Vygotskian hybridizing of motion and mapping: Learning about geometric transformations in block-based programming environments

ABSTRACT

Research on geometric transformations suggests that early learners possess intuitive understandings grounded in motion metaphors, transitioning to mappings. The processes through which students transition between these two conceptions are not fully understood. We propose that Vygotskian hybridizing (related to Vygotsky’s articulation of everyday and scientific concepts) may provide a lens for thinking about the relationship between these conceptions. Design features of block-based programming environments provide affordances to support hybridizing by providing a co-action space for learning. We conducted a comparative case study of four grade seven and eight students working in a Scratch task (Code the Quilts) and a game (Transformations Quest) to construct understandings of geometric transformations. Our findings suggest: (1) students hybridized their personal experience of motion and mathematical knowledge of mapping to build geometric transformations understandings and (2) the co-action space in which students worked promoted distributed interactions between students, block-based environments, and tasks to support hybridizing.

KEYWORDS:

• Symmetry
• geometric transformations
• hybridizing
• motion and mapping
• Vygotsky
• block-based programming

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical approval

Ethics Certificate number REB18–0304 covered the experimental interviews reported in this research work, issued by the Conjoint Faculties Research Ethics Board (CFREB) at the University of Calgary for the “Students as mathematical and scientific thinkers and modelers” project on April 23, 2018, with expiry date April 23, 2023.

Notes

1. Note: We use [] and bold font to indicate a block procedure belonging to the computational environments in the text. We use only bold font in block procedures in a transcription.

Additional information

Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1742257. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We are grateful to Natalie Major, teacher from the Canadian Rockies Public Schools for her thoughtful comments and collaboration to interview some participants for this study.

Notes on contributors

Jesús E. Hernández-Zavaleta

Jesús E. Hernández-Zavaleta is a Postdoctoral Scholar at the University of Florida’s College of Education focusing on Equitable and Interactive Mathematical Modeling. His previous appointment at the Werklund School of Education in the University of Calgary focused on the development of mathematical and computational thinking, with particular emphasis on K-12 students. He has also been a classroom teacher at the high school level and a mathematics teacher trainer in Mexico and South America.

Corey Brady

Corey Brady is an Assistant Professor of the Learning Sciences at Vanderbilt University. His research focuses on mathematical and computational modeling, with a particular emphasis on supporting and understanding the collective learning of classroom groups. Prior to entering academia he worked in industry, leading the design and development of Texas Instruments’ TI-Navigator system (2001-2006). He has also been a classroom teacher, at middle school, high school, and community college levels. Brady holds degrees in Pure Mathematics (MS), English Literature (MA), and Mathematics Education (PhD).

Sandra Becker

Sandra Becker is Postdoctoral Scholar at the University of Calgary’s Werklund School of Education. Her recently completed PhD research focuses on the affordances of elementary school makerspace environments as teacher professional learning studios when designing for interdisciplinary curricular study. Prior to entering the PhD program, Sandra taught elementary school, both as a classroom teacher and teacher librarian.

Douglas B. Clark

Doug Clark is the Werklund Research Chair of Design-Based Learning at the University of Calgary’s Werklund School of Education. His research focuses on the design of digital learning environments, students’ learning processes, and the opportunities of design for teachers and students. Doug has been awarded multiple funded grants from the US National Science Foundation, Department of Education, and the US National Academy of Education/Spencer Foundation.