Esther Levenson has written an article called

Fifth-grade students’ use and preferences for mathematically and practically based explanations. The article was published online in

Educational Studies in Mathematics a few days ago. What Levenson refers to as “practice based explanations” are related to what others refer to as real-life connections, students’ informal knowledge, etc. Practice based explanations do not rely on mathematical notions only, and include explanations that use manipulatives and explanations that are based on real-life contexts. Obviously, this implies that there is a variety of explanations to consider, and Levenson provides a nice overview of some relevant literature within this field. She also discusses students’ evaluations of explanations, and she thereby enters a discussion of the different types of knowledge you need to have.

The study she reports from is a combination of quantitative and qualitative analysis of data from a total of 105 students in 5th grade (in Israel). Data were collected from two questionnaires, in addition to follow-up interviews with some of the students.

Here is the abstract of Levenson’s article:

This paper focuses on fifth-grade students’ use and preference for mathematically (MB) and practically based (PB) explanations within two mathematical contexts: parity and equivalent fractions. Preference was evaluated based on three parameters: the explanation (1) was convincing, (2) would be used by the student in class, and (3) was one that the student wanted the teacher to use. Results showed that students generated more MB explanations than PB explanations for both contexts. However, when given a choice between various explanations, PB explanations were preferred in the context of parity, and no preference was shown for either type of explanation in the context of equivalent fractions. Possible bases for students’ preferences are discussed.

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