ERIC Number: ED668548
Record Type: Non-Journal
Publication Date: 2021
Pages: 271
Abstractor: As Provided
ISBN: 979-8-5381-3384-0
ISSN: N/A
EISSN: N/A
Available Date: 0000-00-00
Progressions in Mathematical Reasoning: A Case Study of Two Teachers' Levels of Units Coordination
Cody Harrington
ProQuest LLC, Ph.D. Dissertation, University of Colorado at Denver
This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning. The purpose of the study is to link levels of units coordination and teachers' growth in order to predict teachers' ability to successfully construct new mathematical reasoning and pedagogy through professional development and intervention. This qualitative case study addresses three research questions: 1) What pathways of reasoning, markers and transitions, may teachers go through? That is, what changes in their multiplicative and fractional reasoning schemes could be inferred? 2) To what extent, and in what ways, do teachers' levels of units coordination affect their learning pathway? and 3) How do teachers' levels of units coordination affect their ability to recognize levels of units in their students? The study involves two participating elementary teachers, Nancy and Marsha, who engaged in a project titled, "Student-Adaptive Pedagogy for Elementary Teachers (AdPed)," in which specific interventions were put into place to foster a conceptual understanding of multiplicative and fractional reasoning. Four main contributions to the field are discussed: 1) Expansion of the mathematical knowledge for teaching construct to include the analysis of teachers' levels of units coordination and the effect on their specialized knowledge of content, 2) a new methodological approach to examining mathematical knowledge for teaching that includes the collection of qualitative data through one-on-one intervention and coaching sessions, 3) a theoretical extension to the mathematical knowledge for teaching construct that includes a constructivist lens, specifically a linkage with the hypothetical learning trajectory construct, and 4) Implications for researchers in the field. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]
Descriptors: Mathematics Instruction, Multiplication, Fractions, Mathematical Logic, Teacher Competencies, Intervention, Faculty Development, Elementary School Teachers, Mathematical Concepts, Concept Formation, Knowledge Level, Knowledge Base for Teaching
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A
Author Affiliations: N/A