Algebraic developmental teaching an example from a grade one classroom
2014 (English)Conference paper (Refereed)
The issue in this paper is grade one students´ emerging understanding of the equalsign in an algebraic meaning inspired by the Davydov curriculum. The mainstreamunderstanding that young students must start with arithmetic, mainly throughoperations with quantity and numbers in order to develop both an understanding ofnumbers and to develop a pre-algebraic thinking has been questioned during thelatest decades . What if the arithmetic foundations in the mathematics teaching inthemselves create problems for some students in relation to developing andexpanding a theoretical thinking and reasoning beyond concrete numericoperations? What if such problems hinder students to develop a morecomprehensive understanding of numbers and different number systems;mathematical structures; symbols and models as tools for mathematical work?Vygotsky and his contemporary colleagues argued, as a numbers of researchersinternationally, that through an early introduction to algebraic work and reasoningstudents are given the opportunity to develop a theoretical understanding that willfunction as a foundation for all kinds of arithmetic operations as well as for algebraicreasoning and problem-solving. This paper reports preliminary results from a pilotstudy in a Swedish grade one that indicates that students when working withassignments inspired by the Davydov programme gave examples of an algebraicreasoning in relations to the equal sign that students in the parallel class did notmaster. When students in an interview (3 month of project) were presented toexpressions as A+B=C and M+N= P for the first time all but one of the 28 could, inrelation to artefacts/signs, exemplify in a multiple ways the expressions and arguehow they know if it was true or not. The parallel class (28) were introduced to theequal sign with numbers as presented in the textbook (algebraic traditions). Whenshown the expressions A+B=C only few students related that to a mathematics -most associated the expressions to the alphabet.
SYM34Transforming Davydov's Learning Activity Curricula into NewContexts - examples from Canada, Italy and Sweden
Eriksson, Inger Eriksson1, Polotskaia, Elena2*, Savard Annie2, Jansson Anders1*, Eriksson Helena1*, Fermsj Roger1*, Mellone Maria3*,
1Stockholm University, email@example.com
2McGill University, firstname.lastname@example.org
3Universit degli Studi di Napoli Federico II
Over the last decades there has been a growing interest in what in Westerncountries has been described as Davydov’s learning activity curriculum ordevelopmental teaching. Most interest has been given to mathematics teaching.Jeane Schmittau (Binghamton University), together with her colleague Ann Morris, isperhaps one of the first researchers that started to explore Davydov´s curriculum formathematics. There are several researches who showed that students that havebeen introduced to mathematics following Davydov´s programme at the end of yearthree, have shown a mathematical problem solving capacity and mathematicalreasoning that many students in higher grades don´t have (see for example Kinard &Kozulin, 2010; Morris & Schmittau, 2004; Schmittau, 2005). Barbara Doguherty(University of Hawaii & University of Missouri) is another researcher thatsystematically has introduced Davydov’s curriculum in US. The Davydov-tradition,or rather the Elkonin and Davydov-tradition has been developed within the frames ofVygotsky´s work. With a cultural-historical activity approach, education has toenhance students´ development, for instance by organizing for an educativeenvironment that creates a zone of proximal development. Which learning trajectoryis made available for students depends on what activities students are engaged in.Learning activity is developed in order to engage students in reflective work from thevery beginning of their education. Thus different subjects can be used as a mean forthe development of reflection consisting of (a) a phase of analysis of the problems,the ends and the means (b) take others´ perspectives into account, and (c) to reviewoneÂ´s own solutions. In relation to mathematics the concept of learning activity iscombined with ideas of ascending from the abstract to the concrete. In the Davydovcurriculum this implies that students are first to be introduced to algebraic thinkingand reasoning. This is an idea that in many countries is contradictory to the teachingtraditions, which often is built on an arithmetic tradition. In this symposium researchrepresenting different national contexts all have worked with the Davydov curriculumrelated to mathematic teaching. Their work and findings are compared anddiscussed.
Place, publisher, year, edition, pages
learning activity, mathematics
Research subject Didactics
IdentifiersURN: urn:nbn:se:su:diva-114304OAI: oai:DiVA.org:su-114304DiVA: diva2:791086
ISCAR, Sydney, 29 September- 3 October, 2014.
Detta paper ingick i symposiet: Transforming Davydov's Learning Activity Curricula into NewContexts - examples from Canada, Italy and Sweden2015-02-262015-02-262015-03-13