Learning actions indicating algebraic thinking in multilingual classrooms

Helena Eriksson,Inger Eriksson

doi:10.1007/s10649-020-10007-y

Helena Eriksson, Inger Eriksson

Open Access

https://doi.org/10.1007/s10649-020-10007-y

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Abstract

This article discusses algebraic thinking regarding positive integers and rational numbers when students, 6 to 9 years old in multilingual classrooms, are engaged in an algebraic learning activity proposed by the El’konin and Davydov curriculum. The main results of this study indicate that young, newly arrived students, through tool-mediated joint reflective actions as suggested in the ED curriculum, succeeded in analysing arithmetical structures of positive integers and rational numbers. When the students participated in this type of learning activity, they were able to reflect on the general structures of numbers established as additive relationships (addition and subtraction) as well as multiplicative relationships (multiplication and division) and mixtures thereof, thus a core foundation of algebraic thinking. The students then used algebraic symbols, line segments, verbal, written, and gesture language to elaborate and construct models related to these relationships. This is in spite of the fact that most of the students were second language learners. Elaborated in common experiences staged in the lessons, the learning models appeared to bridge the lack of common verbal language as the models visualized aspects of the relationships among numbers in a public manner on the whiteboard. These learning actions created rich opportunities for bridging tensions in relation to language demands in the multilingual classroom.

Highlights

The overall interest of this article is to exemplify and discuss how learning activity suggested by Davydov (1990) can enhance algebraic thinking through collective tool-mediated reflections in a multilingual classroom in Sweden, as students explore positive integers and rational numbers
The main results of this study indicate that young, newly arrived students, through tool-mediated joint reflective actions as suggested in the ED curriculum, succeeded in analysing arithmetical structures of positive integers and rational numbers
These types of joint action apparently succeed in mediating mathematical concepts and visualising tacit mathematical aspects of joint actions that, for example, Adler (2001) and Storch (2017) argue are of importance when teaching mathematics in multilingual classrooms

Summary

Introduction

The overall interest of this article is to exemplify and discuss how learning activity suggested by Davydov (1990) can enhance algebraic thinking through collective tool-mediated reflections in a multilingual classroom in Sweden, as students explore positive integers and rational numbers.When teaching mathematics to the youngest students, everyday language and everyday experiences are often used to illustrate mathematical concepts (Adler, 2019). Transparency such as joint collective actions with the use of mediating tools in well-organised teaching situations is vital when teaching in multilingual classrooms (Storch, 2017) These types of actions are addressed in Davydov and El’konin (the ED curriculum) specially-designed activity for instructions—the learning activity—aiming at theoretical thinking. In algebraic work, analyses of structures may focus on relationships within arithmetic using both letters and number symbols, not just as operations with specific numerical examples (Kaput, 2008) In such analyses, the meaning of the equal sign is in focus instead of using it as an operation sign (Kieran, 2018). Spoken language and gestures can be used to specify explorations of mathematical situations (ibid.)

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