A learning study : exploring algebraic expressions through “learning models” in Grade 5

• The issue of the paper is what aspects must be built into a assignment so it can serve as a mediating tool enabling students to explore algebraic expressions.Algebra has a unique position in mathematics as it is found in all mathematical areas. The introduction of algebra is in most cases arithmetic in its basis (eg. Kieran, 2006; Lins & Kaput, 2004; Radford, 2010). According to Greer (2008) teaching in algebra needs to create the conditions for students to develop abilities such as algebraic reasoning, making algebraic generalizations and using algebraic representations rather than learning a number of procedures. The data used in this paper is from a learning study in grade 5 (11 year old students) comprising three research lessons focusing on algebraic reasoning. Learning activity was used as a theoretical framework, both when designing and analyzing the research lessons. Variation theory (Marton, 2015) is commonly used as a theoretical framework in learning studies but in this case we have chosen to use learning activity (Davydov, 2008).Learning model is a key concept in Davydov’s theory of learning activity. In learning activity the aim is to give students opportunity to gain access to theoretical content that is built into eg. algebraic expressions. A learning model can be iconic (sketches or drawings) or symbolic (eg. algebraic expressions). “Models are a particular kind of abstraction, where the visually perceived and represented connections and relations of the material or semiotic elements reinforce the essential relations of the object” (Davydov, 2008, p. 95). Further a learning model in learning activity aims to enhance students’ collective discussions and reflections.In the paper we will exemplify how we analyzed the students’ work (video recorded) and iteratively developed a learning model. Furthermore, we will discuss how to set a learning model in motion in communicative situations during the research lessons.

Ämnesord

SAMHÄLLSVETENSKAP  -- Utbildningsvetenskap -- Didaktik (hsv//swe)

SOCIAL SCIENCES  -- Educational Sciences -- Didactics (hsv//eng)

Nyckelord

Learning study

Learning models

Learning activity

Algebraic expressions

Mathematics

Didactics

didaktik

Publikations- och innehållstyp

ref (ämneskategori)

kon (ämneskategori)