The purpose of this qualitative study is to increase the knowledge of how Montessori teachers include mathematically gifted pupils through differentiated teaching. This was accomplished through semi-structured interviews with nine Montessori teachers from all over Sweden. The teachers were asked to describe how they plan their teaching, how they execute it and to share their thoughts and attitudes regarding this part of their job.    The results show that the Montessori teachers in this study use differentiated teaching based on the Montessori principles of individualisation. They make individual lesson plans for every pupil, based on the pupil’s level of knowledge, interests and needs. These plans are made together with the pupils, who thus have an impact on their own education. As the lesson plans are put into practice the pupils get to choose what to do when, during three hour work cycles. This means there are many different activities happening at the same time in the Montessori classroom. This seems to be beneficial to mathematically gifted pupils, as they appear to be offered an education at their individual level of knowledge. They are also able to set their own work pace and thus advance at their own speed. The Montessori manipulatives are important to the teachers, but the mathematically gifted pupils are able to leave them behind quickly and instead work with more abstract mathematics.    The study also shows that the teachers consider it exceedingly important that the mathematically gifted pupils are challenged and stimulated. For that reason, the teachers do not limit the pupils’ knowledge acquisition. The pupils are allowed to advance much further than what is expected at their age. In addition, the results of this study show that the Montessori teachers view working with gifted pupils as a positive and fun challenge and they consider it important to include these pupils in their teaching, instead of letting them work on their own.    The results of this study may also suggest that Montessori schools can be beneficial to mathematically gifted pupils. / Syftet med denna kvalitativa studie är att öka kunskapen om hur montessorilärare inkluderar matematiskt särbegåvade elever genom en differentierad undervisning. Detta gjordes genom semistrukturerade intervjuer med nio montessorilärare från hela Sverige. Samtliga undervisar, eller har undervisat, i matematik i årskurs f-3 och de har alla erfarenhet av matematiskt särbegåvade elever. Montessorilärarna ombads beskriva hur de planerar sin undervisning, hur de genomför den rent praktiskt samt att reflektera kring den här aspekten av deras jobb.    Resultatet visar att montessorilärarna differentierar undervisningen utifrån montessoripedagogikens principer om individualisering. De gör i stort sett helt individuella planeringar för varje elev som baseras på individens nivå, intressen och behov. Denna planering görs tillsammans med eleverna, som alltså kan påverka sin undervisning. När undervisningen sedan omsätts i praktik görs detta under arbetspass som är tre timmar långa. Där får eleverna själva välja vad de vill arbeta med och när. Detta innebär att det pågår en mängd olika aktiviteter samtidigt. Detta tycks vara gynnsamt för de matematiskt särbegåvade eleverna, då de tycks få en undervisning på just deras nivå. De kan också själva välja arbetstempo och därmed avancera i sin takt. Montessorimaterielen har en stor plats i lärarnas undervisning, men de särbegåvade eleverna kan, enligt de intervjuade lärarna, snabbt övergå till en abstrakt matematik.   Resultatet visar också att lärarna anser att det är av stor vikt att de matematiskt särbegåvade eleverna får utmaning och stimulans och begränsar dem därför inte i deras kunskapsinhämtning. Eleverna tillåts avancera långt över sin årskurstillhörighet. Studien visar dessutom att lärarna ser de särbegåvade eleverna som en positiv och rolig utmaning och att de tycker att det är viktigt att dessa elever inkluderas i undervisningen, istället för att lämnas ensamma i sin inlärning.    Sammantaget kan studien tyda på att montessoripedagogiken kan vara gynnsam för matematiskt särbegåvade elever.

This licentiate thesis deals with some influencing factors to develop mathematicalabilities among mathematical gifted adolescents. Krutetskii’s structureof the mathematical abilities and Mönks’ triadic model of giftedness isused as a theoretical framework.The thesis consists of two articles with different aims. The first aim is toinvestigate to what extent the students had participated in various mathematicalactivities during their years in school and what impact the students attachto these activities. The second aim was to examine some aspects of the importanceof motivation for the mathematically gifted adolescents.To answer the research questions data was collected with a questionnaireand an interview study of a total of 27 finalists in a national mathematicalcompetition for students in Swedish upper secondary schools.Generally the students were positive about the activities they had participatedin. Specifically acceleration in the subject and mathematical competitionsstand out as particularly significant activities according to the students.The study shows the significance of mathematical activities providing aframework to relate to, which will make the progression more visible for thestudents. Such activities could be mathematical competition problem solvingor acceleration in the subject.The results of the study indicates that intrinsic motivation together withextrinsic motivation with integrated or identified regulation are the most importanttypes of motivation. All students in the study had both intrinsic motivationand some type of extrinsic motivation. / Denna licentiatuppsats handlar om påverkansfaktorer som bidrar till att utvecklamatematiska förmågor hos matematiskt begåvade ungdomar. Somövergripande teoretiskt ramverk för studien används Krutetskiis struktur av dematematiska förmågorna samt Mönks begåvningsmodell.Uppsatsen består av två artiklar med olika syften. Den första artikeln syftartill att undersöka i vilken utsträckning studiens ungdomar har deltagit i olikamatematiska aktiviteter under sina år i skolan och vilken betydelse de tillmäterdessa aktiviteter. Den andra artikelns syfte är att undersöka några aspekter avmotivationens betydelse hos de matematiskt begåvade ungdomarna.För att besvara frågeställningarna samlades data in med en enkät- och intervjustudiemed totalt 27 finalister i Skolornas matematiktävling.Generellt uttalade sig eleverna positivt om de verksamheter som de hadedeltagit i under skoltiden. Speciellt framkom acceleration i ämnet och matematiktävlingarsom särskilt betydelsefulla. Studien indikerar betydelsen av attde matematiska verksamheterna ger en ram att relatera till, vilket gör utvecklingenmer synlig för eleverna. Sådana aktiviteter kan vara problemlösninginom tävlingsmatematik eller acceleration i ämnet.Resultaten av den andra studien visar att inre motivation tillsammans medyttre motivation med integrerad eller identifierad kontroll är de viktigaste formernaav motivation hos studiens deltagare. I studien framkommer också attingen av deltagarna endast hade inre motivation för ämnet. Tvärtom hadesamtliga deltagare både inre motivation och autonom yttre motivation.

