Multiplicative Meaning in Physics

• In Event: 45.082 - Multiplicative Models of Situations Across Disciplines

Abstract

Objectives: Research on models and meanings of multiplication has tended to focus on elementary and middle-school students as they solve school problems typically encountered in those grades. Furthermore, when the multiplicative understandings of more adult populations are considered, the tendency has been to look at adults solving problems that are characteristic of the tasks presented to students in the early grades. In this talk, I will look at a different context: advanced college students solving physics problems. My aim will be to compare the meanings ascribed to multiplicative relations by this more advanced population to those of younger students. I will ask: Do we see a subset of the early grade meanings of multiplication? Do entirely new meanings appear?

Theoretical perspective: In prior work, I have argued that physics students learn to understand equations in terms of a set of meanings I call symbolic forms (Sherin 2001). Each symbolic form consists of an association between a conceptual schema and a symbol template. In essence, the conceptual schema is the “meaning,” and the symbol template is the specification of how to represent that meaning in terms of a symbolic expression.

Method & Data Sources: I draw on data in which five pairs of third-semester physics students worked together to solve problems, following an IRB-approved protocol. Each pair was recorded as they worked at a whiteboard. The sessions were between 1 and 1.5 hours, with each pair participating in four to six sessions. The analysis of the data focused on interpretation and construction events. Interpretation events were moments where students stated the meaning of an expression they had written; in construction events students wrote a new symbolic expression based on a meaning that they wanted to express. In total, 144 interpretation events and 75 construction events were identified. Ultimately these events were all coded in terms of symbolic forms.

Results: In this talk, I focus on the subset of symbolic forms that were related to multiplication. Some of these symbolic forms, such as scaling and proportionality, are closely related to meanings identified by researchers examining the learning of multiplication in the early grades. However, I will also show that some identified symbolic forms did not have any obvious relationship to the early-grade meanings of multiplication.

Significance: This latter observation, I will argue, has important implications for research and instruction in the early grades. In particular, it raises two fundamental questions: (1) Does instruction in multiplication in the early grades prepare students for the wide array of later uses of multiplication, and (2) does it simply miss some of the meanings that young children ascribe to multiplication?

Author

• Bruce Sherin, Northwestern University