By

*Lisa Sindorf and Joyce Ma*-July 2015

### PAPER CITATION

Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. *Learning and Instruction, 16 (3), 183–198.*

Educators in informal science are exploring ways to involve learners in analyzing and interpreting data. One method for fostering these skills is data visualization. However, designing visualizations of data for learners can be challenging, especially when the visualizations show more than one data type or format.

This Ainsworth paper refers to presentation of more than one way of visually representing a concept as *multiple external representations.* In this framework, “external representations” show an abstract idea, like acceleration, as something learners can perceive in the real world, like a graph of velocity over time. A simple version of multiple external representation would be to combine a graph of velocity and an animation of a motorcycle’s position as it goes down a hill.

**Research Design**

This paper proposes a three-part framework for understanding how multiple external representations can support learning: **De**sign, **F**unctions, and **T**asks, or **DeF**T.

The **design** parameters that are unique to multiple external representations include:

- The
*number*of different representations - What
*type of information*the representations show - The
*forms*of the representations, such as text, graphs, or equations - The
*sequence*in which learners may encounter the representations - The
*connections*or relationships between the representations

Multiple external representations have three possible **functions**:

- The information in multiple representations may be
*complementary*, allowing learners different ways to access the material. For example, a table of velocity over time displays precise values while a graph more clearly shows the relationship between velocity and time. - Multiple representations may
*constrain*the interpretation. For instance, a concrete animation of a motorcycle rolling down a hill will constrain the interpretation of an accompanying line graph of velocity over time, helping learners more easily make sense of it. - Multiple representations may help with
*constructing understanding*by enabling learners to integrate two or more ways of visualizing data. For example, learners may come to understand graphs of acceleration, velocity, and distance by relating them to each other and to an animation.

Educators must also consider the **tasks **learners may need to perform using the multiple external representations. Tasks can include:

- Understanding the
*form*of the representation, for example, knowing how to read the axes of a graph - Grasping the
*relationship*between the representation and the concept, for example, being able to map a point on a graph to velocity at a given time *Selecting*an appropriate representation, for example, knowing when to choose a line graph to represent change over time*Constructing or inventing**an appropriate representation, for example, being able to create a line graph that captures the relevant qualities of a motorcycle’s motion*

**Research Findings**

Ainsworth’s framework suggests two questions educators can use in designing data visualizations that include *multiple external representations*:

- What skills and prior experience do learners come with? Learners who are not familiar with the external representations used may need guidance. Alternatively, the design could emphasize familiar representations over less familiar ones—for example, a map instead of a box-and-whisker plot.
- What functions are the external representations intended to support?
- If the function of the representations is to
*complement*one another, the design should focus on representing the content and aligning with learners’ prior experiences. Less attention can be paid to helping learners understand the relationships among the representations. For example, if learners are exploring how a motorcycle moves through a city, one representation might show the motorcycle’s position on a map, and another might show a graph of the motorcycle’s velocity over time. - If the function of the representations is to
*constrain*interpretation and use, the design should explicitly connect the representations. The representations should be available simultaneously and perhaps be dynamically linked. For example, the motorcycle’s speed could be represented by a graph and its changing position on the map could be animated. As the animated motorcycle moves, its velocity on the corresponding graph could be highlighted. - If the function of the representations is to help learners
*construct*a deeper understanding, the design must support learners with the demanding tasks of translating between representations and drawing inferences. Each representation might repeat some of the same information, or multiple representations might be visible at the same time. For example, to show that the motorcycle’s velocity is influenced by its position—for example, it slows down when going around turns—the representations must support learners in connecting the two types of information so they can make generalizations about the relationship between speed and position.

- If the function of the representations is to

**Theoretical Basis**

Ainsworth takes a cognitive, rather than a social-cultural, perspective on external representations, based on Palmer’s (1977) definition:

An external representation consists of (1) the represented world, (2) the representing world, (3) what aspects of the represented world are being represented, (4) what aspects of the representing world are doing the modeling and (5) the correspondence between the two worlds.(p. 184)

The DeFT framework synthesizes prior work in cognitive science and learning to reconcile findings about the benefits and challenges of using multiple external representations. It attempts to address the limitations of prior theories, including the cognitive theory of multimedia learning and cognitive load theory, that have focused on working memory and the limited capacity of different sensory modalities.

**Implications for Practice**

Learners face a number of challenges when they engage with representations of data. Informal science practitioners can facilitate learners’ understanding by considering prior experiences with data visualization and by clarifying the purpose of the multiple representations. Further research will need to look more closely at effective ways to support learners as they connect with and interpret data. Each dataset or group of representations will have a unique purpose and offer its own challenges.