Designing Sets of Instructional Examples to Accomplish Different Goals of Instruction - eScholarship

Designing Sets of Instructional Examples to Accomplish Different Goals of Instruction Tina Schorr (t.schorr@iwm-kmrc.de) Virtual Ph.D. Program: Knowledge Acquisition and Knowledge Exchange with New Media Konrad-Adenauer-Str. 40, D-72072 Tuebingen (Germany) Peter Gerjets (p.gerjets@iwm-kmrc.de) Dept. of Applied Cognitive Science, Knowledge Media Research Center Konrad-Adenauer-Str. 40, D-72072 Tuebingen (Germany) Katharina Scheiter (k.scheiter@imw-kmrc.de) Dept. of Applied Cognitive Psychology and Media Psychology, Institute of Psychology Konrad-Adenauer-Str. 40, D-72072 Tuebingen (Germany) Yiannis Laouris (laouris@cyber.cy.net) Cyprus Neuroscience and Technology Institute Promitheos 5, 1065 Nicosia (Cyprus) Abstract In this paper we discuss issues of instructional design with regard to different goals of instruction in the context of learning from examples. Two different approaches for iden- tifying suitable instructional methods are considered: First, a cognitive task analysis is presented that examines prob- lem-solving strategies applicable for solving mathematical word problems from a cognitive-modeling perspective. The second approach is based on a review of empirical findings on designing instructional examples. Together, these con- siderations lead to the selection of two instructional meth- ods that are expected to foster learning with respect to dif- ferent goals of instruction. This assumption is tested in two experimental studies presented in this paper. Problem-Solving Strategies for Mathematical Word Problems: A Cognitive Task Analysis When considering different options of designing instructional material it is important to take into account which instruc- tional goal is to be accomplished. For example, in the case of learning from examples, this goal could consist in ena- bling a learner to solve problems that are either rather similar or dissimilar to the instructional examples. For solving such problems a learner needs to possess specific prerequisites (e.g., knowledge, time to perform different strategies). In order to enable the learner to acquire these prerequisites by studying instructional material, an instructional designer needs a precise conception of the prerequisites that are needed and therefore have to be imparted by the material. In order to acquire information on how problems in question can be solved and which prerequisites are therefore needed it is help- ful for an instructional designer to perform a cognitive task analysis. This can be done by using cognitive modeling as a method of task analysis, i.e., by constructing computer mod- els to simulate a human problem-solver’s behavior based on cognitive theories (Gray & Altmann, 2001). Cognitive models are characterized by a high precision that is achieved by the necessity of stating explicit and formalized assumptions in order to get running computer models (Zach- ary, Ryder, & Hicinbothom, 1998). Because of its high pre- cision a cognitive modeling approach allows for a detailed comparison of different problem-solving strategies (Rittle- Johnson & Koedinger, 2001) as well as for the derivation of instructional methods based on the theoretical assumptions which are specified in cognitive models (Pirolli, 1999). In the cognitive task analysis presented in this paper we examine two different problem-solving strategies applicable for solving mathematical word problems. A strategy can be characterized as a conditional sequence of subgoals and op- erators that is suitable to achieve a particular goal (cf. Pi- rolli, 1999, p. 452). This corresponds to the way strategies are usually represented in cognitive models. Generally, problem-solving strategies can be classified as search-based, example-based, or schema-based, respectively. Search-based strategies like means-end analysis are appropri- ate to solve puzzle problems like the Tower of Hanoi (cf. Newell & Simon, 1972) which do not presuppose domain- specific prior knowledge (knowledge-lean problems according to VanLehn, 1989). However, more complex tasks (like solving mathematical word problems) require example-based or schema-based strategies that operate on a rather elaborated knowledge base. Example-based strategies use concrete knowledge about example problems and their solutions. Within this group of example-based strategies different strategies can be distinguished that vary in the extent they make use of example information. Compared to example- based strategies, schema-based strategies use more abstract knowledge representable as generalized, automated problem- solving schemata (e.g. Sweller, van Merrienboer, & Paas, 1998). According to VanLehn (1989, p. 545) a schema con- sists of „information about the class of problems the schema applies to and information about their solutions”. Example- based and schema-based strategies correspond to two main