Jag undervisar i matematikdidaktik för förskollärare, blivande grundskollärare och speciallärare i matematik. Jag är inblandad i självständiga arbeten där jag handleder arbeten som fokuserar matematiska resonemang och specialpedagogik. 

Jag disputerade med en avhandling som bygger på ett arbete med undervisningsutvecklande forskning genomfört tillsammans med lärarkollegor i grundskolan. Arbetet genomfördes som ett nätverk av learning studies. I avhandlings- och utvecklingsarbetet använde vi lärandeverksamhet som  teoretisk grund för undervisning. Det arbetet ledde in mig på ett intresse för hur kollektiva matematiska resonemang kan utvecklas i olika typer av elevegrupper. Lärandeverksamheterna fokuserade olika matematiska innehåll tillsammans med lärare och elever i förskoleklass och grundskolans alla årskurser.

Forskningsprojekt jag deltagit i:

Att göra matematik och naturvetenskap relevant inom undervisning för hållbar utveckling.

Problemsituationer, lärandemodeller och undervisningsstrategirer - PLUS. 

 

 

 

 

 

I urval från Stockholms universitets publikationsdatabas

• Lärares möjligheter att främja elevers teoretiska arbete med geometriska begrepp – lärandeverksamhet om cirkel

  2024. Helena Eriksson (et al.). Forskning om undervisning och lärande 12 (3), 22-38

  Artikel

  Sammanfattning

  I följande artikel diskuteras vad som karaktäriserar lärares handlingar som främjar elevers engagemang, i en lärandeverksamhet där de tillsammans med sina klasskamrater utforskar de geometriska begrepp som relaterar till begreppet cirkel. Data består av tre forskningslektioner i årskurs 2 där lärandeobjektet handlar om att reflektera över relationer mellan cirkelns fyra begrepp; mittpunkt, radie, diameter och cirkelbåge. Resultatet visar att lärares handlingar som fokuserade på de geometriska begreppen riktades mot både empiriska och teoretiska aspekter. Indikationer på utveckling av lärande-verksamhet kunde urskiljas i situationer där läraren introducerade, kopplade tillbaka, bekräftade, provocerade, inkluderade och fördjupade detaljer om begreppen som relaterar till cirkel. Med stöd av lärarhandlingar, som bestod av frågor, gester och konstruktioner på den gemensamma tavlan, möjliggjordes elevernas utforskande av begreppet cirkel.

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• Att utveckla algebraiskt tänkande genom lärandeverksamhet: En undervisningsutvecklande studie i flerspråkiga klasser i grundskolans tidigaste årskurser

  2021. Helena Eriksson.

  Avhandling (Dok)

  The aim of this thesis is to develop and explore teaching possible to promote algebraic thinking together with young, multilingual students six to twelve years old. One underlying assumption for the aim is that algebraic thinking can be developed by students participating in learning activities that are characterized by collective mathematical reasoning on relations between quantities of positive whole and rational numbers. Two overall research questions support this work: (1) What in students work indicate algebraic thinking identified in learning activities and as experiences of algebraic thinking? (2) How can learning models manifest in learning activity, in what ways do learning models change and enhance, and which characteristics of learning actions are enabled?   

  Data was produced by interviews and from research lessons with students in lower grades in a multilingual Swedish school. The research lessons were focused on learning activity as suggested by Davydov (1990, 2008/1986), aimed at developing theoretical thinking – here algebraic thinking. They were staged in two research projects conducted as networks of learning studies. In these learning studies, the group of teachers iteratively designed and revised learning activities whereby the students could identify mathematical knowledge and collectively solve mathematical problems. 

  The findings in the articles signal that learning models were developed as rudimentary, preliminary, prototypical and finally symbolic. Rudimentary models were grounded in algebraic thinking when the students analysed problem situations and identified the problem. Preliminary and prototypical models were developed by initiating and formalising actions understood as algebraic thinking. Different tools were initiated by the students and the teachers. These tools were formalised by the students. The students used algebraic symbols and line-segments to think together when comparing different quantities (Article 2). They carried out operations using unknown quantities when reflecting on additive and multiplicative relationships (Article 3). The students also used algebraic symbols to reflect on subtraction as non-commutative (Article 3). The different tools they used interacted on different levels of generalisation (Article 1). Algebraic thinking grounded the students reflections but interacted with, for example, fractional thinking in their arguments during the development of their learning models (Article 4). The different ways of thinking interacted in arguments when developing the rudimentary, the preliminary and the prototypical models. However, in the conclusion of their collective reasoning and in the development of the symbolic learning models, these different ways of thinking were intertwined in the same arguments (Article 4).

  As a conclusion, the four articles signal that learning models including algebraic symbols developed in a learning activity can be used by newly-arrived immigrant students to reflect on structures of numbers.

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• Skapa behov av multiplikation

  2020. Charlotta Andersson (et al.). Nämnaren (4), 11-15

  Artikel

  Kan multiplikation förstås på något annat sätt än som upprepad addition? Här prövar författarna ett nytt sätt att undervisa om multiplikation. Genom att atbeta med indirekt mätning skapas ett behov av multiplikation.

