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Finding new ways of informing iteration between lessons in a learning study: A case of algebraic reasoning
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0002-0252-7223
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0001-8549-9880
2018 (English)Conference paper, Oral presentation with published abstract (Refereed)
Abstract [en]

The issue for this paper is lesson iteration informed by students’ responses to lesson design seen from the theoretical standpoint of learning activity in a learning study on a lesson framing algebraic reasoning.

A body of research (e.g.; Kieran, 2006; Lins & Kaput, 2004; Radford, 2010) suggests that there can be a problem if algebra is introduced from an arithmetic standpoint focusing on finding singelnumerical solutions to tasks.This can lead to students getting stuck in the arithmetical interpretation of algebraically problems and prevent them from using algebra as a tool for general mathematical understanding (e.g. Davydov, 2008; Kieran, 2006; Lins & Kaput, 2004; Radford, 2010).

Learning study can be understood as a lesson study with a focus on a specific object of learning and in combination with an explicit theory of learning (Elliot, 2012). Marton (2015) argues for any functional theory of learning but commonly variation theory is the theory used. During the last years learning activity (Davydov, 2008) has been tested as an alternative and/or complementary theoretical design tool when designing teaching in learning studies (Eriksson, 2017). One design principle when trying to establish a learning activity is that the teacher has to create a situation inviting students to theoretical work (Davydov, 2008). This situation needs to include fundamental aspects of the theoretical knowledge as well as evoke students’ curiosity and urge them to engage in a theoretical work (Eriksson & Jansson, 2017). One difficult act of balance for the teacher is to stage a situation that evokes the curiosity needed for the students to create their own problem/learning task instead of simply solving a teacher assignment.

In this project the data comes from a learning study in year 1 (age 7) with three lesson iterations. Tentative results indicate that small adjustments in lesson design made on the basis of learning activity generates both a higher degree of student reasoning and on a shift from numerical/arithmetical to algebraical conceptual tools. In the presentation we will provide examples of how learning activity has worked as a tool to improve the staging of a situation inviting the students to engage in algebraic reasoning.

Place, publisher, year, edition, pages
2018.
Keywords [en]
Algebraic thinking, Algebraic reasoning, Learning activity, Learning models
National Category
Didactics
Identifiers
URN: urn:nbn:se:su:diva-171423OAI: oai:DiVA.org:su-171423DiVA, id: diva2:1341021
Conference
World Association of Lesson Studies (WALS) International Conference, Beijing, China, 23-26 November, 2018
Projects
Developing algebraic reasoning capability
Funder
Swedish Institute for Educational Research, 2016/151Available from: 2019-08-07 Created: 2019-08-07 Last updated: 2019-09-25Bibliographically approved

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CiteExportLink to record
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  • apa
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