Open-ended tasks which are not completely open: Challenges and creativity

Sigal Klein; Roza Leikin

Open-ended tasks which are not completely open: Challenges and creativity

Department of Mathematics Education

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

Abstract

Mathematics educators argue that open-ended tasks as a powerful tool for the development of students’ creativity in mathematics, while it is well known that solving open-ended tasks is challenging for students. Recently we argued that not every open-ended task is fully open, as even when a task has a multiplicity of solution outcomes completeness of the set of solution outcomes is possible. To make the distinction between openness and multiplicity and avoid ambiguity related to the term ‘openness’ we use the term ‘Multiple Outcomes Tasks’ (MOTs). In this paper we analyze students’ mathematical performance on two MOTs. We consider the completeness of the set of solution outcomes produced by a student as an indicator of his/her creativity due to the unconventionality of MOTs in regular classes. Our findings suggest that MOTs with continuous-infinite set of solution outcomes are more challenging than MOTs with discrete and finite sets.

Original language	English
Title of host publication	Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023
Editors	Michal Ayalon, Boris Koichu, Roza Leikin, Laurie Rubel, Michal Tabach
Publisher	Psychology of Mathematics Education (PME)
Pages	171-178
Number of pages	8
ISBN (Print)	9789659311231
State	Published - 2023
Event	46th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2023 - Haifa, Israel Duration: 16 Jul 2022 → 21 Jul 2022

Publication series

Name	Proceedings of the International Group for the Psychology of Mathematics Education
Volume	3
ISSN (Print)	0771-100X
ISSN (Electronic)	2790-3648

Conference

Conference	46th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2023
Country/Territory	Israel
City	Haifa
Period	16/07/22 → 21/07/22

Bibliographical note

Publisher Copyright:
© 2023, Psychology of Mathematics Education (PME). All rights reserved.

ASJC Scopus subject areas

Mathematics (miscellaneous)
Developmental and Educational Psychology
Experimental and Cognitive Psychology
Education

Cite this

Klein, S., & Leikin, R. (2023). Open-ended tasks which are not completely open: Challenges and creativity. In M. Ayalon, B. Koichu, R. Leikin, L. Rubel, & M. Tabach (Eds.), Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023 (pp. 171-178). (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 3). Psychology of Mathematics Education (PME).

Klein, Sigal ; Leikin, Roza. / Open-ended tasks which are not completely open : Challenges and creativity. Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023. editor / Michal Ayalon ; Boris Koichu ; Roza Leikin ; Laurie Rubel ; Michal Tabach. Psychology of Mathematics Education (PME), 2023. pp. 171-178 (Proceedings of the International Group for the Psychology of Mathematics Education).

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title = "Open-ended tasks which are not completely open: Challenges and creativity",

abstract = "Mathematics educators argue that open-ended tasks as a powerful tool for the development of students{\textquoteright} creativity in mathematics, while it is well known that solving open-ended tasks is challenging for students. Recently we argued that not every open-ended task is fully open, as even when a task has a multiplicity of solution outcomes completeness of the set of solution outcomes is possible. To make the distinction between openness and multiplicity and avoid ambiguity related to the term {\textquoteleft}openness{\textquoteright} we use the term {\textquoteleft}Multiple Outcomes Tasks{\textquoteright} (MOTs). In this paper we analyze students{\textquoteright} mathematical performance on two MOTs. We consider the completeness of the set of solution outcomes produced by a student as an indicator of his/her creativity due to the unconventionality of MOTs in regular classes. Our findings suggest that MOTs with continuous-infinite set of solution outcomes are more challenging than MOTs with discrete and finite sets.",

author = "Sigal Klein and Roza Leikin",

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Klein, S & Leikin, R 2023, Open-ended tasks which are not completely open: Challenges and creativity. in M Ayalon, B Koichu, R Leikin, L Rubel & M Tabach (eds), Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023. Proceedings of the International Group for the Psychology of Mathematics Education, vol. 3, Psychology of Mathematics Education (PME), pp. 171-178, 46th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2023, Haifa, Israel, 16/07/22.

Open-ended tasks which are not completely open: Challenges and creativity. / Klein, Sigal; Leikin, Roza.
Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023. ed. / Michal Ayalon; Boris Koichu; Roza Leikin; Laurie Rubel; Michal Tabach. Psychology of Mathematics Education (PME), 2023. p. 171-178 (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 3).

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

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AB - Mathematics educators argue that open-ended tasks as a powerful tool for the development of students’ creativity in mathematics, while it is well known that solving open-ended tasks is challenging for students. Recently we argued that not every open-ended task is fully open, as even when a task has a multiplicity of solution outcomes completeness of the set of solution outcomes is possible. To make the distinction between openness and multiplicity and avoid ambiguity related to the term ‘openness’ we use the term ‘Multiple Outcomes Tasks’ (MOTs). In this paper we analyze students’ mathematical performance on two MOTs. We consider the completeness of the set of solution outcomes produced by a student as an indicator of his/her creativity due to the unconventionality of MOTs in regular classes. Our findings suggest that MOTs with continuous-infinite set of solution outcomes are more challenging than MOTs with discrete and finite sets.

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Klein S, Leikin R. Open-ended tasks which are not completely open: Challenges and creativity. In Ayalon M, Koichu B, Leikin R, Rubel L, Tabach M, editors, Proceedings of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023. Psychology of Mathematics Education (PME). 2023. p. 171-178. (Proceedings of the International Group for the Psychology of Mathematics Education).

Open-ended tasks which are not completely open: Challenges and creativity

Abstract

Publication series

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Bibliographical note

ASJC Scopus subject areas

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