<p>In this thesis the theoretical framework student ownership of learning (SOL) is developed both theoretically and with qualitative research, based on studies of small-group work in physics with miniprojects and context rich problems. Ownership is finally defined as actions of choice and control, i.e. the realised opportunities to own organisation of the work. The dimension group ownership of learning refers to the groups’ actions of choice and control of the management of the task: how the task is determined, performed and finally reported. The other dimension, the individual student ownership of learning, refers to the individual student's own question/idea that comes from own experiences, interests, or anomalies of understanding; an idea/question that recurs several times and leads to new insights. From literature and from own data, categories are constructed for group and individual student ownership of learning, which have been iteratively sharpened in order to identify ownership in these two dimensions. As a consequence, the use of the framework student ownership of learning is a way to identify an optimal level of ownership for better learning and higher motivation in physics teaching.</p><p>The first part of the thesis gives an overview of the theoretical background to the studies made, and summarises the findings. The second part consists of six articles that report case studies with analyses of audio/video-recorded student cooperative work, and student group discussions, from three collections of data: 1) students working with miniprojects in teacher education, 2) upper secondary school students taking a physics course that includes both context rich problems with group discussions and miniprojects, and 3), aeronautical engineering students working with context rich problems in an introductory physics course at university.</p><p>The thesis describes in a fine-grained analysis the conversation in the groups based on Barnes discourse moves, and finds that ownership and communication are related. Group discussions are found to be an indicator for group ownership of learning and exploratory talks often promotes individual student ownership of learning.</p>

In this thesis the theoretical framework student ownership of learning (SOL) is developed both theoretically and with qualitative research, based on studies of small-group work in physics with miniprojects and context rich problems. Ownership is finally defined as actions of choice and control, i.e. the realised opportunities to own organisation of the work. The dimension group ownership of learning refers to the groups’ actions of choice and control of the management of the task: how the task is determined, performed and finally reported. The other dimension, the individual student ownership of learning, refers to the individual student's own question/idea that comes from own experiences, interests, or anomalies of understanding; an idea/question that recurs several times and leads to new insights. From literature and from own data, categories are constructed for group and individual student ownership of learning, which have been iteratively sharpened in order to identify ownership in these two dimensions. As a consequence, the use of the framework student ownership of learning is a way to identify an optimal level of ownership for better learning and higher motivation in physics teaching. The first part of the thesis gives an overview of the theoretical background to the studies made, and summarises the findings. The second part consists of six articles that report case studies with analyses of audio/video-recorded student cooperative work, and student group discussions, from three collections of data: 1) students working with miniprojects in teacher education, 2) upper secondary school students taking a physics course that includes both context rich problems with group discussions and miniprojects, and 3), aeronautical engineering students working with context rich problems in an introductory physics course at university. The thesis describes in a fine-grained analysis the conversation in the groups based on Barnes discourse moves, and finds that ownership and communication are related. Group discussions are found to be an indicator for group ownership of learning and exploratory talks often promotes individual student ownership of learning.

This thesis reports case studies of students working with context rich problems (CRP) and mini projects (MP) in physics in an upper secondary school class and in a physics teacher education class at university. The students report a big shift from physics in secondary school as fun and easy, to physics in upper secondary school as boring, difficult and with lack of time for reflections and physics talking, but they also found physics as interesting in itself. In order to study how group discussions in physics influence the students learning and to study the phenomena of students’ ownership of learning (SOL) we introduced CRP and MP. We video recorded five groups with 14 teacher students at university in the end of 2002, and five group with 15 students at upper secondary school during the beginning of their second physics course in the spring term in 2003. MP and CRP in physics were used as instructional settings in order to give students possibility to strengthen their holistic understanding and their possibilities to ownership. When students get the opportunity to manage their own learning and studying by open-ended tasks in physics, without the teacher determining all details of the performance, this gives more ownership of learning. The advantage of MPs and CRPs from the student’s point of view is more freedom to act, think and discuss and from the teacher’s view, to get insights of the students’ ability and how they really think in physics. The ownership is found to be crucial for motivation and development of competence. Students’ ownership of learning (SOL) is the students’ influence/impact to affect tasks and the learning environment in such a way that the students have a real opportunity to achieve learning of physics. Students’ ownership of learning (SOL) is found at two levels: Group level: At the start of a task the SOL is determined by the design of the task. The choice of task, the performance (when, how, where), the level of result and presentatio n and report have to be determined by the students themselves. Individual level: A person’s experiences and anomalies of understanding have created unique questions that can create certain aspects of the task that drive this person to be very active and highly motivated. This gives the person a high individual ownership. We developed hypotheses concerning the relation between ownership, motivation and competence and we see some evidence in the cases reported in this thesis. The importance of exploratory talks to enhance learning, and to see aspects of communication as part of the motivation are discussed in the model of ownership, motivation and competence that is proposed.

