PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Exploring student conceptions of binary operation
Page: 166
Students’ conceptions about binary operations often reflect a lifetime of situated learning about concepts such as arithmetic operations and functions in their K-12 years. This prior knowledge base bleeds into their experience of binary operation in abstract algebra, leading students to have differing and incomplete notions of what constitutes a binary operation. We present a qualitative study in which we classify students’ conceptions of binary operation in terms of variation theory and concept image and definition. These frameworks helped us to focus on critical and noncritical aspects of binary operation found in student reasoning. Our results indicate that students’ enacted objects about binary operation fall into one of three domains (i.e. function meaning, arithmetic meaning, and structural meaning) and often depend on task context. Additionally, students’ reasoning reflected a set of critical aspects that diverge from the conventional critical aspects of binary operation.