How to Schedule Multiple Graphical Representations? A Classroom Experiment with an Intelligent Tutoring System for Fractions
Author: Rau, M. A.
Date: 2011-00-00
Type: Reports - Research
Subjects: Intelligent Tutoring Systems,Retention (Psychology),Mathematics,Mathematics Instruction,Mathematical Concepts,Computer Graphics,Visual Aids,Instructional Design,Pretests Posttests,Instructional Effectiveness,Replication (Evaluation),Learning Processes,Sequential Learning,Learning Strategies,Sequential Approach,Elementary School Students

Graphical representations (GRs) of the learning content are often used for instruction (Ainsworth, 2006). When used in learning technology, GRs can be especially useful since they allow for interactions across representations that are physically impossible, for instance by dragging and dropping symbolic statements into a chart that automatically updates to display the information graphically (Moyer, Bolyard, & Spikell, 2002). However, learning with multiple GRs (MGRs) is challenging. An important pre-requisite for benefiting from the multiplicity of different GRs is that students conceptually understand each one of them (Ainsworth, 2006). Fractions are one of the many areas in mathematics in which multiple GRs are used extensively (National Advisory Board Panel, 2008). When designing intelligent tutoring systems (ITS) that use MGRs, designers must decide how to temporally sequence the GRs. How often should the curriculum alternate between GRs? Practice schedules are likely to impact how students understand each GR. In particular, it may matter whether students learning tasks with the same GRs are practiced in a "blocked" manner (e.g., circle--circle--rectangle--rectangle) or are interleaved with practice of other GRs (e.g., circle--rectangle--circle--rectangle). Research on contextual interference shows that interleaving task types (i.e., sequences of tasks that vary in topics) leads to better learning results than blocking task types (Battig, 1972; de Croock, Van Merrienboer, & Paas, 1998). A common interpretation of this finding is that interleaved practice encourages deep processing (de Croock, et al., 1998). Since students cannot hold all relevant knowledge components in working memory, they must reactivate task-specific knowledge throughout the task sequence. When incorporating MGRs in an ITS, a relevant question is: Will students benefit most from blocked or interleaved MGRs? In a prior study, the authors contrasted the effects of interleaving curricular topics while blocking MGRs and interleaving GRs while blocking topics. Their results demonstrated that the benefits from interleaving topics are larger than the benefits of interleaving GRs (Rau, Aleven, & Rummel, 2010). However, the question of whether interleaving GRs "in addition" to interleaving topics leads to better learning remains open. Their study was designed to addresses this question. In addition implementing different practice schedules of MGRs, the authors included SGR control conditions in order to replicate their earlier finding that MGRs lead to higher learning gains than a SGR. The authors' results demonstrate significant learning gains for students who worked with a tutoring system that supports learning with MGRs of fractions. The gains persist until one week after the study when we administered the delayed posttest. These learning gains are consistent for students in the MGR conditions on all posttest scales but fraction comparison. The fact that students' performance on fraction comparison does not improve may be due to the fact that this topic was not the focus of the tutor. The lack of learning gains in the SGR conditions demonstrates that the learning gains in the other conditions are not merely due to learning of the test. Further support for learning with MGRs comes from the finding that the MGR conditions outperformed the SGR conditions on number line items at the delayed posttest. In addition, they found limited evidence that the practice schedule of MGRs matters. Interleaving MGRs (to a full extent or in an increased fashion) is beneficial, albeit they could so far only establish this effect on a subset of measures. The authors therefore carefully conclude that designers of ITS should employ an interleaved practice schedule of MGRs, in order to encourage students to engage in deep processing of GR-specific aspects of the learning content. (Contains 2 figures and 1 table.)