Empirical Research: Emerging Research: Learning with Multiple Graphical Representations in a Complex, Real-world domain: Intelligent Software Tutors for Fractions

Carnegie Mellon University, Pittsburgh PA

Investigators

Abstract

The cognitive science and educational psychology literatures provide ample evidence that instructional materials and activities that judiciously combine multiple representations of learning content (MRs) can have significant learning benefits. Much of this literature has focused on learning with a combination of text and figures; only some of it has focused on learning with multiple graphical representations. In order to benefit from multiple representations, students must connect key information across the different representations. Students typically must be supported in doing so (Ainsworth, 2006). This project studies the use of MRs in the domain of fractions, a very challenging area of mathematics for middle-school students in which graphical representations are used extensively (e.g., pie charts, number lines, fraction strips, set models, etc.) The research focuses on three general (and open) questions that instructional designers face when creating a curriculum that involves the use of MRs: First, when multiple representations of learning materials are used, how frequently should learners switch between representations? Second, what kinds of activities are most effective in helping students make connections between different representations? Third, what fraction of the students? time should be devoted to making connections between representations, relative to activities centered on a single representation? Researchers from Carnegie Mellon University and the University of Freiburg (Germany) investigate these questions in the context of an established educational technology: intelligent tutoring systems. These types of software tutors have been shown to improve students' mathematics learning in a number of scientific studies. A set of authoring tools created in a lab at Carnegie Mellon make the development of these tutors more cost effective and more accessible to education researchers than it used to be. During a three-year grant period, the project will (1) create web-based intelligent tutors as supplemental activities for fractions learning; these tutors support activities in which students work with interactive graphical representations of fractions, and make connections between the representations, and (2) conduct controlled experiments in Pittsburgh middle schools to investigate the three research questions outlined above. The proposed research will result in principles for learning with MRs. It will produce new knowledge about how fraction representations can best be used to support robust learning. The proposed research has the potential to produce more effective fractions instruction in the lower and middle grades, and thereby facilitate later mathematics learning. The proposed software tutors will be made freely available on the Mathtutor website (http://webmathtutor.org).