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Enabling students’ participation in algebraic reasoning with ‘learning models’ as tools for theoretical work
Stockholms universitet, Humanistiska fakulteten, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.ORCID-id: 0000-0003-0764-5728
Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.ORCID-id: 0000-0002-0252-7223
Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.ORCID-id: 0000-0001-8549-9880
Vise andre og tillknytning
2019 (engelsk)Inngår i: NOFA7 Abstracts, 2019Konferansepaper, Oral presentation with published abstract (Fagfellevurdert)
Abstract [en]

The issue for this paper is to discuss conditions for students’ participation in theoretical classroom discussions. In order to develop students’ ability to reason and solve problems algebraically Lins and Kaput (2004) argue that it is important to introduce algebra early in mathematics education. In line with this, researchers working within the sociocultural tradition argue that this may start as early as in first grade (Lins & Kaput, 2004). The so-called Davydov programme (e.g. Schmittau, 2005) is referred to as a promising alternative type of teaching, enhancing young students’ capability to reason algebraically. Central to the Davydov programme is the concept of ’learning model’. Such models (not to be confused with mathematical models) are used to enable students’ elaboration of mathematical phenomena. The characteristics of a learning model is that it materialises central theoretical aspects of a content. Further, it creates specific conditions necessary for students to understand and elaborate on each other’s arguments. However, there are many demanding issues related to the design of such learning models that needs to be further developed. In this paper we address the following research question: What in students’ classroom discussions can be taken as signs of emergent ability to reason algebraically? In this paper we use data from two learning studies conducted in 2017–2018. One in grade 1 (age 7) with three iteratively designed and revised lessons, and one in grade 5 (age 11) with four iteratively designed and revised lessons. We focus especially on how students use learning models as tools to enforce and maintain a collective reasoning indifferent communicative situations. To identify possible algebraic reasoning we have analyzed the communicative situations by drawing upon Toulmin’s (2003) model of argumentation with claim, data, warrant and backing. The tentative results indicate that the ability to work with the learning models not only facilitated an individual student to clarify and substantiate his or her arguments, but also enabled other students to follow and elaborate on the reasoning. This paper also contributes with examples of tasks and especially how to set the tasks in motion to enable students’ theoretical work.

sted, utgiver, år, opplag, sider
2019.
Emneord [en]
Algebraic reasoning, learning activity, Davydov curriculum
HSV kategori
Forskningsprogram
didaktik
Identifikatorer
URN: urn:nbn:se:su:diva-171424OAI: oai:DiVA.org:su-171424DiVA, id: diva2:1341020
Konferanse
NOFA7​, Nordic Conference on​ Teaching and Learning in Curriculum Subjects, Stockholm, Sweden, 13–15 May, 2019
Prosjekter
Developing algebraic reasoning capability
Forskningsfinansiär
Swedish Institute for Educational Research, 2016/151Tilgjengelig fra: 2019-08-07 Laget: 2019-08-07 Sist oppdatert: 2019-09-23bibliografisk kontrollert

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