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Materializing students’ algebraic arguments in classroom discussion – a learning activity perspective
Stockholm University, Faculty of Humanities, Department of Humanities and Social Sciences Education.ORCID iD: 0000-0003-0764-5728
2019 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

General description on research questions, objectives and theoretical framework

Learning activity, is a special form activity within the activity theory tradition. It was first developed by El’konin and Davydov (Davydov, 2008). The underpinning cultural historical and activity theoretical principles give us an understanding that students in order to develop knowledge must be involved in a content rich activity where they can work theoretically with general (abstract) principles and structures of the object of knowledge (Chaiklin, 2002). Further, in order to realize a learning activity, students’ (and teacher’s) actions that forms the theoretical work, must be mediated by proper tools. But which tools can enable what type of knowledge?

In mathematics for the youngest students, that I will discuss in this paper, there is a long tradition that advocate that it is of great importance to use tools that can help students to manipulate with the content in order to understand e.g. numbers – physical things like buttons, toys, fruit, etc. are often used to illustrate e.g. 4+5=. This is often talked about as concrete math-teaching supported by manipulatives. In El'konin and the Davydov program (ED), the main purpose is instead the opposite: to allow students to develop a theoretical understanding of mathematical knowledge (Davydov, 2008). In the ED-program subject specific learning models are used as mediating tools for students in their trying to grasp theoretical aspects of a specific content, e.g. a concept (Gorbov & Chudinova, 2000; Repkin, 2003; Zuckerman, 2004). Aspects that are difficult for students to grasp empirically.

The issue for this paper is, thus, what function learning models can have in mathematical whole class discussions. What can be used as a learning model? And, how can the object of knowledge be elaborated with the help of learning models in whole-class discussions?

Methods/methodology

The paper is using data from several a research project[1] based on learning study as research approach (Carlgren, Eriksson & Runesson, 2017) where the aim was to develop tasks and learning models that could enhance students’ ability to reason algebraically. The research lessons was video-taped and transcribed and analyzed with the help of questions like: what in the planned situation do the students identify as a learning model and how do they use it? Do they transform the learning model and if so in what ways and for what purpose? What indicators can be identified of how the learning model facilitates the whole class discussions? What in the teachers actions, especially communicative actions, facilitate or hindrance in students discussions?

Expected outcomes/preliminary results/implications

In the analysis of the research lesson three functions of the learning models used in whole class discussions were identified. First, a learning model enables individuals to make his or her sometimes rather unclear verbal explanations much more comprehensible both for the student that puts forward an idea and for his or her classmates. Second, a learning model if it is available e.g. on the blackboard for the students' exploration, a verbal argument can be available to the group when the words are no longer heard. Third, the learning model itself can be transformed by the students (or by the teacher) in new ways. Such modelling can make other aspects of the content available.

Further, the analysis also indicates that not only the construction of the learning model is demanding but also the way it is used in as a tool facilitating the classroom discussion.

The construction requires a solid theoretical understanding of the subject. A theoretical structure is not always easy to identify and to find a way to transform such knowing into something that can function as a learning model for students can be even more demanding. In our cases we used learning models from the ED-program or let us be inspired by it (Davydov, Gorbov, Mikulina, & Saveleva, 2012). In addition, we have experienced that how the teacher act in the classroom is of great importance. One requirement, if a teaching situation will be established as a learning activity, is the teachers’ actions. The teacher cannot simply tell the student what to do, how to use the learning model or tell the students what the problem is. Instead, a learning activity will only be established if the students' experiences a need and a motive to solve the problem. A learning activity is thus is very fragile (Eriksson, 2017, Repkin, 2003).

Concluding

Materializing theoretical thinking helps the students to act with agency within a learning activity. In such learning activity abstract structures can be visualized and collaboratively explored.

Place, publisher, year, edition, pages
2019.
Keywords [en]
Learning activity, classroom discussion, learning models, algebraic thinking
National Category
Didactics
Research subject
Didactics
Identifiers
URN: urn:nbn:se:su:diva-171422OAI: oai:DiVA.org:su-171422DiVA, id: diva2:1341014
Conference
Nordic ISCAR, Trondheim, Norway, 18-20 June, 2019
Projects
Developing algebraic reasoning capability
Funder
Swedish Institute for Educational Research, 2017-2019Available from: 2019-08-07 Created: 2019-08-07 Last updated: 2019-08-20

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