Refutation feedback on student proofs beyond counter-examples

Alon Pinto; Jason Cooper

Refutation feedback on student proofs beyond counter-examples

Alon Pinto
, Jason Cooper

Department of Science Teaching

Weizmann Institute of Science

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

Abstract

Feedback on students’ proofs is often intended to promote proof comprehension, yet formulating such feedback is a delicate task. In this study we investigate how refutation can be used for this purpose. We propose to extend Lakatos’ notion of heuristic refutation to feedback that contains a refutation argument, possibly incomplete. Such feedback is heuristic in the sense that interpreting and utilizing it invites mathematical reasoning that can contribute to development of proof comprehension. Based on data from a Real-Analysis course, we show the importance of considering different kinds of refutation that are not based only on counter-examples, and demonstrate the nuances and subtleties of formulating feedback based on such refutation. Our findings suggest how professors can purposefully tailor feedback for particular didactic goals.

Original language	English
Title of host publication	Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM)
Editors	Maria Trigueros, Berta Barquero, Reinhard Hochmuth, Jana Peters
Place of Publication	Hannover, Germany
Pages	303-312
Number of pages	10
State	Published - Mar 2023
Event	Fourth conference of the International Network for Didactic Research in University Mathematics - Hannover, Germany Duration: 19 Oct 2022 → 22 Oct 2022 Conference number: 4

Conference

Conference	Fourth conference of the International Network for Didactic Research in University Mathematics
Abbreviated title	IDRUM 2022
Country/Territory	Germany
City	Hannover
Period	19/10/22 → 22/10/22

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@inproceedings{dfbfd64a0cb2478a8b815cde7b23a02a,

title = "Refutation feedback on student proofs beyond counter-examples",

abstract = "Feedback on students{\textquoteright} proofs is often intended to promote proof comprehension, yet formulating such feedback is a delicate task. In this study we investigate how refutation can be used for this purpose. We propose to extend Lakatos{\textquoteright} notion of heuristic refutation to feedback that contains a refutation argument, possibly incomplete. Such feedback is heuristic in the sense that interpreting and utilizing it invites mathematical reasoning that can contribute to development of proof comprehension. Based on data from a Real-Analysis course, we show the importance of considering different kinds of refutation that are not based only on counter-examples, and demonstrate the nuances and subtleties of formulating feedback based on such refutation. Our findings suggest how professors can purposefully tailor feedback for particular didactic goals. ",

author = "Alon Pinto and Jason Cooper",

year = "2023",

month = mar,

language = "English",

pages = "303--312",

editor = "Maria Trigueros and Berta Barquero and Reinhard Hochmuth and Jana Peters",

booktitle = "Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM)",

note = "Fourth conference of the International Network for Didactic Research in University Mathematics, IDRUM 2022 ; Conference date: 19-10-2022 Through 22-10-2022",

}

Pinto, A & Cooper, J 2023, Refutation feedback on student proofs beyond counter-examples. in M Trigueros, B Barquero, R Hochmuth & J Peters (eds), Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM). Hannover, Germany, pp. 303-312, Fourth conference of the International Network for Didactic Research in University Mathematics, Hannover, Germany, 19/10/22. <https://indrum2022.sciencesconf.org/data/Proceedings_Indrum2022.pdf>

Refutation feedback on student proofs beyond counter-examples. / Pinto, Alon; Cooper, Jason.
Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM). ed. / Maria Trigueros; Berta Barquero; Reinhard Hochmuth; Jana Peters. Hannover, Germany, 2023. p. 303-312.

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

TY - GEN

T1 - Refutation feedback on student proofs beyond counter-examples

AU - Pinto, Alon

AU - Cooper, Jason

N1 - Conference code: 4

PY - 2023/3

Y1 - 2023/3

N2 - Feedback on students’ proofs is often intended to promote proof comprehension, yet formulating such feedback is a delicate task. In this study we investigate how refutation can be used for this purpose. We propose to extend Lakatos’ notion of heuristic refutation to feedback that contains a refutation argument, possibly incomplete. Such feedback is heuristic in the sense that interpreting and utilizing it invites mathematical reasoning that can contribute to development of proof comprehension. Based on data from a Real-Analysis course, we show the importance of considering different kinds of refutation that are not based only on counter-examples, and demonstrate the nuances and subtleties of formulating feedback based on such refutation. Our findings suggest how professors can purposefully tailor feedback for particular didactic goals.

AB - Feedback on students’ proofs is often intended to promote proof comprehension, yet formulating such feedback is a delicate task. In this study we investigate how refutation can be used for this purpose. We propose to extend Lakatos’ notion of heuristic refutation to feedback that contains a refutation argument, possibly incomplete. Such feedback is heuristic in the sense that interpreting and utilizing it invites mathematical reasoning that can contribute to development of proof comprehension. Based on data from a Real-Analysis course, we show the importance of considering different kinds of refutation that are not based only on counter-examples, and demonstrate the nuances and subtleties of formulating feedback based on such refutation. Our findings suggest how professors can purposefully tailor feedback for particular didactic goals.

M3 - Conference contribution

SP - 303

EP - 312

BT - Proceedings of the Fourth Conference of the International Network for Didactic Research in University Mathematics (INDRUM)

A2 - Trigueros, Maria

A2 - Barquero, Berta

A2 - Hochmuth, Reinhard

A2 - Peters, Jana

CY - Hannover, Germany

T2 - Fourth conference of the International Network for Didactic Research in University Mathematics

Y2 - 19 October 2022 through 22 October 2022

ER -

Refutation feedback on student proofs beyond counter-examples

Abstract

Conference

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