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The aim of this chapter, which draws upon data from a design researchproject based on Davydov’s principles of learning activity, is to exemplify the func-tions learning models can have in visualising students’ algebraic thinking whenthey collectively discuss algebraic expressions. The data are comprised of video-taped research lessons in grades 1 and 5, respectively. The analysis indicates that thelearning models enhanced the students’ joint exploration of the idea behind algebraicexpressions and thus materialised their algebraic thinking in the whole-class discus-sions in three ways: (1) materialising an argument, (2) materialising a problem, and(3) materialising a collective memory., Förmågan att föra och följa algebraiska resonemang - utmaningar för grund- och gymnasieskolan

Denna studie behandlar problemet med ojämn struktur och design hos lärplattformar, brist på struktur kan innebära svårigheter med att hitta information vilket kan ha negativ påverkan på studenters upplevelser. Därför blev forskningsfrågan: hur kan strukturen och designen på lärplattformar förbättras för att öka studenternas studieupplevelse? Syftet med studien är att belysa de problem och frustrationer som kan uppstå när universiteten använder sig av allt fler digitala verktyg samt sammanställa förbättringsförslag för framtida kurshemsidor. Studien är kvalitativ och använder sig av en design-baserad forsknings metodik där två tester utfördes. Det första testet utfördes på en befintlig kurshemsida och det andra testet utfördes på en prototyp. Den nya prototypen skapades för studien med en ökad grad av standardiserad struktur som sedan kom att testas av universitetsstudenter. Prototyputvecklingen var iterativ och för att utvärdera sidan användes användbarhetstester med CTA (Concurrent think aloud) och en uppföljande semistrukturerad intervju. Data samlades in och analyserades med hjälp av en tematisk analys. Urvalet bestod av 9 st IT-studenter från Stockholms Universitet med erfarenhet av iLearn och valdes ut med hjälp av ett strategiskt urval. Resultatet visade att studenter upplever att en ökad grad av standardiserad struktur och stilsättning leder till att kurshemsidorna blir enklare att navigera och att det är därför viktigt att ta hänsyn till dessa faktorer vid utvecklingen av nya kurshemsidor. På det första testet uppfattade studenter det som att kurshemsidan har en låg grad av standardisering och att det kan leda till bland annat att man missar viktig information vilket kan vara frustrerande och stressande. Det kom vidare fram att det finns problem när stilsättningen är inkonsekvent eftersom det skadar läsbarheten på sidan. Under det andra testet upplevdes de största problemen såsom ordningsföljden och stilen som lösta. Som resultat av studien upptäcktes ett fl, This study deals with the problem of the lack of structure and design of learning platforms. Lack of structure can mean difficulties in finding information which can have a negative impact on students' experiences. Therefore, the research question became: how can the structure and design of learning platforms be improved to increase the students' study experience? The purpose of the study is to shed light on the problems and frustrations that can arise when universities use more and more digital tools and to compile proposals for future course websites. The study is qualitative and uses a design-based research methodology where two tests were performed. The first test was performed on an existing course homepage and the second test was performed on a prototype. The new prototype was created with an increased degree of standardized structure which was then tested by university students. The prototype development was iterative, the prototype was evaluated with usability tests, CTA (Concurrent think aloud) and a follow-up semi-structured interview. Data were collected and analyzed using a thematic analysis. The sample consisted of 9 IT students from Stockholm University with experience of iLearn and were selected using a strategic selection. The results showed that students feel that an increased degree of standardized structure and style leads to course homepages becoming easier to navigate and that it is therefore important to take these factors into account when developing new course homepages. On the first test, students perceived that the course website has a low degree of standardization and that it can lead to, among other things, missing important information, which can be frustrating and stressful. It was further revealed that there are problems when the style setting is inconsistent because it damages the readability of the page. During the second test, the biggest problems such as order and style were perceived as solved. As a result of the study, a number o

Ingår i Skolverkets lärportalMatematik – Grundskola 7–9Modul: AlgebraDel 8: Algebraiskt tänkande

