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Elementary Teachers’ Understanding and Use of Cognition Based Assessment Learning Progression Materials for Multiplication and Division

Harrison, Ryan Matthew
http://rave.ohiolink.edu/etdc/view?acc_num=osu1330296812

Abstract Details

2012, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
Teachers’ knowledge of mathematical content and children’s mathematical thinking have been identified as critical elements related to teachers’ ability to effectively teach mathematics (Fennema & Franke, 1992; Kazemi & Franke, 2001; Ma, 1999; Peterson, Carpenter, & Fennema, 1989). Literature on teachers’ knowledge suggests that teachers need not only to hold a deep understanding of the mathematics they teach, but also have detailed knowledge of the common correct and incorrect mathematical conceptions their children and research-based knowledge of the progression of the development of children’s mathematical ideas. Research-based learning trajectories and learning progressions of children’s mathematical development represent a potentially valuable resource for teachers to help make sense of children’s thinking, and research on teachers’ use and understand of such materials is much needed. This study investigated teachers’ understanding and use of the Cognition Based Assessment (CBA) learning progression materials for multiplication and division concepts. The data sources included structured clinical interviews based around teachers’ use of the CBA materials in analyzing written student work episodes, determining learning goals based on student work, and proposing instructional plans to help students progress in their mathematical understanding. Additionally, three case studies of teachers using the CBA materials in live one-on-one teaching and assessment situations are investigated. Analysis of teachers’ use and understanding of the CBA materials consisted of grounded theorizing and retrospective analysis, involving iterations of hypothesis/conjecture formation based on data, hypothesis/conjecture testing, and hypothesis/conjecture revision. The study had several key findings. First, as complexity of either the CBA level, or a student’s mathematical reasoning within the CBA framework increased, so did the inconsistency and variation in teachers’ interpretations of the student thinking. This finding led to the conceptualization of teachers’ consistent, partially consistent, and inconsistent use of CBA materials. A second important finding was that CBA language and research-based descriptions of children’s thinking were occasionally quite challenging for teachers to interpret or understand. The terminology and conceptual ideas embedded in the CBA multiplication and division framework occasionally involved mathematical or technical descriptions that led to inconsistent teacher conceptualizations and misinterpretations of the CBA framework. A third important finding was that CBA consistent conceptualizations of student thinking within the CBA framework were frequently related to learning goals and instructional plans that were more informed by children’s thinking. This relates to similar findings by the research related to Cognitively Guided Instruction (CGI) (Fennema et al., 1996; Franke, Carpenter, Levi, & Fennema, 200; Kazemi & Franke, 2001; Peterson, Carpenter, & Fennema, 1989). Overall, the data demonstrated that the CBA multiplication and division learning progression materials could become a powerful framework for teachers to analyze their own instruction and assessment of children’s mathematical thinking.
Michael Battista, PhD (Advisor)
Patricia Brosnan, PhD (Committee Member)
Karen Irving, PhD (Committee Member)
398 p.
Mathematics Education
learning progressions; learning trajectories; teacher knowledge

Recommended Citations

Citations

  • Harrison, R. M. (2012). Elementary Teachers’ Understanding and Use of Cognition Based Assessment Learning Progression Materials for Multiplication and Division [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1330296812

    APA Style (7th edition)

  • Harrison, Ryan. Elementary Teachers’ Understanding and Use of Cognition Based Assessment Learning Progression Materials for Multiplication and Division. 2012. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1330296812.

    MLA Style (8th edition)

  • Harrison, Ryan. "Elementary Teachers’ Understanding and Use of Cognition Based Assessment Learning Progression Materials for Multiplication and Division." Doctoral dissertation, Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1330296812

    Chicago Manual of Style (17th edition)

osu1330296812
968
© 2012, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.