Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction

J.S. Lodder; B.J. Heeren; J.T. Jeuring

doi:10.4204/EPTCS.313.2

Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction

J.S. Lodder, B.J. Heeren, J.T. Jeuring

Research output: Chapter in Book/Report/Conference proceeding › Conference Article in proceeding › Academic › peer-review

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Abstract

Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.

Original language	English
Title of host publication	Proceedings 8th International Workshop on Theorem Proving Components for Educational Software
Subtitle of host publication	EPTCS 313 Natal, Brazil, 25th August 2019
Editors	Pedro Quaresma, Walther Neuper, João Marcos
Publisher	Cornell University
Pages	17–34
Number of pages	18
Volume	313
DOIs	https://doi.org/10.4204/EPTCS.313.2
Publication status	Published - 28 Feb 2020
Event	8th International Workshop on Theorem proving components for Educational software - Natal, Brazil Duration: 25 Aug 2019 → 25 Aug 2019 Conference number: 8 https://www.uc.pt/en/congressos/thedu/thedu19

Publication series

Series	Electronic proceedings in theoretical computer science
Volume	313
ISSN	2075-2180

Workshop

Workshop	8th International Workshop on Theorem proving components for Educational software
Abbreviated title	ThEdu'19
Country/Territory	Brazil
City	Natal
Period	25/08/19 → 25/08/19
Internet address	https://www.uc.pt/en/congressos/thedu/thedu19

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10.4204/EPTCS.313.2Licence: CC BY

2002.12552v1Final published version, 555 KBLicence: CC BY

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Lodder, J. S., Heeren, B. J., & Jeuring, J. T. (2020). Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction. In P. Quaresma, W. Neuper, & J. Marcos (Eds.), Proceedings 8th International Workshop on Theorem Proving Components for Educational Software : EPTCS 313 Natal, Brazil, 25th August 2019 (Vol. 313, pp. 17–34). Cornell University. https://doi.org/10.4204/EPTCS.313.2

Lodder, J.S. ; Heeren, B.J. ; Jeuring, J.T. / Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction. Proceedings 8th International Workshop on Theorem Proving Components for Educational Software : EPTCS 313 Natal, Brazil, 25th August 2019. editor / Pedro Quaresma ; Walther Neuper ; João Marcos. Vol. 313 Cornell University, 2020. pp. 17–34 (Electronic proceedings in theoretical computer science, Vol. 313).

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title = "Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction",

abstract = "Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.",

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editor = "Pedro Quaresma and { Neuper}, Walther and Marcos, {Jo{\~a}o }",

booktitle = "Proceedings 8th International Workshop on Theorem Proving Components for Educational Software",

address = "United States",

note = "8th International Workshop on Theorem proving components for Educational software, ThEdu'19 ; Conference date: 25-08-2019 Through 25-08-2019",

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Lodder, JS, Heeren, BJ & Jeuring, JT 2020, Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction. in P Quaresma, W Neuper & J Marcos (eds), Proceedings 8th International Workshop on Theorem Proving Components for Educational Software : EPTCS 313 Natal, Brazil, 25th August 2019. vol. 313, Cornell University, Electronic proceedings in theoretical computer science, vol. 313, pp. 17–34, 8th International Workshop on Theorem proving components for Educational software, Natal, Brazil, 25/08/19. https://doi.org/10.4204/EPTCS.313.2

Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction. / Lodder, J.S.; Heeren, B.J.; Jeuring, J.T.
Proceedings 8th International Workshop on Theorem Proving Components for Educational Software : EPTCS 313 Natal, Brazil, 25th August 2019. ed. / Pedro Quaresma; Walther Neuper; João Marcos. Vol. 313 Cornell University, 2020. p. 17–34 (Electronic proceedings in theoretical computer science, Vol. 313).

Research output: Chapter in Book/Report/Conference proceeding › Conference Article in proceeding › Academic › peer-review

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PY - 2020/2/28

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N2 - Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.

AB - Structural induction is a proof technique that is widely used to prove statements about discrete structures. Students find it hard to construct inductive proofs, and when learning to construct such proofs, receiving feedback is important. In this paper we discuss the design of a tutoring system, LogInd, that helps students with constructing stepwise inductive proofs by providing hints, next steps and feedback. As far as we know, this is the first tutoring system for structural induction with this functionality. We explain how we use a strategy to construct proofs for a restricted class of problems. This strategy can also be used to complete partial student solutions, and hence to provide hints or next steps. We use constraints to provide feedback. A pilot evaluation with a small group of students shows that LogInd indeed can give hints and next steps in almost all cases.

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M3 - Conference Article in proceeding

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BT - Proceedings 8th International Workshop on Theorem Proving Components for Educational Software

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Lodder JS, Heeren BJ, Jeuring JT. Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction. In Quaresma P, Neuper W, Marcos J, editors, Proceedings 8th International Workshop on Theorem Proving Components for Educational Software : EPTCS 313 Natal, Brazil, 25th August 2019. Vol. 313. Cornell University. 2020. p. 17–34. (Electronic proceedings in theoretical computer science, Vol. 313). doi: 10.4204/EPTCS.313.2

Providing Hints, Next Steps and Feedback in a Tutoring System for Structural Induction

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