Denna studie behandlar problemet med ojämn struktur och design hos lärplattformar, brist på struktur kan innebära svårigheter med att hitta information vilket kan ha negativ påverkan på studenters upplevelser. Därför blev forskningsfrågan: hur kan strukturen och designen på lärplattformar förbättras för att öka studenternas studieupplevelse? Syftet med studien är att belysa de problem och frustrationer som kan uppstå när universiteten använder sig av allt fler digitala verktyg samt sammanställa förbättringsförslag för framtida kurshemsidor. Studien är kvalitativ och använder sig av en design-baserad forsknings metodik där två tester utfördes. Det första testet utfördes på en befintlig kurshemsida och det andra testet utfördes på en prototyp. Den nya prototypen skapades för studien med en ökad grad av standardiserad struktur som sedan kom att testas av universitetsstudenter. Prototyputvecklingen var iterativ och för att utvärdera sidan användes användbarhetstester med CTA (Concurrent think aloud) och en uppföljande semistrukturerad intervju. Data samlades in och analyserades med hjälp av en tematisk analys. Urvalet bestod av 9 st IT-studenter från Stockholms Universitet med erfarenhet av iLearn och valdes ut med hjälp av ett strategiskt urval. Resultatet visade att studenter upplever att en ökad grad av standardiserad struktur och stilsättning leder till att kurshemsidorna blir enklare att navigera och att det är därför viktigt att ta hänsyn till dessa faktorer vid utvecklingen av nya kurshemsidor. På det första testet uppfattade studenter det som att kurshemsidan har en låg grad av standardisering och att det kan leda till bland annat att man missar viktig information vilket kan vara frustrerande och stressande. Det kom vidare fram att det finns problem när stilsättningen är inkonsekvent eftersom det skadar läsbarheten på sidan. Under det andra testet upplevdes de största problemen såsom ordningsföljden och stilen som lösta. Som resultat av studien upptäcktes ett fl, This study deals with the problem of the lack of structure and design of learning platforms. Lack of structure can mean difficulties in finding information which can have a negative impact on students' experiences. Therefore, the research question became: how can the structure and design of learning platforms be improved to increase the students' study experience? The purpose of the study is to shed light on the problems and frustrations that can arise when universities use more and more digital tools and to compile proposals for future course websites. The study is qualitative and uses a design-based research methodology where two tests were performed. The first test was performed on an existing course homepage and the second test was performed on a prototype. The new prototype was created with an increased degree of standardized structure which was then tested by university students. The prototype development was iterative, the prototype was evaluated with usability tests, CTA (Concurrent think aloud) and a follow-up semi-structured interview. Data were collected and analyzed using a thematic analysis. The sample consisted of 9 IT students from Stockholm University with experience of iLearn and were selected using a strategic selection. The results showed that students feel that an increased degree of standardized structure and style leads to course homepages becoming easier to navigate and that it is therefore important to take these factors into account when developing new course homepages. On the first test, students perceived that the course website has a low degree of standardization and that it can lead to, among other things, missing important information, which can be frustrating and stressful. It was further revealed that there are problems when the style setting is inconsistent because it damages the readability of the page. During the second test, the biggest problems such as order and style were perceived as solved. As a result of the study, a number o

Ingår i Skolverkets lärportalMatematik – Grundskola 7–9Modul: AlgebraDel 8: Algebraiskt tänkande

Ingår i Skolverkets lärportalMatematik – Grundskola 7–9Modul: AlgebraDel 8: Algebraiskt tänkande

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.

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.

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.

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.

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.

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.

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.

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.

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.

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

The aim of this article is to exemplify and discuss what teachers using learning activity need to consider when planning and supporting students’ collective theoretical work on algebraic expressions. Data are from two iteratively developed research lessons in two Grade 7 classes. The analysis focuses on students’ tool-mediated actions, the mathematical content processed, how the content is dealt with, and on identifying the crucial aspects that enable collective theoretical work. The result provides examples of how the content of the task, its design, and its tools, as well as the teacher’s and students’ tool-mediated actions are crucial factors in the promotion of collective theoretical work., Förmågan att föra och följa algebraiska resonemang

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

Vad krävs för att undervisningen ska skapa förutsättningar för elever att engageras i kreativa och reflektiva resonemang om algebraiska uttryck? Davydovs lärandeverksamhetsteori tillhandahåller principer som kan användas av lärare för att designa en undervisning som möjliggör för elever att delta i ett teoretiskt och kvalificerande arbete. Presentationen kommer att diskutera dessa faktorer samt ge exempel på hur uppgifter kan utformas och iscensättas för att möjliggöra detta., Developing algebraic reasoning capability

