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Meaning making through collective argumentation

Osama Swidan

Department of Science & Technology Education

The role of students’ argumentative discourse in their exploration of the graphic relationship between a function and its antiderivative

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Motivation

Swidan et al. (2020) explored how students, through an interrogative process, disclose the mathematical meaning of the indefinite integral

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Theortical lenses

Meaning Making

Phenomenological assumption that there is “no such thing as true seeing”, but “there is only seeing as” (Rota, 1991, p. 239).
Meaning making of a mathematical object is conceived as a progressive disclosure of the mathematical ideas at stake.

Argumentation

Broad definition like that employed by Hanna (2020), who claims that “argumentation includes any technique that aims at persuading others that one’s reasoning is right,” (p. 564).
Krummheuer who defines argumentation as any given situation that "contains several statements that are related to each other in a specific way and that by this take over certain functions for their interactional effectiveness" (Krumheuer,1995, p. 247).

1- In this paper, our starting point is the key phenomenological assumption, pointed out by Rota, that there is “no such thing as true seeing”, but “there is only seeing as” (Rota, 1991, p. 239).

3- In this study, we adopt a broad definition like that employed by Hanna (2020), who claims that “argumentation includes any technique that aims at persuading others that one’s reasoning is right,” adding that “the concept also implies exchange and cooperation in forming and criticizing arguments so as to arrive at the best conclusion despite imperfect knowledge” (p. 564).

4- Krummheuer defines argumentation as any given situation that "contains several statements that are related to each other in a specific way and that by this take over certain functions for their interactional effectiveness" (Krumheuer,1995, p. 247).

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Aim & Research Questions

This study aims at exploring the role of argumentation in the process of shared meaning making.

Research questions

What types or components can we identify in the argumentative discourse employed by the high school students when they use digital tools to make sense of the indefinite integral concept?
How do the various types of argumentative discourse relate to the students’ use of the tool to disclose the mathematical relationships between the two graphs?

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Digital tool

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Main Findings

Three layers of meanings: disclosing objects, disclosing relationships, disclosing functional relationships
The utterances of the students were predominantly transactive.

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The utterances of the students while engaging with the digital tool were predominantly transactive. In other words, their questions and statements to one another tended to be clearly connected to the utterances that came before them, suggesting that using the digital tool and working on the task in pairs, using the same screen, kept the students’ discussion focused and coherent.

These questions repeatedly stimulated argumentative activity as the students interacted with one another, and with the digital tool, disclosing the mathematical objects in the tool - in our case, the function graph and the antiderivative function graph - and the relationship between them.

We found that the students engaged most prominently in describing what they have observed on the screen, and either substantiating or advancing a preceding argument.

Advance-type statements were also particularly abundant in the students’ interaction, and played a crucial role in fostering the transition between one layer of disclosure to the next one

the dragging tool played a central role in helping the students advance and build upon their arguments.

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Using a digital tool prompted the students to ask Clarify, Agree and Justify-type questions.
These questions stimulated the disclosure of the mathematical objects in the tool

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Students engaged in describing what they have observed on the screen, and either substantiating or advancing a preceding argument.
Describing 🡪 Justification
The DT allows students to produce evidence with which to substantiate and justify their arguments.
The dragging tool played a central role in helping the students advance and build upon their arguments
Advance-type statements played a crucial role in fostering the transition between one layer of disclosure to the next one.

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This study brings together three main themes, each of which is important for mathematics education research - namely, meaning making, questioning, and argumentation.

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