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  • 1.
    Andersson, Charlotta
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Andrén, Sanna
    Eriksson, Helena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Tuominen, Jane
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Skapa behov av multiplikation2020Ingår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 4, s. 11-15Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    Abstract [sv]

    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.

  • 2. Andersson, Charlotta
    et al.
    Andrén, Sanna
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Tuominen, Jane
    Skapa behov av multiplikation2020Ingår i: Nämnaren : tidskrift för matematikundervisning, ISSN 0348-2723, nr 4, s. 11-15Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [sv]

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

  • 3.
    Bergkvist, Anna-Mia
    et al.
    Södertörn University.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik. Stockholm University.
    Collective Activities?: Agency in Teaching Situations2021Konferensbidrag (Refereegranskat)
    Ladda ner fulltext (pdf)
    fulltext
  • 4.
    Eriksson, Helena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Dalarna University, Sweden. Municipality of Borlänge, Sweden.
    Algebraic thinking and level of generalisation: students’ experiencing of comparisons of quantities2019Ingår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 24, nr 3-4, s. 131-151Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 5.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet.
    Algebraic thinking and level of generalisation: students’ experiencing of comparisons of quantities2019Ingår i: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 4, nr 3-4Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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 learning activity theory are discussed.

  • 6.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Algebraiskt tänkande i undervisning2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 7.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Algebraiskt tänkande i undervisning2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 8.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Algebraiskt tänkande i undervisning2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 9.
    Eriksson, Helena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Att utveckla algebraiskt tänkande genom lärandeverksamhet: En undervisningsutvecklande studie i flerspråkiga klasser i grundskolans tidigaste årskurser2021Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    Att utveckla algebraiskt tänkande genom lärandeverksamhet
    Ladda ner (jpg)
    Omslagsframsida
  • 10.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Att utveckla algebraiskt tänkande genom lärandeverksamhet: En undervisningsutvecklande studie i flerspråkiga klasser i grundskolans tidigaste årskurser2021Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 11.
    Eriksson, Helena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Dalarna University, Sweden.
    Identifying algebraic reasoning about fractions2018Ingår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg, Lovisa Sumpter, Umeå, Sweden: PME , 2018, Vol. 1, s. 255-262Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    fulltext
  • 12.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Identifying algebraic reasoning about fractions2018Ingår i: Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education / [ed] Ewa Bergqvist, Magnus Österholm, Carina Granberg, Lovisa Sumpter, Umeå, Sweden: PME , 2018, s. 255-262Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 13.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Rationella tal som tal: Algebraiska symboler och generella modeller som medierande redskap2015Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 14.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Teaching algebraic thinking within early algebra – a literature review2022Konferensbidrag (Refereegranskat)
    Abstract [en]

    There is a lack of overview regarding previous empirical studies within the early algebra research field. Consequently, the aim of this study is to propose one way to organise how algebraic thinking can be operationalised when teaching students five to twelve years old. The study is conducted as a literature review. The results show six categories of operationalising algebraic thinking with these young students. These categories can briefly be organised as three traditions: (1) arithmetic thinking tradition developing arithmetic thinking first, (2) developing arithmetic and algebra at the same time,or (3) algebraic thinking tradition developing algebraic thinking first. This method of organisation highlights one tradition of algebraic thinking where more research is needed - the tradition in which algebraic thinking is developed first. This tradition, as stated in the results, includes the category algebraic work.

    Ladda ner fulltext (pdf)
    fulltext
  • 15.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Uppgifter för algebraiskt tänkande2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 16.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet.
    Bergkvist, Anna-Mia
    Södertörns högskola.
    Öppna eller stängda skolor – en fråga även om bildning och lärande2020Ingår i: S.O.S - Skola och Samhälle, ISSN 2001-6727Artikel i tidskrift (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 17.
    Eriksson, Helena
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Dalarna University, Sweden .
    Eriksson, Inger
    Stockholms universitet, Humanistiska fakulteten, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Learning actions indicating algebraic thinking in multilingual classrooms2021Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 106, nr 3, s. 363-378Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    fulltext
  • 18.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik. Stockholm University.
    Eriksson, Inger
    Stockholm University.
    Learning actions indicating algebraic thinking in multilingual classrooms2021Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 106, nr 3, s. 363-378Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    fulltext
  • 19.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik.
    Eriksson, Inger
    Stockholms universitet, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Matematik som teoretiskt arbete - utveckling av matematiska modeller för rationella tal i åk 42016Ingår i: Forskning om undervisning och lärande, ISSN 2000-9674, E-ISSN 2001-6131, Vol. 4, nr 1, s. 6-24Artikel i tidskrift (Refereegranskat)
    Abstract [sv]

