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Item Open Access Learner Agency in Mathematics When Classroom Instruction Incorporates Voice, Choice, and Opportunity in Demonstrating Understandings(University of Wyoming Libraries, 2026-05-06)This action research study grew out of my desire to rethink what mathematics learning looked like in my seventh-grade classroom. Over time, I began to question how often students were being asked to simply follow directions rather than actively participate in their learning in meaningful ways. This study focused on how voice, choice, and opportunity shaped students’ experiences in mathematics and how intentional changes in my teaching influenced student engagement, classroom interactions, and my own growth as a teacher. The study took place in my advanced seventh-grade mathematics classroom and centered on my shift away from a more traditional, teacher-directed approach toward one that gave students more flexibility in how they demonstrated understanding. Rather than collecting formal student interviews or surveys, I relied on ongoing teacher reflection, classroom observation, and classroom artifacts to examine what changed as I implemented more choice-based learning experiences. Through this reflective process, I noticed important shifts in both my students and myself. Students appeared more engaged, more willing to share their thinking, and more open to taking risks when they were given meaningful opportunities to make decisions about their learning. I also saw changes in my own role as I moved from being the primary director of learning to more of a facilitator. Overall, this study suggests that creating space for voice, choice, and opportunity can support learner agency and contribute to a more engaging middle grades mathematics classroom.Item Open Access Using Manipulatives to Enhance Students’ Comprehension and Engagement(University of Wyoming Libraries, 2026-04-27)Mathematics is a subject in both primary and secondary education that plays a critical role in developing foundational academic skills. Because of this, mathematics instruction should actively engage students in constructing their own understanding, helping them develop conceptual knowledge through hands-on, interactive lessons that promote self-discovery of concepts. Fractions are the building blocks for conceptual understanding in later subject areas such as algebra and proportional reasoning. The purpose of this study was to examine how manipulatives, taught through the Concrete–Representational–Abstract (CRA) model, could support students’ conceptual understanding and achievement when learning to divide fractions while keeping them engaged. The study design used was a mixed-methods approach, incorporating pre- and post-tests, surveys, and focus group interviews; the pre- and post-test data, in conjunction with the survey, supported quantitative analysis, while the survey and focus groups contributed to qualitative insights. The findings showed that manipulative use when teaching fraction division enhances conceptual understanding and achievement while keeping students actively engaged in the lessons. The researcher concluded that using manipulatives when teaching dividing fractions not only improved academic achievement and strengthened conceptual understanding, but that increased engagement also contributed to these outcomes. These findings suggest that teachers should incorporate manipulatives more consistently within instruction to support both understanding and engagement, particularly when teaching abstract mathematical concepts. Future research should examine the effectiveness of manipulative use across different grade levels and mathematical topics.Item Open Access The Role of Routines, Norms, and Instructional Structures in Supporting Collaborative Learning in a Secondary Mathematics Classroom(University of Wyoming Libraries, 2026-04-28)This action research study examined how the consistent implementation of classroom routines, norms, and instructional structures influenced the organization, participation, and facilitation of collaborative learning in a secondary mathematics classroom. Grounded in sociocultural learning theory and reflective practice, this study addressed the gap between the intention to implement collaborative, student-centered learning and the challenge of sustaining it in daily practice. Using a qualitative, teacher-driven action research design, data were collected across six consecutive lessons through video recordings, reflective journals, and lesson transcripts. Analysis revealed three key findings. First, consistent collaborative routines improved classroom organization and instructional flow by creating a predictable environment that reduced uncertainty and allowed greater focus on mathematical thinking. Second, explicitly taught norms and accountability structures increased equitable participation and expanded access to mathematical discourse. Third, as these structures became internalized, the teacher’s role shifted from managing behavior to facilitating student thinking and supporting the co-construction of knowledge. These findings suggest that collaborative learning is most effective when supported by intentional, consistently implemented structures. This study highlights the role of instructional design and reflective practice in creating classroom environments where collaboration, equitable participation, and meaningful mathematical discourse can be sustained.Item Open Access Understanding Before Executing: A Literature Review of Conceptual Fraction Instruction and Its Implications for Upper Elementary Students and Teachers(University of Wyoming Libraries, 2026-04-28)Fractions remain one of the most persistently challenging topics in upper elementary mathematics despite decades of curricular reform. This extended literature review examines the long-term benefits of teaching fractions conceptually before procedurally in upper elementary classrooms, with fraction division serving as the primary focal concept through which this argument is examined, synthesizing research from the 1990s through contemporary systematic reviews. Three interconnected theoretical frameworks guide this analysis: the Conceptual vs. Procedural Knowledge Framework, the Mathematics Achievement Prediction Framework, and the Proficiency Development Framework. Together, these frameworks demonstrate that conceptual-first instruction provides the cognitive foundation for meaningful fraction learning and fraction division understanding specifically, predicts sustained mathematical achievement, and supports knowledge transfer to ratios, proportional reasoning, and algebra. The review also addresses significant counterpoints, including the persistence of whole number bias, which is particularly consequential for fraction division where whole number intuitions about division are most directly contradicted, individual variation in development pathways, and limitations of traditional part-whole instructional approaches. These counterpoints refine rather than undermine the central argument, pointing toward a more nuanced position: procedural instruction alone is demonstrably insufficient, conceptual understanding must come first to initiate meaningful learning, and teachers must remain responsive to individual students as conceptual and procedural knowledge develop in tandem. A consistent finding across the literature is that effective conceptual instruction depends fundamentally on teachers' own conceptual understanding, as many elementary teachers lack the mathematical depth necessary to teach fractions meaningfully. The evidence affirms that improving fraction instruction requires not merely resequencing content, but transforming mathematical experiences through investment in teacher preparation and instructional practices that prioritize conceptual depth over procedural coverage.Item Open Access Funding Recreation in Wyoming Communities: A Guide to Revenue Mechanisms, Partnerships, and Financing Tools for Local Governments(University of Wyoming Libraries, 2026-04-24)Funding Recreation in Wyoming Communities: A Guide to Revenue Mechanisms, Partnerships, and Financing Tools for Local Governments (Wangen, April 2026) is a practical legal guide produced by the Jay Kemmerer WORTH Institute in collaboration with the College of Law’s Gina Guy Center for Land and Water Law. The report surveys the primary funding mechanisms Wyoming law allows counties, municipalities, school districts, and unincorporated communities to build and maintain recreation infrastructure, from trails and parks to aquatic centers and community facilities. The guide organizes these tools into six categories: excise taxes (including Special Purpose Excise Taxes, municipal excise taxes, and lodging/tourism taxes); public recreation districts and mill levies; joint powers agreements and boards; improvement and service districts; county and municipal bonding authority; and state and federal grant programs, including the newly established Wyoming Outdoor Recreation and Tourism Trust Fund (ORTTF) and the Recreational Trails Program (RTP). For each mechanism, the report identifies the governing Wyoming statutes, outlines legal requirements and procedural limits, and illustrates practical application through Wyoming case examples such as the Casper SPET, the Albany County Recreation Board, and the Pinedale Aquatic Center. Quick-reference tables throughout make it a useful desk reference for local officials, planners, and community stakeholders evaluating how to finance recreation projects in their jurisdictions.
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