Studien har som mål att upptäcka hur elevers lösningar skiljer sig vid tre olika svårighetsgrader inom slutna problemlösningar i årskurs 2. Trettiofyra34 elever deltar i studien och genomför sex stycken problemlösningsuppgifter. Teoretiskt vilar studien på ett ramverk över representationsformer och Heddens (1986) teori. Ramverket beskriver fem olika representationsformer och de är talade symboler, skrivna symboler, bilder, omvärldssituationer och manipulativa modeller. Heddens (1986) teori handlar om hur elevers kunskapsutveckling sker i fyra nivåer från konkret nivå, semikonkret nivå, semiabstrakt nivå till abstrakt nivå. Analysen inriktas på elevernas lösningar till de slutna problemlösningsuppgifterna där fokuset ligger på vilken representationsform som dominerar i varje svårighetsgrad samt vilka nivåer som eleverna uppvisar genom sina representationsformer. I resultatet uppkom det att uppgift 5 var svår. Resultatet uppvisar att eleverna visar en större variation i sina representationsformer vid en lägre svårighetsgrad än vid högre svårighetsgrader då eleverna vid högre svårighetsgrader oftare använder representationsformer som är kopplade till den abstrakta nivån. Därmed visar resultatet att eleverna i studien har en tendens att låsa sig vid vissa representationsformer eller glömma dem när svårighetsgraden på problemlösningarna höjs.

<p>This thesis reports case studies of students working with context rich problems (CRP) and mini projects (MP) in physics in an upper secondary school class and in a physics teacher education class at university. The students report a big shift from physics in secondary school as fun and easy, to physics in upper secondary school as boring, difficult and with lack of time for reflections and physics talking, but they also found physics as interesting in itself. In order to study how group discussions in physics influence the students learning and to study the phenomena of students’ ownership of learning (SOL) we introduced CRP and MP. We video recorded five groups with 14 teacher students at university in the end of 2002, and five group with 15 students at upper secondary school during the beginning of their second physics course in the spring term in 2003. MP and CRP in physics were used as instructional settings in order to give students possibility to strengthen their holistic understanding and their possibilities to ownership. When students get the opportunity to manage their own learning and studying by open-ended tasks in physics, without the teacher determining all details of the performance, this gives more ownership of learning. The advantage of MPs and CRPs from the student’s point of view is more freedom to act, think and discuss and from the teacher’s view, to get insights of the students’ ability and how they really think in physics. The ownership is found to be crucial for motivation and development of competence.</p><p><em>Students’ ownership of learning (SOL) is the students’ influence/impact to affect tasks and the learning environment in such a way that the students have a real opportunity to achieve learning of physics.</em></p><p>Students’ ownership of learning (SOL) is found at two levels:</p><p><strong>Group level:</strong> At the start of a task the SOL is determined by the design of the task. The choice of task, the performance (when, how, where), the level of result and presentatio n and report have to be determined by the students themselves.</p><p><strong>Individual level:</strong> A person’s experiences and anomalies of understanding have created unique questions that can create certain aspects of the task that drive this person to be very active and highly motivated. This gives the person a high individual ownership. We developed hypotheses concerning the relation between ownership, motivation and competence and we see some evidence in the cases reported in this thesis. The importance of exploratory talks to enhance learning, and to see aspects of communication as part of the motivation are discussed in the model of ownership, motivation and competence that is proposed.</p>

