Fostering the Acquisition of Transferable Problem-Solving Knowledge with an Interactive Comparison Tool and Dynamic Visualizations of Solution Procedures

Fostering the Acquisition of Transferable Problem-Solving Knowledge with an Interactive Comparison Tool and Dynamic Visualizations of Solution Procedures Julia Schuh (j.schuh@iwm-kmrc.de) Virtual Ph.D. Program: Knowledge Acquisition and Knowledge Exchange with New Media Konrad-Adenauer-Strasse 40, 72072 Tuebingen, Germany Peter Gerjets (p.gerjets@iwm-kmrc.de) Multimedia and Hypermedia Research Unit, Knowledge Media Research Center Konrad-Adenauer-Strasse 40, 72072 Tuebingen, Germany Katharina Scheiter (k.scheiter@iwm-kmrc.de) Department of Applied Cognitive Psychology and Media Psychology, University of Tuebingen Konrad-Adenauer-Strasse 40, 72072 Tuebingen, Germany Abstract Learning from worked-out examples is seen as a very efficient way to foster the acquisition of problem schemas. In this paper we demonstrate that computer-based instruction provides pos- sibilities to further enhance example-based learning. In an ex- periment carried out with 59 pupils with an average age of 14.0 years from a German high school we first demonstrated that a tool which prompted learners to compare examples across dif- ferent problem categories in the domain of algebra fostered per- formance on near transfer problems, which differed from the instructional examples with regard to their surface features. However, only the dynamic visualizations of the examples’ solution procedures additionally improved performance on far transfer problems, which differed from instructional examples with regard to their structural features. It is assumed that while the comparison tool supports the induction of an abstract prob- lem schema, the visualizations help to understand relations be- low the category level, which is required to successfully adapt known solution procedures to changes in the problem structure. Keywords: skill acquisition; problem solving; visualization; animation; worked-out examples; transfer Acquiring Transferable Problem-Solving Knowledge from Worked-Out Examples The problem-solving knowledge that is characteristic for ex- pertise in well-structured domains like mathematics, science, or programming is usually assumed to consist of interrelated and hierarchically organized sets of problem schemas (Sweller, van Merrienboer, & Paas, 1998; VanLehn, 1996). Problem schemas are cognitive structures that represent problem categories together with category-specific solution procedures in an abstracted way. Schemas can be acquired by either solving or studying concrete instances of problem cate- gories (i.e., example problems). However, they go far beyond these concrete instances by highlighting structural problem features that are important for a problem’s category member- ship and by detaching these structural features from merely incidental surface features of the domain context or cover story that are irrelevant to the problem’s solution. Because of their abstract nature problem schemas allow to efficiently solve problems that belong to one of the represented problem categories. Once a to-be-solved problem has been identified as belonging to a known problem category the relevant schema can be retrieved from memory, can then be instanti- ated with the information that is specific to the problem, and finally the category-specific solution procedure attached to the schema can be executed in order to generate a solution. Studying worked examples (i.e., example problems together with a step-by-step solution) has been demonstrated to be an efficient instructional method to foster the acquisition of problem schemas (for an overview see Atkinson, Derry, Renkl, & Wortham, 2000). With regard to problem-solving transfer, abstracting prob- lem schemas from concrete examples is assumed to be a piv- otal cognitive process to overcome the so-called near-transfer problem, which occurs when learners have to deploy knowl- edge that has been acquired in one concrete problem-solving situation to solve structurally equivalent problems that merely differ with regard to their superficial problem features. How- ever, the availability of problem schemas per se does not seem to be sufficient to tackle the far-transfer problem that occurs when learners have to solve novel tasks that do not fall into known problem categories and that accordingly require an adaptation of a known solution procedure. To improve learners’ ability for far transfer it is necessary to help them understand relations below the category level, that is, rela- tions holding irrespective of category membership such as relations between individual structural task features and indi- vidual solution steps (Gerjets, Scheiter, & Catrambone, 2004). Understanding the rationale behind the overall solution procedure might result in more meaningful knowledge on modular solution elements that enables learners to directly translate individual structural task features into characteristics of the problem solution. This knowledge might be much more helpful than conventional knowledge on problem categories and solution recipes for adapting solution procedures to novel problems beyond the known categories (cf. Catrambone,