Browsing by Author "Karen Hollebrands, Committee Member"

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    Connections among Representations: The Nature of Students' Coordinations on a Linear Function task
    (2007-07-05) Adu-Gyamfi, Kwaku; Ernest Stitzinger, Committee Member; Karen Hollebrands, Committee Member; Lee V. Stiff, Committee Member; Karen S. Norwood, Committee Chair
    This study focuses on students' translations between and coordinations among representations of linear function after having being explicitly taught functions via multiple representational approaches. The purpose of the study was to investigate the nature of connections performed among representations of linear function by students whose instructional experiences have been based on multiple representational approaches. In class examinations and task based interviews were conducted with a purposefully chosen sample of students from the Intermediate Algebra through Multiple Representations course in order to elucidate patterns in students' connections among representations of linear function. Two types of connections were identified in the work of students from the study namely, procedural and foundational connections. This was the case in their translations between and their coordinations among representations of linear function. This study showed that students who performed procedural translations between the given representations of linear function knew of procedures for working within both source and target representations and for moving from given source representations to specified target representations but not the preservation of meaning requirement under a translation. The study showed that students who performed procedural coordinations were restricted in their ability to relate specific representations of linear function or to utilize specific constructs in relating representations of linear function together.
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    Investigating the Role of Equipartitioning and Creating Internal Units in the Construction of a Learning Trajectory for Length and Area.
    (2010-11-04) Nguyen, Kenny; Jere Confrey, Committee Chair; Karen Hollebrands, Committee Member; Allison McCulloch, Committee Member; Paola Sztajn, Committee Member; Jeffrey Thompson, Committee Member
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    Preparing Pre-service Elementary Teachers to Teach Mathematics with Learning Trajectories
    (2010-04-30) Mojica, Gemma Foust; Jere Confrey, Committee Chair; Pam Arroway, Committee Member; Karen Hollebrands, Committee Member; Allison McCulloch, Committee Member
    In the past two decades, research on learning has focused on understanding how students think and how that thinking becomes more sophisticated over time. Some researchers have verified sufficient consistency and robustness in their findings relating to these constructs, which they have articulated in the form of learning trajectories. While an articulation of such constructs has contributed greatly to the knowledge base of how students learn, the field has just begun to explore the extent to which learning trajectories can be integrated into the practice of teaching. Though useful at the level of curriculum, assessment, and standards development, it remains to be shown that learning trajectories can be incorporated into teachers’ practice and become a tool to understand students’ thinking, for planning instructional activities, for interacting with students during instruction, and for assessing students’ understandings. Thus, bringing learning trajectories into the classroom through teacher education is one critical area of knowledge that needs to be investigated. This study addresses to what extent and in what ways can pre-service elementary teachers use a learning trajectory for equipartitioning to build models of student thinking. Over an eight-week period, within an elementary mathematics methods course, 56 pre-service teachers (PSTs) participated in this design study. Data included the following: video & audio recordings of class meetings, researcher's notes of class meetings and school-based experiences, pre- and post-test data, clinical interviews and analysis of interviews, and other artifacts. Findings from this study indicate that PSTs used an equipartitioning learning trajectory to 1) deepen their understanding of mathematics and knowledge for teaching mathematics; 2) build more precise and adequate models of student thinking; and 3) incorporate models of student thinking into instructional practices.
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    Teachers' Uses of a Learning Trajectory for Equipartitioning
    (2009-12-02) Wilson, Peter Holt II; Jere Confrey, Committee Chair; Karen Hollebrands, Committee Member; Allison McCulloch, Committee Member; Roger Woodard, Committee Member
    Recent work by some researchers has focused on synthesizing what is known about students' thinking of particular concepts. These syntheses elaborate core progressions called learning trajectories that articulate how thinking matures from informal ideas to increasingly complex understandings. Though useful at the level of curriculum, assessment, and standards development, it remains to be shown that learning trajectories can be incorporated into teachers’ practice and become a tool to understand students’ thinking, for planning instructional activities, for interacting with students during instruction, and for assessing students’ understandings. Further, the impact of such incorporation in the classroom on students’ learning is unknown. This design study investigated K-2 teachers’ uses of a learning trajectory for equipartitioning in instruction. Thirty-three teachers participated in 20 hours of professional development focused on a learning trajectory for equipartitioning and key instructional practices including clinical interviewing, task selection and adaptation, analysis of student work, and classroom interactions. A subset of the participants was observed teaching a lesson on equipartitioning and gains in students' learning were measured with pilot items for a diagnostic assessment system. Findings from the study indicate that the introduction of the learning trajectory assisted teachers to varying degrees in building more precise and adequate models of students’ thinking, identifying specifically what students need to learn next, deepening their own understandings of equipartitioning, and facilitating coherent instruction. These findings suggest that learning trajectories can act as a tool for coordinating (1) a student’s behaviors and verbalizations with cognition, (2) various models of thinking among groups of students, and (3) these models with instructional practices.
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    Using Dynamic Geometry Software to Develop Students’ Conceptual Understanding of Angle
    (2010-08-06) Lineberry, Carrie; Karen Keene, Committee Chair; Molly Fenn, Committee Member; Karen Hollebrands, Committee Member