Mathematically and practically-based explanations: individual preferences and sociomathematical norms

This paper is an initial investigation of teachers’ and students’ preferences for mathematically-based (MB) and practically-based (PB) explanations and the relationship between those preferences and sociomathematical norms. The study focuses on one fifth grade teacher and two of her students and discusses three issues. The first issue concerns students’ abilities to understand and accept MB explanations. The second issue concerns the choices teachers make regarding the types of explanations they introduce to their classes and the basis for these choices. The third issue concerns the place of the individuals’ preferences within the sociomathematical norms of the class. The findings indicate that elementary school students are capable of understanding MB explanations and some might even prefer them. We also found that although a teacher might personally prefer MB explanations, this preference may be set aside for didactical considerations. Finally, we discuss the complex relationship between individual preferences for MB and PB explanations and sociomathematical norms.