    Undervisning om rationella tal på mellanstadiet är ett erkänt svårt område. Eleverna har till exempel svårt att förstå att tal i bråkform och decimaltal kan representera samma värde eller att tal i bråkform har en bestämd plats på tallinjen, det vill säga att de är tal. I den här artikeln diskuteras och exemplifieras hur elever kan engageras i ett teoretiskt utforskande av tal i blandad form. Grunden för elevernas utforskande bestod i situationer där eleverna fick göra jämförelser av trästavar som inte gick jämt upp - det saknades ”en liten bit”. Utifrån dessa jämförelser kunde eleverna i gemensamma diskussioner skapa en generell modell för tal i blandad form, det vill säga en modell som också kunde beskriva mätningar som inte gick jämnt upp. Analysen visar bland annat att arbetet med modellen gjorde det möjligt för eleverna att diskutera heltalsdelar i förhållande till bråkdelar i tal i blandad form. Artikeln bygger på data från en serie Learning studies som genomfördes i en årskurs 4 på en interkulturell skola under 2012 – 2013.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 20.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Eriksson, Inger
    Stockholms universitet.
    Problemsituationer, lärandemodeller och undervisningsstrategier (PLUS): Design av ett professionsstöd för yngsta elevernas förståelse av positionssystemet2022Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 21.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Eriksson, Inger
    Stockholms universitet.
    Bengtsson, Henning
    Österskärsskolan.
    Uppgifter för algebraiskt tänkande2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 22.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Gracie, Jeffrey
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Halldén, Marit
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Åkerstedt, Johan
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Kommunikation och resonemang i problemlösning2021Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 23.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Hedefalk, Maria
    Markkanen, Peter
    Sumpter, Lovisa
    Fair sharing and division – mathematical reasoning regarding integers and fractions in preschool and preschool class2024Ingår i: Proceedings of Cerme 13 / [ed] Paul Drijvers, Csaba Csapodi, Hanna Palmér, Katalin Gosztonyi and Eszter Kónya, Alfréd Rényi Institute of Mathematics, Budapest, Hungary and ERME , 2024, s. 2096-2103Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper identifies and discusses children’s mathematical reasoning in preschool and preschool class when they work with a fair sharing case. The case came from a selection of cases designed to promote collective mathematical as well as ethical reasoning. Data comes from six children’s work when sharing four paper biscuits between three soft toys, first when the children were five years old and then, a year later, when they were six years old. The results show that their reasoning, both when they were five and six, used mathematical and ethical arguments. In preschool class, the students were able to use each other’s arguments in collective reasoning to identify, predict, and verify their reasoning. The students began to measure the fraction parts of a remainder but could not evaluate the conclusion with respect to what is aspects for division; equal numbers and equal size. The results also signal that teacher’s input, of posing evaluating questions, appears to stimulate the reasoning.

