Matsuda, Noboru
(2005)
THE IMPACT OF DIFFERENT PROOF STRATEGIES ON LEARNING GEOMETRY THEOREM PROVING.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
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.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
4 February 2005 |
| Date Type: |
Completion |
| Defense Date: |
10 November 2004 |
| Approval Date: |
4 February 2005 |
| Submission Date: |
9 December 2004 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Intelligent Systems |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Geometry; Intelligent Tutoring System; Problem Solving; Strategy; Theorem Proving |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-12092004-173903/, etd-12092004-173903 |
| Date Deposited: |
10 Nov 2011 20:09 |
| Last Modified: |
15 Nov 2016 13:54 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/10240 |
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