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

This licentiate thesis deals with compulsory school students’ expressed emotions and motivation towards mathematics. Theoretically, it has been guided by Hannula’s meta-theory on affect (e.g., 2012), of which emotion and motivation are part. In this thesis, emotion is defined using models from Schirmer (2015), and motivation correspondingly by Shunk et al. (2010). In the analysis, a model for emotion developed by Lövheim (2012), and models for motivation proposed by Ryan & Deci (e.g., 2000) and later further developed by Sumpter (2012), were adopted. This thesis focuses on two studies. In the first study, in search of nuanced knowledge about students’ experiences of mathematics, a primarily qualitative approach was adopted in interviews conducted with 19 primary school students. The results reported in Paper I (Nyman & Sumpter, 2019) confirm previous research which found that students express both intrinsic and extrinsic motivation for doing mathematics. But the results also indicate further motivational nuances, and I propose a division of each dimension into six subcategories. The results reported in Paper II (Nyman, in press) indicate that students’ negative emotions towards mathematics are directed towards themselves, as shame or distress, and not externally as anger. The results also indicate that there are connections between emotion and other affective concepts such as motivation and social dimensions, but also more technical aspects, for example, being allowed to listen to music. The second study, reported in Paper III (in preparation), gathered questionnaire data from 222 grade 8 and grade 9 students, and aimed to compare differences between the two grades as well as between boys and girls. The results show that the only significant difference between boys and girls is on issues relating to motivation: Girls generally express being more extrinsically motivated to doing mathematics than boys.

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

The issue for this paper is to discuss what can explain that students in different grades seem to experience a phenomenon in more or less the same way and thus, need to discern the same critical aspects in teaching. Data comes from a three-year-long learning study project conducted in four different Swedish schools, in K–9: preschool, grade 4, 6 and 9 respectively. Understanding what students yet need to learn in relation to a specific content is of importance if to organize a teaching situation where students can work in a zone of proximal development (Vygotsky, 1986). Within the theory of variation the concept of critical aspects is regarded as bearing such information for teachers to use when designing teaching (Marton, 2005; Runesson, 2013). In the research project we used phenomenography as a theoretical framework in search for critical aspects. Phenomenography is a research approach aiming to understand qualitatively different ways of experiencing a phenomenon. A basic assumption is that we, on the basis of what we have experienced in life, what situations and problems we encountered, experience a phenomenon in a specific way (Marton, 1981; Eriksson, 1999). But the ways we experience a phenomenon do not vary very much. This is believed to be because the contexts and activities do not vary at all. A phenomenographical analysis tends to result in a limited but qualitatively different way of experiencing a phenomenon (Eriksson, 1999). Critical aspects can be identified when comparing different ways of experiencing a phenomenon. The research question addressed in this paper is what possible explanations can be found that students in different grades seem to experience a phenomenon in more or less the same way and thus, need to discern the same critical aspects in teaching. In order to identify critical aspects groups of students from each grade were interviewed when presented algebraic expressions and some possible answers. The interviews were transcribed and ph, Developing algebraic reasoning capability

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

Presentationen syftar till att diskutera hur undervisning kan skapa förutsättningar för att elever engageras i kreativa och reflektiva resonemang om olika komponenters funktion och relation i algebraiska uttryck. Under senare år har intresset för klassrumskommunikationen ökat och därmed även intresset att studera utvecklingen av elevers förmåga att argumentera och delta i matematiska diskussioner i klassrummet (Larsson, 2015; Lithner, 2008). Mot bakgrund av detta uppstår frågor som (1) vilka redskap kan användas i klassrumskommunikationen för att främja innehållsrika, kreativa och reflektiva klassrumsdiskussioner samt (2) hur kan redskapen användas för att främja detta. Lärandeverksamhetsteori (Davydov, 2008) tillhandahåller fyra principer om hur undervisning,uppgifter och klassrumskommunikation kan utformas för att skapa förutsättningar för elever att engageras i ett teoretiskt arbete: problemsituationer, lärandemodeller, motsättningar och kollektiva reflektioner. Idén med en problemsituation är att den ska få eleverna att engageras i ett teoretiskt arbete gällande det avsedda kunskapsinnehållet. Lärandemodeller fungerar i det arbetet som ett nödvändigt visualiserande redskap för eleverna, såväl i utforskandet av innehållsliga aspekter som i de kollektiva reflektiva diskussionerna (Gorbov & Chudinova, 2000). Motsättningar fungerar som en drivkraft som upprätthåller det teoretiska arbetet (Davydov, 2008). Ide kollektiva reflektionerna uppmanas – och utmanas – eleverna till att försöka förklara andras i ljuset av sina egna förklaringar. De utmanas därmed i sitt teoretiska tänkande (Zuckerman, 2004). Presentationen grundar sig i en del av ett mer omfattande forskningsprojekt med det övergripande syftet att utforska hur undervisningen, i termer av uppgifter och arbetssätt, kan utformas och utvecklas för att bidra till att eleverna utvecklar en algebraisk resonemangsförmåga. I presentationen kommer följande fråga att fokuseras: Hur kan principerna för lärandeverksa, Developing algebraic reasoning capability