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• Algebraic and fractional thinking in collective mathematical reasoning

  2021. Helena Eriksson, Lovisa Sumpter. Educational Studies in Mathematics 108 (3), 473-491

  Artikel

  This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the El´konin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic thinking. Further analysis showed that these arguments were characterised by interplay between fractional and algebraic thinking except in the conclusion stage. In the conclusion and the evaluative arguments, these two types of thinking appeared to be intertwined. Another result is the discovery of a new type of argument, identifying arguments, which deals with the first step in task solving. Here, the different types of arguments, including the identifying arguments, were not initiated only by the teachers but also by the students. This in a multilingual classroom with a large proportion of students newly arrived. Compared to earlier research, this study offers a more detailed analysis of algebraic and fractional thinking including possible patterns within the collective mathematical reasoning. An implication of this is that algebraic and fractional thinking appear to be more intertwined than previous suggested.

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• Learning actions indicating algebraic thinking in multilingual classrooms

  2021. Helena Eriksson, Inger Eriksson. Educational Studies in Mathematics 106 (3), 363-378

  Artikel

  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.

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• Algebraic thinking and level of generalisation: students’ experiencing of comparisons of quantities

  2019. Helena Eriksson. Nordisk matematikkdidaktikk, NOMAD 24 (3-4), 131-151

  Artikel

  This article explores grade 1 students’ different ways of experiencing quantity comparisons after participating in teaching designed as a learning activity using tasks from the Davydov curriculum. A phenomenographic analysis generated three hierarchical ways of experiencing comparisons: counting numerically, relating quantities, and conserving relationships. The first category comprises arithmetic ways of thinking, whereas the second and third categories comprise algebraic ways of thinking. Algebraic thinking was identified as reflections on relationships between quantities at different levels of generalisation. The implications of these results in relation to learning activity theory are discussed.

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• Identifying algebraic reasoning about fractions

  2018. Helena Eriksson. Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, 255-262

  Konferens

  The issue for this paper is to identify algebraic reasoning through students´sense-making actions, during a lesson, where students and a teacher develop learning models for mixed numbers. The analysis focuses the students’ work, trying to make sense of the unknown fractional part of the number. This unknown part was elaborated when the students suggested to “add a little bit more” to construct equality. The un-known part developed to a fractional part with help of an emerging learning model containing algebraic symbols: B=W+p/a. In this activity. The potentialities in the students’ algebraic reasoning were identifyed as: an additive relationship between the integer and the fractional part of the number, and a multiplicative relationship between the numerator and the denominator in this fractional part.

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• V. V. Davydov: Philosophy, influences, and educational ideas

  2018. Luis Radford (et al.). ISCAR 2017 Book of Abstracts, 369-369

  Konferens

  V. V. Davydov has inspired a great deal of educational research in various western schools of education in generaland mathematics education in particular. This symposium on some of Davydov’s educational ideas, theirphilosophical background and intellectual influences, is located within the theme of “Foundations: Theoretical andresearch approaches.” It brings together scholars who, from different perspectives and backgrounds, have beenworking within the field of Activity Theory and Davydov’s ideas. Its goal is twofold. First, the symposium endeavorsto offer a critical appraisal of some of Davydov’s central concepts and to discuss the question of the philosophicalinfluence in Davydov’s work. Second, it aims to present some current applications of Davydov’s approach to theteaching and learning of mathematics as well as to offer a contrast between Davydov’s approach and otherapproaches in mathematics education.

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• Fractions and algebraic reasoning

  2017. Helena Eriksson, Lovisa Sumpter.

  Konferens

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• Setting an object of knowledge in motion through Davydov’s learning activity

  2017. Inger Eriksson, Helena Eriksson. Book of Abstracts, 111-111

  Konferens

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• Rationella tal som tal: Algebraiska symboler och generella modeller som medierande redskap

  2015. Helena Eriksson.

  Avhandling (Lic)

  In this study the teaching of mathematics has been developed in relation to rational numbers and towards a learning activity. At the same time topic-specific mediated tools have been studied. The iterative model for learning study has been used as research approach.

  The purpose of the study was to explore what in an algebraic learning activity enables knowledge of rational numbers to develop. The specific questions answered by the study are how an algebraic learning activity can be formed in an otherwise arithmetic teaching tradition, what knowledge is mediated in relation to different mediated tools and what in these tools that enable this knowledge.

  The result of the study shows how an algebraic learning activity can be developed to support the students to understand rational numbers even in an arithmetic teaching tradition. The important details that developed the algebraic learning activity were to identify the problem to create learning tasks and the opportunity for the students to reflect that are characteristic of a learning activity. The result also shows that the mediating tools, the algebraic symbols and the general model for fractional numbers, have had significant importance for the students' possibilities to explore rational numbers. The conditions for the algebraic symbols seem to be the possibilities for these symbols to include clues to the meaning of the symbol and that the same symbol can be used in relation to several of other mediated tools. The conditions in the general model consisted of that the integer numbers and the rational numbers in the model could be distinguished and that the students could reflect on the meaning of the different parts. The general model consists of the algebraic symbols, developed in the learning activity. The algebraic symbols make the structure of the numbers visible and the general model mediates the structure of additive and multiplicative conditions that are contained in a rational number.

  The result of the study contributes in part to the field of mathematics education research by examining Elkonin's and Davydov's Mathematical Curriculum in a western teaching practice and in part to a development of the model of Learning study as a didactical research approach by using an activity-theoretical perspective on design and analysis.

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