Mathematically based and practically based explanations

Esther Levenson, Pessia Tsamir and Dina Tirosh have written an interesting article about Mathematically based and practically based explanations in the elementary school: teachers’ preferences. Their article was published online in Journal of Mathematics Teacher Education on Friday. In this article, the authors make interesting connnections between research on teachers' knowledge and beliefs. Although their focus is on knowledge and beliefs in relation to the use of explanations (and they distinguish between mathematically and practically based explanations) in the classroom, the article makes a nice contribution to extending our understanding of the way these concepts are related. The part of teachers' knowledge (and beliefs) that the authors discuss is related to students' thinking, or even a sub-category of that. In this respect, they make valuable contributions to what Deborah Ball and her colleagues refer to as Knowledge of Content and Students, but their focus is also in the borderline of what is referred to as Knowledge of Content and Teaching. The links to research concerning teachers' beliefs is also interesting, althought the authors don't go into great detail here. They are, of course, aware of this, and explain that they have only given "a glimpse into the complexity of the relationship between teachers' knowledge and beliefs", in particular with focus on teachers' use of explanations.

Here is the abstract of their article:

This article focuses on elementary school teachers’ preferences for mathematically based (MB) and practically based (PB) explanations. Using the context of even and odd numbers, it explores the types of explanations teachers generate on their own as well as the types of explanations they prefer after reviewing various explanations. It also investigates the basis for these preferences. Results show that teacher-generated explanations include more MB explanations than PB explanations. However, many still choose to use mostly PB explanations in their classrooms, believing that these explanations will be most convincing to their students. The implications for teacher education are discussed.