When Constant in a Proportional Relationship Isn’t Constant—A Sign of Not-So-Shared Understandings

Teacher knowledge, especially of proportional reasoning, is important, particularly in middle school grades in the United States. In this instrumental case study, one teacher’s understanding of constant as it relates to proportions and how that understanding shifted over the course of a six hour professional development experience is discussed. The professional development focused on three important components of proportional reasoning: quantity, covariation, and constant. The teacher had access to knowledge about some, but not all, characteristics of proportional relationships. She understood that both quantities need to covary but did not constrain this relationship to multiplication. She paid persistent attention to a relationship other than the constant relationship between quantities. The knowledge that was public to the facilitator during the professional development did not reveal the persistent attention Dora paid to a relationship other than the constant relationship between quantities. The results highlight the complicated task of making sense of teachers’ reasoning and suggests three key considerations for teacher education.