How to Use Multiple Graphical Representations to Support Conceptual Learning: Research-Based Principles in the Fractions Tutor

• In Event: Improving Instruction About Fractions: Different Approaches to Supporting Teachers and Students in the Classroom

Abstract

Most learning environments in the STEM disciplines use multiple graphical representations along with textual descriptions and symbolic representations. Multiple graphical representations are powerful learning tools because they can emphasize complementary aspects of complex learning contents (Ainsworth, 2006). However, to benefit from multiple graphical representations, students need to engage in a number of learning processes (Ainsworth, 2006). Educational technologies offer novel opportunities to support these learning processes by making graphical representations interactive and by providing individualized instructional support for students’ interactions with them. Yet, these opportunities are under-researched, as most prior research has taken a symbol-systems approach by focusing only on multiple representations that use different symbol systems, such as text and one additional graphical representation (Mayer, 2005; Schnotz & Bannert, 2003).

To address the open question of how to enhance students’ benefit from multiple graphical representations that use the same symbol system, we conducted a series of five classroom experiments and lab studies with over 3,000 students in grades 4-6. Each experiment tests the effectiveness of different types of instructional support for students’ learning with multiple graphical representations. Experiment 1 compares the effects of multiple over a single graphical representation and the effects of prompting students to self-explain the relation between graphical and symbolic representations. Results show that multiple graphical representations lead to better learning than a single graphical representation, provided that students receive self-explanation prompts. Experiment 2 contrasts sequences of task types and graphical representations. The results show that interleaving task types while blocking graphical representations promotes students’ learning from multiple graphical representations more so than interleaving graphical representations while blocking task types. Building on Experiment 2, Experiment 3 investigates whether graphical representations should also be presented in an interleaved, rather than in a blocked fashion. An analysis of learning outcomes and tutor log data demonstrates that interleaving graphical representations enhances students’ benefits from multiple graphical representations. Experiment 4 investigates the effects of different types of instructional support for connection making between multiple graphical representations. The results show that a combination of support designed to help students actively make sense of the connections and of support designed to help students become fluent in making these connections is needed for students to benefit from multiple graphical representations, compared to a single graphical representation. Finally, Experiment 5 investigates different sequences of connectional sense-making support and connectional fluency-building support. The results lead to the conclusion that receiving support for making sense of connections first is a prerequisite to students’ benefit from subsequent connectional fluency-building support.

We conducted this research within the context of an effective educational technology: an intelligent tutoring system for fractions. In addition to investigating how best to support students’ learning with multiple graphical representations, each experiment also served to iteratively improve the Fractions Tutor (Rau, Aleven, Rummel, & Rohrbach, 2013). The Fractions Tutor incorporates the instructional design principles that we identified in our classroom experiments and has been repeatedly shown to lead to significant and lasting learning gains.

Authors

• Martina A Rau, Carnegie Mellon University

• Vincent Aleven, Carnegie Mellon University

• Nikol Rummel, Institute of Education - Ruhr-Universität Bochum