    Ladda ner fulltext (pdf)
    fulltext
  • 24.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Hedefalk, Maria
    Sumpter, Lovisa
    Preschool children’s collective mathematical reasoning about sharing2022Ingår i: A Mathematics Education Perspective on early Mathematics Learning – POEM 2022 Gothenburg, Sweden 12–13 May 2022, 2022, s. 1-8Konferensbidrag (Refereegranskat)
    Abstract [en]

    This study focuses on sharing, both in equal parts (groups) or unequal parts. Children at age five attending preschool, are faced with two different tasks where the mathematical properties in their reasoning, or when mathematical reasoning was replaced with an ethical reasoning is analysed. When performing division, different strategies were used, and the norm of fair share was often expressed. It was easier for the children to allocate resources when the dividend was larger than the divisor, and when dealing with a fraction, the cardinality of the number of parts appeared to be a prominent property compared to property ‘equal size’ of the parts. There were also indications of ethical reasoning where the child used different claims to convince their peer. There was a tension between the norm of equal sharing and the solutions with unequal parts. One implication is that if wanting to challenge children’s mathematical reasoning in a division task, it could be fruitful to look at fractions instead of repeating tasks where the dividend is larger than the divisor.

    Ladda ner fulltext (pdf)
    fulltext
  • 25.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Hedefalk, Maria
    University of Uppsala.
    Sumpter, Lovisa
    Stockholm University; University of Oslo, Norway.
    The Tension Between Division and Fair Share2024Ingår i: Teaching Mathematics as to be Meaningful – Foregrounding Play and Children’s Perspectives: Results from the POEM5 Conference, 2022 / [ed] Palmér, Hanna; Björklund, Camilla; Reikerås, Elin; Elofsson, Jessica, Cham: Springer Publishing Company, 2024, s. 69-79Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    This study focuses on sharing, both in equal parts (groups) or unequal parts. Children at age five attending preschool, are faced with two different tasks working in pairs. The analysis focus on the mathematical properties in the reasoning, or when mathematical arguments were replaced with an ethical reasoning. When performing division, different strategies were used, and the norm of fair share was often expressed. It was easier for the children to allocate resources when the dividend was larger than the divisor, and when dealing with a fraction, the cardinality of the number of parts appeared to be a prominent property compared to property ‘equal size’ of the parts. There were also indications of ethical reasoning where the child used different claims to convince their peer. There was a tension between the norm of equal sharing and solutions with unequal parts. One implication is that if wanting to challenge children’s mathematical reasoning in a division task, it could be fruitful to look at fractions instead of repeating tasks where the dividend is larger than the divisor.

    Ladda ner fulltext (pdf)
    fulltext
  • 26.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Nyman, Martin
    Kista grundskola; Åbo Akademi.
    Tambour, Torbjörn
    Stockholms universitet.
    Uppgifter för algebraiskt tänkande2023Övrigt (Övrig (populärvetenskap, debatt, mm))
    Ladda ner fulltext (pdf)
    fulltext
  • 27.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Petersson, Annika
    Arbeta i annan bas än bas tio på lågstadiet: ett modellarbete om positionssystemet2024Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 28.
    Eriksson, Helena
    et al.
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik. Dalarna University, Sweden .
    Sumpter, Lovisa
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Algebraic and fractional thinking in collective mathematical reasoning2021Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 108, nr 3, s. 473-491Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 29.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik. Stockholm University.
    Sumpter, Lovisa
    Stockholm University.
    Algebraic and fractional thinking in collective mathematical reasoning2021Ingår i: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 108, s. 473-491Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

    Ladda ner fulltext (pdf)
    fulltext
  • 30.
    Eriksson, Helena
    et al.
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Sumpter, Lovisa
    Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Fractions and algebraic reasoning2017Konferensbidrag (Refereegranskat)
    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 31.
    Eriksson, Inger
    et al.
    Stockholms universitet, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Setting an object of knowledge in motion through Davydov’s learning activity2017Ingår i: Book of Abstracts, 2017, s. 111-111Konferensbidrag (Refereegranskat)
  • 32.
    Eriksson, Inger
    et al.
    Stockholms universitet, Humanistiska fakulteten, Institutionen för ämnesdidaktik. Örebro University, Sweden.
    Eriksson, Helena
    Dalarna University, Sweden.
    Nyman, Martin
    Stockholm City, Sweden.
    Wettergren, Sanna
    Stockholms universitet, Humanistiska fakulteten, Institutionen för ämnesdidaktik. Åbo Academy University, Finland.
    Challenges when implementing the Elkonin-Davydov curriculum in mathematics2022Ingår i: The relation between mathematics education research and teachers’ professional development / [ed] L. Mattson; J. Häggström; M. Carlsen; C. Kilhamn; H. Palmér; M. Perez; K. Pettersson, Linköping: Svensk förening för matematikdidaktisk forskning (SMDF) , 2022, Vol. 16, s. 121-124Konferensbidrag (Refereegranskat)
    Abstract [en]