Fundação de Apoio a Pesquisa e à Inovação Tecnológica do Estado de Sergipe - FAPITEC/SE / The interaction within the classroom is one of the key variables in the process of teaching and learning, but these interactions between students and teachers usually do not occur in the methodologies adopted by most physics teachers. In addition, physical education and their evaluation are anchored to mathematical techniques without any connection to the everyday student. Thus, the student only memorizes the "formulas", without seeking relationships with concepts already learned by them, causing learning meaningless. Thus, we believe that social interaction linked to the collaborative activity can give meaning to the process of teaching and learning, as students build their knowledge by interacting collectively. In this way, the main objective of this research is to know the perceptions of students about the Rich Issues in Context, which is a type of collaborative teaching methodology in higher education, as well as their behavior while collaborative group in a discipline of Physics B in Federal University of Sergipe. In total, 15 students participated, the data were collected through non-participant observation and semi-structured group interview, conducted in two groups, and a survey applied to all students in the discipline. The results regarding the roles of each member of the group revealed that at times the students failed to perform their roles effectively, but then we noticed that they cooperated in the development of activities. In addition, students reported that in collaborative learning they learn from their classmates and with respect to Rich Problems in Contexts, we found that students understand the benefits of this activity and do not see this task as a way to decrease the amount of activity of each student. / A interação dentro da sala de aula é uma das principais variáveis no processo de ensino e aprendizagem, mas essas interações entre alunos e professores geralmente não ocorrem nas metodologias adotadas pela maioria dos docentes de física. Além disso, o ensino de física e a sua avaliação encontram-se ancorados a técnicas matemáticas sem qualquer ligação com o cotidiano do aluno. Dessa forma, o aluno apenas memoriza as “fórmulas”, sem buscar relações com conceitos já aprendidos pelos mesmos, provocando uma aprendizagem sem significado. Assim, acreditamos que a interação social atrelada com a atividade colaborativa possa dar significado ao processo de ensino e aprendizagem, uma vez que os alunos constroem seus conhecimentos interagindo coletivamente. De tal modo, o objetivo principal dessa pesquisa é saber quais as percepções dos alunos acerca dos Problemas Ricos em Contexto, que é um tipo de metodologia de ensino colaborativo no Ensino Superior, bem como seus comportamentos enquanto grupo colaborativo em uma disciplina de Física B na Universidade Federal de Sergipe. No total participaram 15 estudantes e os dados foram recolhidos através de observação não participante e entrevista semiestruturada em grupo, realizadas em dois grupos, além de um inquérito por questionário aplicado a todos os alunos da disciplina. Os resultados com relação aos papéis desempenhados por cada membro dos grupos revelaram que em alguns momentos os alunos não conseguiram exercer seus papéis com eficácia, mas por outro lado observamos que eles colaboraram no desenvolvimento das atividades. Além disso, os alunos relataram que na Aprendizagem Colaborativa eles aprenderam com os próprios colegas de classe e com relação aos Problemas Ricos em Contextos, verificamos que os alunos compreenderam os benefícios dessa atividade e não viram essa tarefa como uma forma de diminuir a quantidade de atividade de cada aluno.

Denna kvalitativa studie fokuserar på att undersöka hur kreativa och imitativa resonemang kommer till uttryck i en lågstadiekontext. Genom observationer av videoinspelningar av när 20 elever i årskurs 3 arbetar med rika problem har vi kommit fram till fem teman som beskriver tillfällen där kreativa och imitativa resonemang uttrycks. Dessa är när: elever utgår från tidigare matematiska kunskaper, elever använder sig av bilder eller plockmaterial, elever tar hjälp från andra, elever gissar sig fram, och elever diskuterar de matematiska förutsättningarna. Resultatet visar att kreativt resonemang förekommer i alla teman, och att de ofta är tätt sammanflätade med de imitativa resonemang som förekommer.

Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa ett matematiskt problem. Vi genomförde en observation och nio individuella intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i yttre och inre representationer. Strategier som bilder, grafiska framställningar och matematiska symboler (siffror) hör till de yttre representationerna, då de består av konkreta bilder som eleverna måste se framför sig på papper när de löser matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är samtliga strategier som tillhör de inre representationsformerna. Med inre representationer menar vi det som sker i huvudet, det eleverna inte behöver se framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än väljer till sin problemlösning är det oundvikligt att använda sig av någon form av inre representationsform, för att tänka måste alla göra oberoende av vilken lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde individens behov. / The purpose of the study was to discern which strategies pupils employ when they solve a mathematical problem. We carried through one observation and nine individual interviews with pupils in school year 3. They were asked to solve a mathematical problem, which was observed. On the basis of the pupils’ solutions, we carried out interviews in order to determine which strategies they chose to employ. The outcome of the pupils’ solutions showed several problem solving strategies. These were divided into external and internal representations. Strategies such as pictures, graphs and mathematical symbols (numerals) are external representations, as they consist of concrete pictures that the pupils must see in front of them on a paper when solving mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all strategies that belong to internal modes of representation. With internal representations, we mean what happens inside our heads – what pupils need not see in front of them in order to solve a problem. We found that the pupils’ solutions contained combinations of several different strategies. Irrespective of which strategy or strategies the pupil choose in his or her problem solving, it is inevitable to use some variety of internal representations; everyone has to think, regardless of the strategy chosen and the problem solving skills of the pupil. When pupils are young, it may be difficult for them to present the flow of their problem solving processes in writing. Consequently, as teachers we must have time to familiarize ourselves with how the pupil thinks in order to develop our teaching on the basis of the needs of the individual pupil.

<p>Syftet med studien var att ta reda på vilka strategier elever väljer när de ska lösa</p><p>ett matematiskt problem. Vi genomförde en observation och nio individuella</p><p>intervjuer med elever i årskurs 3. De fick lösa ett matematiskt problem som</p><p>observerades. Utifrån elevernas lösningar genomförde vi sedan intervjuer för att</p><p>ta reda på vilka strategier de valt att använda för att lösa problemet. Resultatet av</p><p>elevernas lösningar visade på flera olika lösningsstrategier. Dessa delades in i</p><p>yttre och inre representationer. Strategier som bilder, grafiska framställningar och</p><p>matematiska symboler (siffror) hör till de yttre representationerna, då de består av</p><p>konkreta bilder som eleverna måste se framför sig på papper när de löser</p><p>matematiska problem. Huvudräkning, automatiserad kunskap och ”tänkande” är</p><p>samtliga strategier som tillhör de inre representationsformerna. Med inre</p><p>representationer menar vi det som sker i huvudet, det eleverna inte behöver se</p><p>framför sig för att kunna lösa problemet. Vi fann att elevlösningarna innehöll</p><p>kombinationer av flera olika strategier. Vilken eller vilka strategier eleven än</p><p>väljer till sin problemlösning är det oundvikligt att använda sig av någon form av</p><p>inre representationsform, för att tänka måste alla göra oberoende av vilken</p><p>lösningsstrategi som väljs och hur duktiga problemlösare eleverna än är. När</p><p>eleverna är unga kan det vara svårt och ovant för dem att skriftligt redovisa hur</p><p>lösningsprocessen gått till. Därför måste vi lärare ha tid att sätta oss in i hur</p><p>eleven tänker för att kunna bygga vidare undervisningen utifrån den enskilde</p><p>individens behov.</p> / <p>The purpose of the study was to discern which strategies pupils employ when they solve</p><p>a mathematical problem. We carried through one observation and nine individual</p><p>interviews with pupils in school year 3. They were asked to solve a mathematical</p><p>problem, which was observed. On the basis of the pupils’ solutions, we carried out</p><p>interviews in order to determine which strategies they chose to employ. The outcome of</p><p>the pupils’ solutions showed several problem solving strategies. These were divided</p><p>into external and internal representations. Strategies such as pictures, graphs and</p><p>mathematical symbols (numerals) are external representations, as they consist of</p><p>concrete pictures that the pupils must see in front of them on a paper when solving</p><p>mathematical problems. Mental arithmetic, automated knowledge and “thinking” are all</p><p>strategies that belong to internal modes of representation. With internal representations,</p><p>we mean what happens inside our heads – what pupils need not see in front of them in</p><p>order to solve a problem. We found that the pupils’ solutions contained combinations of</p><p>several different strategies. Irrespective of which strategy or strategies the pupil choose</p><p>in his or her problem solving, it is inevitable to use some variety of internal</p><p>representations; everyone has to think, regardless of the strategy chosen and the</p><p>problem solving skills of the pupil. When pupils are young, it may be difficult for them</p><p>to present the flow of their problem solving processes in writing. Consequently, as</p><p>teachers we must have time to familiarize ourselves with how the pupil thinks in order</p><p>to develop our teaching on the basis of the needs of the individual pupil.</p>

