set of Rational Numbers: A Descriptive Case Study(2015-12) Pettis, ChristyThe mathematical knowledge needed for teaching is a specialized form of mathematical knowledge, (Ball, Thames, & Phelps, 2008). One important area of mathematical understanding for elementary teachers is the area of number and numeration. Mathematically, the sets of whole and rational numbers and their corresponding notational systems are deeply interconnected. Ensuring that preservice elementary teachers understand the ways these sets of numbers and notations are connected, both mathematically and developmentally, is a critical component of teacher education coursework. This study is a descriptive case study (Yin, 2014) documenting preservice elementary teachers’ ways of understanding the relationships among fractions, decimals, and the sets of rational and irrational numbers. The unit of analysis was a single class of preservice elementary teachers participating in an eight-week instructional unit designed to support them in making explicit connections between concepts related to number and numeration. The broad agenda for this study is to support the development of curricula that may productively and efficiently develop preservice teachers’ understandings of the connections among fractions, decimals, and the sets of rational and irrational numbers. This study extends prior work on bridging tools (Abrahamson & Wilensky, 2007) by documenting how two bridging tools were used to promote understanding of the connections between fraction and decimal notation. Results from early in the unit indicate that preservice elementary teachers’ initial understandings of the connections among fractions, decimals, and the set of rational numbers were limited and often inaccurate. Limited understandings of decimal notation were also documented. Finally, the preservice teachers primarily used symbolic representations to explain the connection between fractions and decimals. After the unit, the preservice teachers showed a more connected understanding of the relationships among fractions, decimals, and the set of rational numbers. The majority of preservice teachers demonstrated the ability to use multiple, non-symbolic representations in order to find and explain connections between fractions and decimals. Widespread understandings of decimal notation were documented, but these understandings were applied inconsistently. Together, the results suggest that a connected approach to curriculum design shows promise as a way to address multiple areas of preservice teachers’ content understandings simultaneously.