Relational Mapping: An Interactive Perspective on Classroom-Level Analogy Support

• In Event: Investigating Cognition and Motivation at the Classroom Level

Abstract

Purpose: We investigated how teachers and students construct analogies, and whether their construction and use are associated with learning outcomes at the classroom level. While prior work has examined how instructors support and use analogies in the classroom (Richland, Holyoak, and Stigler, 2004; Richland, Zur, & Holyoak, 2007), no work has examined whether the frequency or type of analogy construction relates to classroom learning.

Framework: We based our coding on Gentner’s (1983) definition of analogy as a comparison that maps relations – that is, a predicate taking two or more arguments – from a base to a target. In other words, an analogy does not simply compare a feature such as color or size in one object to a feature in another. Rather, it compares a relation in a source object, such as the relation between the procedures for calculating the circumference and area of a circle, to a relation in a target object, such as the relation between the procedures for calculating the perimeter and area of a square. This is especially important for predictions about what is learned with relational mapping. For example, mapping a relation across objects rather than specific features conveys more structural detail about the concepts underlying the comparison. Relational mapping also enables learners to draw inferences about the target structure and promotes conceptual learning and transfer (Gentner, Loewenstein, & Thompson, 2003; Kurtz, Miao, & Gentner, 2001; Novick & Holyoak, 1991; Rittle-Johnson & Star, 2007), making it a powerful instructional tool.

Method and data sources: We used the Measures of Effective Teaching database to sample 40 classroom videos (20 high achieving and 20 low achieving as measured by value-added conceptual math scores). We coded classroom talk for instances of analogies and their features. Specifically, we coded for instances in which a teacher or student identified a source object, a target object, and an explicit relational mapping between the objects. All instances of relational mapping were coded based on the types of objects being used (e.g., two concrete math problems), conceptual distance between objects (e.g., two highly similar problems), information conveyed in the analogy (e.g., a point about a general procedure) and who constructed the analogy components (i.e., teacher, students, or both). We will examine associations between the proportion of talk spent on analogies and class math achievement. We will also examine the associations between specific types of analogies used, such as co-constructed versus teacher constructed, and learning outcomes.

Results: Data coding and analysis is ongoing. We hypothesize that high achieving classrooms will make more analogies than low achieving classrooms. We also expect that analogies that are co-constructed (teacher with the students) will be most strongly related to math achievement outcomes. Results will provide an improved understanding of how analogy support emerges naturally in the classroom, and how teachers can best construct analogies for their learning goals.

Authors

• J. Elizabeth Richey, Miami University - Oxford

• Tatum Walker, University of Pittsburgh

• Corrine Green, Purdue University

• Timothy James Nokes-Malach, University of Pittsburgh