The issue for this paper is to discuss how a lesson can be structured to enable students to engage in creative and reflective discussions about the function for and relation between components in algebraic expressions. In recent years, interest in the communicative elements of mathematics education has increased internationally, and then with a special focus on the development of students' mathematical thinking and their ability to reason, argue and participate in mathematical classroom discussions (Kieran, 2001; Larsson, 2015; Lithner, 2008 ; Radford & Barwell, 2016). Based on the above, questions can be raised about which tools are used and how they can be used to promote content-rich, creative and reflective classroom discussions. The theory of learning activity (Davydov, 2008) provides four principles on how teaching, tasks and classroom communication can be designed to enable students engage in a theoretical work: (1) the creation of problem situations, (2) the creation and establishment of learning models, (3) the creation or advancement of contradictions and (4) joint reflexive action. The function of a problem situation is to challenge students to be active in a theoretical work where the processing of the problem gives the students the opportunity to work with aspects of the knowledge content that they have not yet distinguished. Learning models should enable the students to theoretically explore the abstract (general) of a given object and further serving as a tool for classroom communication and reflective discussions (Gorbov & Chudinova, 2000). Contradictions are historically developed tensions and the idea of contradictions can be used in the design of problem situations to challenge students to engage in a theoretical work (Davydov, 2008: Zuckerman, 2003). The idea of collective reflections is also central to learning activity, because the students are challenged in their own theoretical thinking by trying to explain someone else’s thoughts and, Developing algebraic reasoning capability

The issue for this paper is to discuss conditions for students’ participation in theoretical classroom discussions. In order to develop students’ ability to reason and solve problems algebraically Lins and Kaput (2004) argue that it is important to introduce algebra early in mathematics education. In line with this, researchers working within the sociocultural tradition argue that this may start as early as in first grade (Lins & Kaput, 2004). The so-called Davydov programme (e.g. Schmittau, 2005) is referred to as a promising alternative type of teaching, enhancing young students’ capability to reason algebraically. Central to the Davydov programme is the concept of ’learning model’. Such models (not to be confused with mathematical models) are used to enable students’ elaboration of mathematical phenomena. The characteristics of a learning model is that it materialises central theoretical aspects of a content. Further, it creates specific conditions necessary for students to understand and elaborate on each other’s arguments. However, there are many demanding issues related to the design of such learning models that needs to be further developed. In this paper we address the following research question: What in students’ classroom discussions can be taken as signs of emergent ability to reason algebraically? In this paper we use data from two learning studies conducted in 2017–2018. One in grade 1 (age 7) with three iteratively designed and revised lessons, and one in grade 5 (age 11) with four iteratively designed and revised lessons. We focus especially on how students use learning models as tools to enforce and maintain a collective reasoning indifferent communicative situations. To identify possible algebraic reasoning we have analyzed the communicative situations by drawing upon Toulmin’s (2003) model of argumentation with claim, data, warrant and backing. The tentative results indicate that the ability to work with the learning models not only facilitate, Developing algebraic reasoning capability

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

In this paper, we study year 2 and year 5 students’ expressed motivations for doing mathematics. The responses were analysed using thematic analysis; first with a deductive approach using themes from previous research, and then an additional inductive analysis searching for new themes. The results show that the children express both intrinsic motivation (cognitive-oriented and emotional-oriented), as well as extrinsic motivation (including outward and compensation). Two new categories of cognitive intrinsic motivation were found—normative and personal. The results also indicated an interplay not only between the different categories but also within categories, signalling that expressed motivation is double-layered. Some implications are discussed., Special Issue: The International Conference of Mathematical Views 2018 – Selected Papers.

Syftet med denna artikel är att beskriva och diskutera vilka funktioner lärandemodeller kan ha för att främja yngre elevers kollektiva diskussioner om algebraiska uttryck. Artikeln bygger på data från ett designforskningsprojekt baserat på Davydovs principer för lärandeverksamhet, bestående av videofilmade forskningslektioner i årskurs1 och 5. Analysen fokuserar på vad som skapar förutsättningar för helklassdiskussioner om algebraiska uttryck, hur de drivs framåt och kvalificeras samt vilka funktioner lärandemodeller kan ha för elevernas utforskande av matematiska strukturer och relationer i algebraiska uttryck. Resultatet indikerar att lärandemodeller som medierande redskap gör det möjligt för eleverna att föra kreativa och reflekterande diskussioner om algebraiska uttryck och deras komponenter., The aim for this article, which draws upon on data from a design research project based on Davydov’s principles of learning activity, is to discuss which functions learning models can have to promote students’ collective discussions on algebraic expressions. The data is comprised of videotaped lessons in Grade 1 and 5 respectively. The analysis focuses on conditions for qualifying whole-class discussions and the functions learning models can have for the students’ collective exploration of mathematical structures and relationships in algebraic expressions. The result indicates that learning models as mediating tools enable the students to conduct creative and reflective discussions on algebraic expressions and their components.