    Teachers interested in developing students’ possibilities to take part in joint discussions in problem-solving often have to deal with challenges regarding norms in the mathematics classrooms. Dominating classroom norms is a factor in mathematics teaching, be it of social or sociomathematical type. Here we address challenges in relation to norms experienced when attempting to create possibilities for mathematics learning, starting at a general and algebraical point rather than a specific and arithmetical one. We draw on two projects that explored the Elkonin-Davydov curriculum in Swedish classrooms. The results indicate that norms, of different kinds, are impedimental in different ways, when performing a theoretical work in mathematics teaching. 

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    fulltext
  • 33. Eriksson, Inger
    et al.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Nyman, Martin
    Wettergren, Sanna
    Challenges when implementing the Elkonin-Davydov curriculum in mathematics2022Ingår i: The relation between mathematics education research and teachers’ professional development: Proceedings of MADIF 13 / [ed] Linda Mattsson, Johan Häggström, Martin Carlsen, Cecilia Kilhamn, Hanna Palmér, Miguel Perez, Kerstin Pettersson, Göteborg: Svensk förening för MatematikDidaktisk Forskning - SMDF, 2022, s. 121-124Konferensbidrag (Refereegranskat)
    Abstract [en]

    Teachers interested in developing students’ possibilities to take part in joint discussions in problem-solving often have to deal with challenges regarding norms in the mathematics classrooms. Dominating classroom norms is a factor in mathematics teaching, be it of social or sociomathematical type. Here we address challenges in relation to norms experienced when attempting to create possibilities for mathematics learning, starting at a general and algebraical point rather than a specific and arithmetical one. We draw on two projects that explored the Elkonin-Davydov curriculum in Swedish classrooms. The results indicate that norms, of different kinds, are impedimental in different ways, when performing a theoretical work in mathematics teaching.

    Ladda ner fulltext (pdf)
    fulltext
  • 34.
    Grundén, Helena
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Åkerstedt, Johan
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Problemlösning som mål och medel2021Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 35.
    Hedefalk, Maria
    et al.
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Eriksson, Helena
    Markaanen, Peter
    Sumpter, Lovisa
    Five Year Olds in Between Sharing and Division2022Ingår i: Philosophy of Mathematics Education Journal, ISSN 1465-2978, E-ISSN 1465-2978, nr 39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Sharing and division are two concepts that have overlapping properties, and both are connected to the interpretation of fairness. In the present study, we study preschool children’s work with a case where eight biscuits were shared between soft toys. The focus is onthe different arguments that the children express. The results show that children use both ethical arguments and mathematical arguments in their solutions. Some of the arguments can be categorised as ‘Fair sharing related to number of pieces only’ or ‘Fair sharing employing ad hoc attempts at equal size’. The arguments that were coded as sharing not associated with mathematical sense of fairness were either classified as ethical reasoning or play. In the discussion, we raise the need of the combination of ethical reasoning and mathematical arguments if we want to create situations for children to develop critical thinking.