Syftet med studien var att undersöka hur lärare i årskurs F-3 undervisar problemlösning i matematik för att främja elevers problemlösningsförmåga. Denna kvalitativa studie avgränsas till sex lärare som undervisar i årskurserna F-3 som är verksamma på skolor i Mellansverige. Studiens empiri är baserat på lärarnas återgivningar om hur de planerar och genomför sin undervisning i problemlösning i matematik. Resultatet visade att samtliga lärare kopplar problemlösning till vardagliga sammanhang där undervisningen bör ha variation för att eleverna ska utvecklas och uppnå problemlösningsförmågan. När det kom till lärarnas planering av undervisningen utgår lärarna från de tre didaktiska områdena syfte, metod och innehåll där alla tre områdena behöver vara välplanerade och strukturerade. Problemlösningsuppgifterna kan variera och innehålla både öppna och slutna frågor, med ett respektive fler svarsalternativ. Ord, begrepp, strategier och representationsformer är även viktiga områden som läraren behöver betona samt undervisa om. Resultatet visade även att samarbete och diskussioner utgör två avgörande och betydelsefulla arbetsformer för att eleverna ska få möjlighet att utveckla problemlösningsförmågan. Slutsatsen med studien är att lärarens planering och genomförande i problemlösning utgör en väsentlig roll för att eleverna ska kunna utveckla problemlösningsförmågan. Det är lika viktigt att undervisa om strategier och representationsformer som att arbeta genom samarbete och diskussioner med klasskompisar och lärare om olika elevlösningar och svar. / The purpose of this study was to investigate how primary school teachers in preschool class to year 3 teach about problem-solving in mathematics to further support students' problem-solving ability. This qualitative study is limited to six teachers who teach preschool class to year 3 who are active in schools in the central parts of Sweden. The empirical study is based on the teachers' representations of how they plan and carry out their teaching of problem solving in mathematics. The results showed that all teachers link problem solving to everyday contexts where teaching should have variety for students to develop and achieve problem solving ability. When it came to teachers' planning of teaching, they are based on the three didactic areas of purpose, method, and content, where all three areas need to be well-planned and structured. The problem-solving tasks can vary and contain both open and closed questions, with one or more answer alternatives. Words, concepts, strategies, and forms of representation are also important areas that the teacher needs to emphasize and teach about. The results also showed that collaboration and discussions constitute two crucial and important working methods for the students to have the opportunity to develop problem-solving ability. The conclusion of the study is that the teacher's planning and implementation in problem-solving constitutes an essential role for the students to be able to develop problem- solving ability. It is just as important to teach about strategies and forms of representation as to work through collaboration and discussions with classmates and teachers about different student solutions and answers.