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Class discussions enabling discerning algebraic properties - developed in learning study iteration
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0001-8549-9880
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0002-0252-7223
2019 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

The issue for this paper is to discuss how a lesson can be structured to enable students to engage in creative and reflective discussions about the function for and relation between components in algebraic expressions.

In recent years, interest in the communicative elements of mathematics education has increased internationally, and then with a special focus on the development of students' mathematical thinking and their ability to reason, argue and participate in mathematical classroom discussions (Kieran, 2001; Larsson, 2015; Lithner, 2008 ; Radford & Barwell, 2016). Based on the above, questions can be raised about which tools are used and how they can be used to promote content-rich, creative and reflective classroom discussions.

The theory of learning activity (Davydov, 2008) provides four principles on how teaching, tasks and classroom communication can be designed to enable students engage in a theoretical work: (1) the creation of problem situations, (2) the creation and establishment of learning models, (3) the creation or advancement of contradictions and (4) joint reflexive action. The function of a problem situation is to challenge students to be active in a theoretical work where the processing of the problem gives the students the opportunity to work with aspects of the knowledge content that they have not yet distinguished. Learning models should enable the students to theoretically explore the abstract (general) of a given object and further serving as a tool for classroom communication and reflective discussions (Gorbov & Chudinova, 2000). Contradictions are historically developed tensions and the idea of contradictions can be used in the design of problem situations to challenge students to engage in a theoretical work (Davydov, 2008: Zuckerman, 2003). The idea of collective reflections is also central to learning activity, because the students are challenged in their own theoretical thinking by trying to explain someone else’s thoughts and putting it in relation to their own (Zuckerman, 2004).

The aim of this study is to examine how mathematics education can be designed to develop students algebraic thinking regarding discussing algebraic expressions. The research question addressed in this paper is: how can learning activity work as a tool for informing iteration between lessons in a learning study regarding enabling students to discern algebraic properties using reflective whole class discussions?

In this project the data comes from a learning study in year 7 (age 13) with four lesson iterations. Learning study (Marton & Tsui, 2004; Marton, 2015) has been used as an approach for data production. The data consists of video recordings from four research lessons and transcriptions of those.

Tentative result indicate that a problem situation can be successfully staged using combinations of well known conceptual parts, such as a rectangle and an algebraic expression, and thus creating a complex situation enabling students to engage in a theoretical work. The implicit familiarity of the conceptual parts in these combinations, in combination with finely tuned “provocations” from the teacher, forces the students to question trivial understanding of algebraic concepts, thus qualifying the discussion and potentially reaching a deeper understanding.

Place, publisher, year, edition, pages
2019.
Keywords [en]
Algebraic properties, Learning activity (Davydov), Whole class discussions
National Category
Didactics
Research subject
Didactics
Identifiers
URN: urn:nbn:se:su:diva-173300OAI: oai:DiVA.org:su-173300DiVA, id: diva2:1352498
Conference
World Association of Lesson Studies (WALS) International Conference, Amsterdam, Netherlands, 3-6 September, 2019
Projects
Developing algebraic reasoning capability
Funder
Swedish Institute for Educational Research, 2016/151Available from: 2019-09-19 Created: 2019-09-19 Last updated: 2019-09-25Bibliographically approved

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