Two problem solving strategies, forward chaining and backward chaining, were compared to see how they affect students' learning of geometry theorem proving with construction. It has been claimed that backward chaining is inappropriate for novice students due to its complexity. On the other hand, forward chaining may not be appropriate either for this particular task because it can explode combinatorially. In order to determine which strategy accelerates learning the most, an intelligent tutoring system was developed. It is unique in two ways: (1) It has a fine grained cognitive model of proof-writing, which captured both observable and unobservable inference steps. This allows the tutor to provide elaborate scaffolding. (2) Depending on the student's competence, the tutor provides a variety of scaffolding from showing precise steps to just prompting students for a next step. In other words, the students could learn proof-writing through both worked-out examples (by observing a model of proof-writing generated by the tutor) and problem solving (by writing proofs by themselves). 52 students were randomly assigned to one of the tutoring systems. They solved 11 geometry proof problems with and without construction with the aid from the intelligent tutor. The results show that (1) the students who learned forward chaining showed better performance on proof-writing than those who learned backward chaining, (2) both forward and backward chaining conditions wrote wrong proofs equally frequently, (3) both forward and backward chaining conditions seldom wrote redundant or wrong statements when they wrote correct proofs, (4) the major reason for the difficulty in applying backward chaining lay in the assertion of premises as unjustified propositions (i.e., subgoaling). These results provide theoretical implications for the design of tutoring systems for problem solving.
| Identifer | oai:union.ndltd.org:PITT/oai:PITTETD:etd-12092004-173903 |
| Date | 04 February 2005 |
| Creators | Matsuda, Noboru |
| Contributors | Peter Brusilovsky, Kurt VanLehn, Christian Schunn, James Greeno, Kenneth Koedinger |
| Publisher | University of Pittsburgh |
| Source Sets | University of Pittsburgh |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.pitt.edu/ETD/available/etd-12092004-173903/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Pittsburgh or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
Page generated in 0.0022 seconds