Prospective Teachers’ Reasoning While Pair Programming Geometric Patterns
Restricted (Penn State Only)
- Author:
- Dinc, Emre
- Graduate Program:
- Learning, Design, and Technology
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 17, 2024
- Committee Members:
- Susan Land, Program Head/Chair
Susan Land, Major Field Member
Xiangquan Yao, Outside Unit Member
Rose Zbiek, Outside Field Member
ChanMin Kim, Chair & Dissertation Advisor - Keywords:
- mathematical reasoning
block-based programming
algebraic thinking
prospective teachers
cognitive mechanisms
constructionism
instrumental sociogenesis
pattern generalization
visual cues
rule generation
pair programming
geometric patterns
dynamic objects
pattern recognition
visualization
colalboration
recursive reasoning - Abstract:
- There are challenges and potential underemphasis on algebraic thinking, specifically, recognizing and using relations instead of objects, in preservice teacher education. By conducting a qualitative analysis of video and screen recordings, block code, process entries, and semi-structured post-interviews, this study investigates how and why paired prospective elementary teachers use objects to generate rules while solving geometric pattern problems and programming geometric patterns within a visual programming platform. Employing a multiple case design, I examined how three pairs generalized geometric patterns and programmed geometric patterns, guided by the conceptual framework grounded in constructionism and instrumental sociogenesis. The findings indicated that pairs (a) used visual cues, explored patterns, and generated rules, (b) explored, identified, and expressed relations by using dynamic objects, (c) engaged in and applied recursive reasoning in programming of geometric patterns through their unique selection and arrangement of blocks, and (d) turned Scratch into an instrument for mathematical investigations. Findings are discussed, including their implications for research and practice.