The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks

Miriam N. Wallach; Einat Heyd-Metzuyanim; Ram Band

The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks

Miriam N. Wallach, Einat Heyd-Metzuyanim, Ram Band

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

Abstract

We introduce a tool for mapping tasks and their implementation based on the commognitive theory and realization trees. This tool, the Discourse Mapping Tree (DMT), first maps a priori the subdiscourses involved in solving a task, then, a posteriori the discussion of this task in a class. This affords examination of both the mathematical potential of tasks and of how an implementation takes up this potential. We exemplify the DMT on a lesson about linear transformations in a discussion-based linear algebra workshop. The tool highlighted the students’ and instructor’s role in authoring links between subdiscourses. It also displayed that the instructor was more responsible for meta-level links, while the students made object-level links more readily and easily.

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
Pages	315-322
Number of pages	8
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	4
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

ASJC Scopus subject areas

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

Cite this

Wallach, M. N., Heyd-Metzuyanim, E., & Band, R. (2023). The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks. 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. 315-322). (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 4).

Wallach, Miriam N. ; Heyd-Metzuyanim, Einat ; Band, Ram. / The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks. 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. 2023. pp. 315-322 (Proceedings of the International Group for the Psychology of Mathematics Education).

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abstract = "We introduce a tool for mapping tasks and their implementation based on the commognitive theory and realization trees. This tool, the Discourse Mapping Tree (DMT), first maps a priori the subdiscourses involved in solving a task, then, a posteriori the discussion of this task in a class. This affords examination of both the mathematical potential of tasks and of how an implementation takes up this potential. We exemplify the DMT on a lesson about linear transformations in a discussion-based linear algebra workshop. The tool highlighted the students{\textquoteright} and instructor{\textquoteright}s role in authoring links between subdiscourses. It also displayed that the instructor was more responsible for meta-level links, while the students made object-level links more readily and easily.",

author = "Wallach, {Miriam N.} and Einat Heyd-Metzuyanim and Ram Band",

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Wallach, MN, Heyd-Metzuyanim, E & Band, R 2023, The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks. 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. 4, pp. 315-322, 46th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2023, Haifa, Israel, 16/07/22.

The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks. / Wallach, Miriam N.; Heyd-Metzuyanim, Einat ; Band, Ram.
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. 2023. p. 315-322 (Proceedings of the International Group for the Psychology of Mathematics Education; Vol. 4).

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

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Wallach MN, Heyd-Metzuyanim E , Band R. The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks. 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. 2023. p. 315-322. (Proceedings of the International Group for the Psychology of Mathematics Education).

The discourse mapping tree as a tool for analyzing the potential and implementation of linear algebra tasks

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