Presentationen syftar till att fördjupa diskussionen kring hur en undervisning kan designas för att elever så tidigt som i årskurs 1 kan ges möjlighet att resonera kring algebraiska uttryck. Forskare i det matedidaktiska fältet (se t.ex. Kaput, 2008; Kieran, 2006; Lins & Kaput, 2004; Stacy & Chick, 2004; Radford, 2010, 2014) belyser att det kan finnas en problematik när undervisningen i algebra endast introduceras i en aritmetisk tradition där numeriska lösningar och rätt svar fokuseras. Detta då elever fastnar i numeriska lösningar i stället för generella resonemang och slutsatser (se t.ex. Davydov, 2008; Kaput, 2008; Kieran, 2006; Lins & Kaput, 2004; Stacy & Chick, 2004; Radford, 2010, 2014). Att kunna resonera i algebraiska termer är ett av de sätt som matematik kommuniceras på. Vidare är det ett av de sätt som matematisk kunskap etableras som sann. Att elever redan i de tidigare åldrarna ges möjlighet att utveckla en förmåga att föra och följa algebraiskt utformade resonemang blir därför en viktig målsättning för undervisningen. Dock behövs det kunskap om hur en undervisning som möjliggör för elever att utforska algebraiska situationer där sådana resonemang inkluderas kan arrangeras. Samt hur det är möjligt att genomföra så tidigt som i årskurs 1. Under höstterminen 2017 och vårterminen 2018 har en forskargrupp bestående av undervisande lärare, forskarstuderande lärare, forskarutbildade lärare samt vetenskapliga ledare genomfört en studie, där vi i en kollaborativ process har utforskat vilka typer av uppgifter och klassrumsdiskussioner som skapar förutsättningar för utveckling och kvalificering av algebraisk resonemangsförmågan hos elever i årskurs 1. Learning study har valts som ansats och metod då den erbjuder ett “maskineri” för att närgånget kunna studera relationen mellan undervisning och elevers lärande. Vidare bygger studien på Davydovs (1962, 2008) arbete avseende design av uppgifter och klassrumskommunikationen samt analys av data. Inle, Developing algebraic reasoning capability

The issue for this paper is lesson iteration informed by students’ responses to lesson design seen from the theoretical standpoint of learning activity in a learning study on a lesson framing algebraic reasoning. A body of research (e.g.; Kieran, 2006; Lins & Kaput, 2004; Radford, 2010) suggests that there can be a problem if algebra is introduced from an arithmetic standpoint focusing on finding singelnumerical solutions to tasks.This can lead to students getting stuck in the arithmetical interpretation of algebraically problems and prevent them from using algebra as a tool for general mathematical understanding (e.g. Davydov, 2008; Kieran, 2006; Lins & Kaput, 2004; Radford, 2010). Learning study can be understood as a lesson study with a focus on a specific object of learning and in combination with an explicit theory of learning (Elliot, 2012). Marton (2015) argues for any functional theory of learning but commonly variation theory is the theory used. During the last years learning activity (Davydov, 2008) has been tested as an alternative and/or complementary theoretical design tool when designing teaching in learning studies (Eriksson, 2017). One design principle when trying to establish a learning activity is that the teacher has to create a situation inviting students to theoretical work (Davydov, 2008). This situation needs to include fundamental aspects of the theoretical knowledge as well as evoke students’ curiosity and urge them to engage in a theoretical work (Eriksson & Jansson, 2017). One difficult act of balance for the teacher is to stage a situation that evokes the curiosity needed for the students to create their own problem/learning task instead of simply solving a teacher assignment. In this project the data comes from a learning study in year 1 (age 7) with three lesson iterations. Tentative results indicate that small adjustments in lesson design made on the basis of learning activity generates both a higher degree of student reaso, Developing algebraic reasoning capability

Vad behöver skolan – en självständigt forskningsbidragande lärarkår, eller en kader av omprogrammeringsbara pedagogiska robotar? Författarna ställer sig frågan om hur lärardriven forskning kan bidra till långsiktig undervisningsutveckling.