Enligt Skollagen har alla elever rätt till den ledning och stimulans de behöver för att utifrån sina egna förutsättningar utvecklas så långt som möjligt. Av denna anledning vill vi genom denna studie undersöka hur algebraiska uppgifter och undervisning inom algebra kan anpassas för att matematiskt begåvade elever ska ges den utmaning och stimulans de behöver för att utvecklas så långt som möjligt. Detta har undersökts genom att genomföra en lektionsserie, bestående av tre lektionstillfällen. Efter att lektionsserien avslutats genomfördes semistrukturerade intervjuer i fokusgrupper med de deltagande eleverna, för att undersöka vad som krävs för att algebraiska uppgifter och undervisning inom algebra ska upplevas som utmanande och stimulerande av matematiskt begåvade elever i årskurs 5. Den teori som använts för att analysera resultaten är positioneringsteorin. De viktigaste resultaten som framkommit är att dessa elever ska erbjudas att arbeta med utmanande uppgifter och att detta med fördel görs genom att låta dem arbeta med dessa i par/grupper, med andra elever på en liknande kunskapsnivå. / According to the School Act, all students have the right to the guidance and stimulation they need to develop to the best of their abilities based on their individual conditions. For this reason, we want to investigate through this study how algebraic tasks and teaching within algebra can be adapted to provide mathematically gifted students with the challenge and stimulation they need to develop to the fullest extent possible. This has been examined by conducting a series of lessons consisting of three class sessions. After the lesson series concluded, semi-structured interviews were conducted in focus groups with the participating pupils to explore what is required for algebraic tasks and algebraic teaching to be perceived as challenging and stimulating by fifth-grade students. The theory used to analyze the results is positioning theory. The most important findings that have emerged are that these pupils should be offered the opportunity to work with challenging tasks, preferably by allowing them to work with these tasks in pairs/groups with other students at a similar level of knowledge.

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Studies have shown that creative mathematically founded reasoning (CMR) outperforms algorithmic reasoning (AR) in regards to retention and (re)construction of knowledge. This suggests that creativity should be encouraged in national high-school mathematics curricula. The aim of the present study is to compare how creativity is framed in different national high-school mathematics curricula, using the following definition: creativity is the characteristics of people, processes, and environments which lead to new and original products that are useful or otherwise attractive to an individual or a society. Utilizing content and discourse analysis, the present study thus contrasts how the high-school mathematics curricula of Singapore, Hong Kong, Sweden, and Norway handle and value creativity, and also examines which role creativity takes in each curricula. Findings suggest that Singapore’s curriculum emphasizes creativity the most, and frequently does so in relation to assessment. Hong Kong’s curriculum is found to emphasize creativity in diverse ways, often using words with connotations to playfulness. Analysis of Sweden’s curriculum indicates a relatively minute focus on creativity, tending to put it in a teacher-centered context. A feature of Norway’s curriculum is an increasing emphasis on creativity as courses approach tertiary education. This also suggests a rising value of creativity in its curriculum. A similar though not as pronounced trajectory is found also in Singapore’s curriculum. In the Asian and Norwegian curricula, creativity is expressed both as a means and an end, while in Sweden’s curriculum it is only seen as an end. The results are discussed in terms of potential reasons for the prominent national features, and the study also includes an evaluation of the aptness of the suggested definition of creativity, a review of the limitations of the study, as well as propositions for further research. Finally, two recommendations are given to the National Agency for Education in Sweden – Skolverket – based on the results of the study: 1) diversify the emphasis on creativity in the curriculum, and 2) ensure alignment between what teachers value and what Skolverket values with respect to creativity.

This diploma thesis is focused on issues connected to possibilities of developement of mathematically talented pupils from the first grade. In the theoretical part there basic terms related to the education of talented pupils in th Czech Republic are summarised and explained. In next part motivation, processes of motivatiom and the most frequent usage of Math competitions as a part of the education in the Czech Republic are presented. The base of the practical part of this diploma thesis is a set of non standardized tasks and problems, whose target is to activate the cognitive developement of talented pupils. Part of the practical part of this thesis is a protocol about an experiment and analysis of the particular tasks and activities for talented pupils. The main aim of this thesis is to emphasise the importance of the developement of talented pupils and compile/form enriching tasks for talented pupils during Maths lessons. KEYWORDS Talent, talent models, motivation, cognitive process, non standardized tasks, aktivity.

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