Teachers Exploring Proportional Reasoning through Digital Representations: Reasoning with Invariance vs. Showing the Answer

• In Event: Advancing Mathematics Teaching and Learning Through Targeted Professional Learning and Digital Supports

Abstract

This study examines how in-service teachers (grades 3-9) engaged with proportional reasoning through digital representations in the context of invariance. Data were collected from two professional development offerings in different settings. Special education middle grade teachers engaged in rich reasoning with invariance, interacted meaningfully with the representations, generalized relationships, used more precise language, applied inductive reasoning, and generated richer example spaces. In contrast, elementary math teachers used the representations to show answers, relied more on deductive reasoning, and were less exploratory. Both groups encountered challenges in working with digital representations, particularly when attending to less common aspects of invariance. Implications for teacher education programs and professional development are discussed.

Authors

• Gal Gili Nagar, University of Massachusetts - Dartmouth

• Chandra H. Orrill, Rethink Learning Labs

• Rachael Eriksen Brown, Pennsylvania State University - Abington

• Kun Wang, Rethink Learning Labs