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Connections between different types of argumentation and students' understanding of mathematical explanations

Research project For students that try to understand mathematics, it is important to get good explanations of how different parts of the subject are connected. How different arguments are presented could affect their understanding of such explanations.

Argumentation and logic are central aspects of mathematics and this is visible both in Swedish national curriculum documents and in international frameworks. The goal of the project is to enhance the understanding of how explicit arguments can be formulated, but also of how they can support students understanding of a presentation, especially if you consider that students’ previous knowledge vary. By identifying how and when explicit arguments can support students’ understanding, the project can contribute to enhance teachers’ instruction, but may also support textbook authors’ work with improving the written material.

Head of project

Ewa Bergqvist
Associate professor, research fellow

Project overview

Project period:

2015-01-01 2018-12-31

Participating departments and units at Umeå University

Department of Science and Mathematics Education, Faculty of Science and Technology

Research subject

Educational sciences, Mathematics

Project description

Mathematical reasoning and logical argumentation are central aspects of mathematics, as evidenced for example by the Swedish curricula, for both primary and secondary schools, and by international frameworks for knowledge in school mathematics. Despite this, research shows that students are given little opportunity to be active with argumentation both at school and at university. A research review also shows that there is very little research about how students understand different types of arguments in mathematics teaching. An overarching purpose of this project is to increase the understanding of how different variants of argumentation in mathematics teaching are related to students' understanding of the presented content.

The overarching purpose includes several different aspects, for example:
- To characterize the variation of argumentation in mathematics education from multiple perspectives, focusing on both written and oral communication.
- To characterize argumentation in mathematics education in comparison with argumentation in other subject areas.
- To experimentally examine the relationship between students’ understanding of the presented mathematical content and types of argumentation in the presentation.

Properties of this project meet several needs in mathematics education research. First, there is a need for more research with a broader approach to characterizing mathematical argumentation, that is, which is not limited to a certain type of argumentation. Second, more research is needed to clarify the methodology of how to decide what in an instance of communication determines whether it can be classified as argumentation. Third, there is a need for more research that examines the relationship between different linguistic forms of argumentation in mathematics and students' understanding of what is presented, where also variation in students’ prior knowledge is taken into account.

Within the project there are plans for many different types of studies using different methods and different types of data in order to gradually provide a deeper understanding of the connections between different types of argumentation and students' understanding of mathematical explanations.