A qualitative multiple case study was conducted to reveal the sense-making processes third-grade students who struggle in mathematics used to build an understanding of fraction concepts. Purposive sampling identified three participants who were struggling in a local school's third grade mathematics classes. This research describes how these participants made sense of fraction concepts through their strengths and struggles while engaged in 15 small-group intervention sessions. Vygotsky's (1934/1986/2012) theory that children's optimal learning is supported by teacher-student interactions was used as an interpretive framework. Tasks were developed over the course of the intervention sessions with consideration of a model developed by Lesh, Post, and Behr (1987) for connecting mathematical representations and the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). Data, including transcripts, tapes, and artifacts, were analyzed using two frameworks. These were Geary's (2003) classification of three subtypes of learning disabilities in mathematics and Anghileri's (2006) descriptions of social-constructivist scaffolding techniques. The first analysis resulted in a description of each participant's strengths and struggles, including alignment with Geary's subtypes, and how these strengths and struggles interacted with participant's construction of knowledge about fractions. The second analysis described episodes of learning that were supported by social-constructivist scaffolding techniques and revealed how participants made sense of fractions through their interactions with each other, the researcher, and intervention tasks. The researcher found that each participant's learning process, including struggles, was unique, with each interacting in different ways with tasks, manipulatives, pictorial representations, and questioning. For each participant, however, scaffolding techniques oriented around prompting and probing questions, participant verbalizations, and interactions with connected fraction representations were critical in their learning process.
Doctor of Philosophy (Ph.D.)
College of Education and Human Performance
Education; Mathematics Education
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Gault, Rebecca, "A Multiple Case Study Examining How Third-Grade Students Who Struggle in Mathematics Make Sense of Fraction Concepts" (2016). Electronic Theses and Dissertations. 5081.