Introduction

1. Debra I. Johanning The University of Toledo Judith Herb College of Education debra.johanning@utoledo.edu CAREER: Teaching Practices That Support Fraction- Based Algorithmic Thinking • Relevant Constructs • Algorithmic Thinking • algorithms emerge as products of • students’ own mathematical activity • involves building algorithms via • development of number sense and • meaning of operations • (Gravemeijer & van Galen, 2003) • Local Instructional Theory • “A local instructional theory describes, with arguments, how enacting a series of • instructional activities can support a specific long-term learning process. It would for example, describe how children first learn informal ways of addition and • subtraction and how they may thereby develop more standard procedures for • addition and subtraction. Or it would describe how children develop calculation • procedures that may or may not be similar to the standard algorithms for • multiplication or division.” (Gravemeijer & van Galen, 2003, p. 117) • Routines of Practice • “Core activities that should occur within a particular domain…core set of practices that a teacher could follow…” (Franke, Kazemi & Battey, 2007, p. 250) • Generic routines, not based on local instructional theories, are lacking in power and may not allow a teacher to make purposeful and effective instructional choices in the moment. • Analytic Framework Guiding Phase One of Study (2009-2012) • Mathematical Development • Representational Modes • Purposefulness • Discursive Considerations • Introduction • In a 2007 review of research on rational number, Lamon reported that “progress is unlikely if researchers do not develop personal research agendas, life-long areas of interest that keep them focused on a significant issue” (p. 661) within the domain. The research and educational activities outlined in this 5-year project focus on advancing the field in the area of fraction operation algorithm development. The major focus is the study of and development of ways to support teacher practice when it aims to engage students in algorithmic thinking associated with fraction operations. • Project Objectives • Understand and document routines of practice (and related instructional theories) that exemplary teachers use as they engage students in algorithmic thinking for fraction operations. • 2. Use outcomes from Objective One to develop a prototypical model of core routines of practice composed from exemplary teachers that support students as they engage in algorithmic thinking for fraction operations. • 3. Design, pilot and study the usability of the prototypical model of core routines of practice as a professional development tool with typical teachers as they engage students in algorithmic thinking for fraction operations. • 4. Identify the core routines of practice from Objective Three that are shown to be productive with typical teachers and explore ways of disseminating them at a larger scale. • Two-Part Framework: Exemplary and Typical Practice • Phase One: Understanding Exemplary Practice • Year 1 and Year 2: Collaborative study of 4 teachers, whose practice is identified as examplary, while teaching CMP Bits and Pieces II unit on fractions operations • Research Focus: • Observation of teaching, video, post-lesson reflections and interviews to unpack each teacher’s practice and articulate their local instructional theory for engaging students in fraction-operation based algorithmic thinking • design individual case studies of each teacher’s local instructional theory and look across cases to articulate routines of practice that support students to engage in algorithmic thinking associated with fraction operations • develop prototypical model of effective practice that can be used to inform Phase Two of the project • Year 3: Continued analysis of Year 1 and Year 2 data and an observational study of typical practice in order to support the tool development and professional development for Phase Two • Phase Two: Supporting Typical Practice • Year 3: Study typical practice in light of Phase One data and findings • Years 3, 4 and 5: Design and pilot professional development materials to support typical teachers working to engage students in fraction-based algorithmic thinking. The professional develop will involve a modified lesson study approach. • Research Focus: •  understanding what aspects of core routines of practice support typical practice (design, study, adjust, study...) • understanding how teachers make use of PD tools in order to support large-scale dissemination • Educational product: PD materials to support teacher practice that engages students in algorithmic thinking associated with fraction operations ACKNOWLEDGEMENTS This research is supported by the National Science Foundation under DR K-12 Grant No. 0952661 and the Faculty Early Career Development (CAREER) Program.