This thesis explores the range of strategies used for educational provision for gifted children in mathematics in a group of schools in England. A review of literature relating to international theory and existing research in gifted education and empirical work into the teaching of gifted mathematicians were carried out. The literature review examined the dominant theories of intelligence and giftedness in general, including the historical background of definitions of giftedness and methods for its measurement, before specifically focusing on the concept of mathematical giftedness. The study was located in primary schools within Greater London, where schools are required to implement the ‘Gifted and Talented’ policy of the UK government. The research was conducted in two stages during the school years 2007-2008 and 2008-2009. The first stage involved a questionnaire survey sent to primary schools within five Local Educational Authorities. For the second stage of the research, which constituted the main study, a case study approach was used. The main methods of data collection employed within the case study were observations of mathematics lessons, semi-structured interviews with children nominated as able or gifted mathematicians and their teachers, as well as analysing documentary evidence (i.e., school policy, teacher’s planning, children’s assessment records and children’s written work). It was found that schools were responding to the policy in pragmatic terms, although no specific training was provided for practising teachers or school co-ordinators as part of the national training programme in making provision for mathematically gifted children. In practice, in classrooms, it was found that teachers’ level of confidence and expertise, the level of focused attention given to gifted children, the level of support and extension through higher-order questioning, as well as the size of the class and the nature of the work set were factors which affected the progress, perceptions and attitudes of children who were nominated to be able mathematicians. There is a paucity of research which has investigated aspects of provision for gifted and talented children, particularly in mathematics, in the UK. By specifically addressing this topic, this study makes a distinct contribution to current literature in both understanding aspects of mathematical giftedness and the range of provision used. This study makes a particular contribution to finding out how practising teachers in England are responding to a government initiative, which should be of interest to both policy-makers and practitioners. This thesis also presents examples for organising and teaching mathematics to gifted children at higher cognitive levels, within regular classrooms; this may be of interest to audiences internationally, including countries where there are no policies of provision for mathematically gifted children.

Denna fältöversikt kartlägger olika aspekter av matematisk begåvning med särskild fokus på reguljär matematikundervisning. Av forskningsfältet framhålls och exemplifieras varierade synsätt på hur matematikundervisning kan utformas för att erbjuda matematiskt begåvade elever en positiv kunskapsutveckling. De mångfacetterade och varierande infallsvinklarna som finns att tillgå kan göra det svårt för lärare att välja ut lämpliga strategier, metoder och anpassningar för de matematiskt begåvade eleverna de själv har i sina klasser. Resultaten av fältet indikerar att lärares ämneskunskaper och pedagogiska kompetens har störst inverkan på vilket stöd och bemötande elever erbjuds. Det som källorna även framhåller är att begåvade elever behöver identifieras. Identifikationsprocesser beskrivs som en kartläggning av elevernas förmågor, kunskaper och inlärningsstilar men bör även innehålla kontinuerlig utvärdering, analysering och återkoppling av elevers kunskapsutveckling. I källor föreslås det att matematiskt begåvade elever gynnas av individuellt utformad undervisning som inkluderar utmananande och snabbt accelererande uppgifter som med fördel även utgår från elevernas egna intresseområden. / This survey presents a summary of strategies and methods for mathematically gifted individuals’ whit special focus on regular education. Researches exemplify a various spectra of learning environments and methods for gifted students. Although, it can be challenging for teachers to figure out what constitutes an optimal learning environment for mathematically gifted students. According to findings it’s of most interest for gifted children’s positive knowledge development that teachers are professional in both pedagogical and theoretical manners. Manny sources also indicate that mathematically gifted students first of all need to be identified as talented. The identification processes will serve as a form of map in which gifted students skills, knowledge and learning styles are gathered and it also consists of a continual evaluating of student learning processes and knowledge development. Data exemplify that gifted students’ knowledge needs to be challenged and rapidly accelerate in order to interest and motivate them in their learning process. Findings also show that gifted students require personalized solutions that advantageously are originated from students own interests to ensure a positive knowledge development.

The purpose of this study is to examine whether Olympiad participation can develop problem-solving skills in mathematically-gifted learners from disadvantaged schools. My methodological approach was QUAN→Qual, using a quasi-experimental design with a non-equivalent comparison group. I chose two schools from the same disadvantaged area, and identified the top 50 Grade 7 learners in each school by mathematics marks. The study consisted of a pre-test, three mathematics sessions and a post-test. The Study Orientation in Mathematics Questionnaire (SOM) (Maree, Prinsloo, & Claassen, 2011) was used as the pre- and post-test, and a focus group explored the learners’ experience of the SOM. In the mathematics sessions, the intervention group worked through past papers of the SA Mathematics Challenge (South African Mathematics Foundation, 2018), and the alternative intervention group completed worksheets from a Department of Basic Education workbook. My study revealed a positive relationship between success in traditional Mathematics and Study Attitude, Study Habits and overall Study Orientation, and an interaction between disadvantage and success in Mathematics. Participants were less disadvantaged than their surroundings would indicate, and had higher Mathematics anxiety than expected for their achievement level. The intervention did not increase problem-solving behaviour and both the quantitative and qualitative findings showed that the participants found the Olympiad type questions unfamiliar and difficult. This unfamiliarity is indicative of the limited enrichment opportunities for mathematically-gifted learners in disadvantaged areas of South Africa. Greater experience of Mathematics Olympiads is suggested to help mathematically-gifted disadvantaged learners live up to their problem-solving potential. / Dissertation (MEd)--University of Pretoria, 2020. / Educational Psychology / MEd (LSGC) / Unrestricted

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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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.