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. However, to benefit from multiple graphical representations, students need to engage in a number of learning processes. 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.

To address the open question of how to enhance students' benefit from multiple graphical representations that use the same symbol system, I conducted a series of five classroom experiments and lab studies with over 3,000 students in grades 4-6. Each experiment tested 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 re-presentations while blocking task types. Building on Experiment 2, Experiment 3 investigates whether (in addition to moderately interleaving task types) 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 (while moderately in-terleaving task types) enhances students' benefits from multiple graphical representations. Furthermore, Experiment 3 replicates the finding from Experiment 1 that multiple graphical representations lead to better learning than a single one. 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.

A further contribution of my thesis work is the development of an intelligent tutoring system for fractions that leads to significant and robust gains in students' conceptual and procedural knowledge of 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 while employing user-centered techniques. To develop the Fractions Tutor, I made use of a novel methodology to resolve stakeholder conflicts that inevitably arise in complex educational settings.

I consolidate my empirical findings in a novel theoretical framework that describes the learning processes that students perform when learning with multiple graphical representations. This framework extends existing theoretical frameworks, which have solely focused on learning with representations that use different symbol systems (such as text accompanied with one additional graphical representation), rather than on learning with multiple representations using the same symbol system (such as multiple graphical representations). My theoretical framework proposes that in order to benefit from multiple graphical representations, students need to conceptually understand each individual graphical representation and to use each graphical representation fluently to solve domain-specific problems, students need to conceptually understand the connections between different graphical representations, and they need to become fluent in making these connections.

In sum, my thesis work contributes (1) an empirically validated set of instructional design principles for the effective use of multiple graphical representations, (2) a theoretical framework for learning with multiple graphical representations that use the same symbol system, (3) an effective tutoring system for fractions learning, and (4) a new methodology for resolving design conflicts that often occur in real educational settings.

263 pages

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