    Ladda ner fulltext (pdf)
    fulltext
  • 36.
    Hedefalk, Maria
    et al.
    Uppsala universitet, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Markaanen, Peter
    Stockholm University.
    Sumpter, Lovisa
    Stockholm University; University of Oslo.
    Five Year Olds in Between Sharing and Division2022Ingår i: Philosophy of Mathematics Education Journal, ISSN 1465-2978, nr 39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Sharing and division are two concepts that have overlapping properties, and both are connected to the interpretation of fairness. In the present study, we study preschool children’s work with a case where eight biscuits were shared between soft toys. The focus is onthe different arguments that the children express. The results show that children use both ethical arguments and mathematical arguments in their solutions. Some of the arguments can be categorised as ‘Fair sharing related to number of pieces only’ or ‘Fair sharing employing ad hoc attempts at equal size’. The arguments that were coded as sharing not associated with mathematical sense of fairness were either classified as ethical reasoning or play. In the discussion, we raise the need of the combination of ethical reasoning and mathematical arguments if we want to create situations for children to develop critical thinking.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 37. Nilsson, Carina
    et al.
    Magnusson, Malin
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Rättvis fördelning (och division): men, om någon är ledsen och hungrig?2024Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 38. Radford, Luis
    et al.
    Eriksson, Inger
    Stockholms universitet, Humanistiska fakulteten, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Freiman, Viktor
    Eriksson, Helena
    Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Polotskaia, Elena
    Boublil-Ekimova, Helena
    V. V. Davydov: Philosophy, influences, and educational ideas2018Ingår i: ISCAR 2017 Book of Abstracts: Taking a 360° view of the landscape of cultural-historical activity theory: The state of our scholarship in practice, 2018, s. 369-369Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 39. Radford, Luis
    et al.
    Eriksson, Inger
    Stockholms universitet, Institutionen för de humanistiska och samhällsvetenskapliga ämnenas didaktik.
    Freiman, Viktor
    Eriksson, Helena
    Högskolan Dalarna, Akademin Utbildning, hälsa och samhälle, Matematikdidaktik. Stockholms universitet, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.
    Polotskaia, Elena
    Boublil-Ekimova, Helena
    V. V. Davydov: Philosophy, influences, and educational ideas2017Ingår i: Book of Abstracts, 2017, s. 369-369Konferensbidrag (Refereegranskat)
    Abstract [en]

    V. V. Davydov has inspired a great deal of educational research in various western schools ofeducation in general and mathematics education in particular. This symposium on some ofDavydov’s educational ideas, their philosophical background and intellectual influences islocated within the theme of “Foundations: Theoretical and research approaches.” It bringstogether scholars who, from different perspectives and backgrounds, have been working withinthe field of Activity Theory and Davydov’s ideas. Its goal is twofold. First, the symposiumendeavors to offer a critical appraisal of some of Davydov’s central concepts and to discuss thequestion of the philosophical influence in Davydov’s work. Second, it aims to present somecurrent applications of Davydov’s approach to the teaching and learning of mathematics as wellas to offer a contrast between Davydov’s approach and other approaches in mathematicseducation.To achieve its goal, the symposium is organized in two parts. The first part consists offour presentations. The second part consists of a debate and interaction with the audience.

  • 40.
    Sumpter, Lovisa
    et al.
    Stockholms universitet; Oslo universitet.
    Hedefalk, Maria
    Uppsala universitet, Humanistisk-samhällsvetenskapliga vetenskapsområdet, Fakulteten för utbildningsvetenskaper, Institutionen för pedagogik, didaktik och utbildningsstudier.
    Eriksson, Helena
    Högskolan Dalarna.
    Markaanen, Peter
    Stockholms universitet.
    Att göra matematik relevant inom undervisning för hållbar utveckling2022Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 41.
    Sumpter, Lovisa
    et al.
    Stockholms universitet; Oslo universitet.
    Hedefalk, Maria
    Uppsala universitet.
    Markkanen, Peter
    Stockholms universitet.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Att göra matematik relevant inom undervisning för hållbar utveckling: Divisionen 8/3 med flerspråkiga 5 åringar2022Konferensbidrag (Övrigt vetenskapligt)
    Ladda ner fulltext (pdf)
    fulltext
  • 42.
    Teledahl, Anna
    et al.
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Eriksson, Helena
    Högskolan Dalarna, Institutionen för lärarutbildning, Matematikdidaktik.
    Palmér, Hanna
    Högskolan Dalarna, Institutionen för information och teknik, Materialteknik. Linnéuniversitetet.
    Representationer och strategier i problemlösning2021Övrigt (Övrig (populärvetenskap, debatt, mm))
1 - 42 av 42
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