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Huvudräkning är den av de matematiska förmågorna vi lär oss i skolan som vi sedan oftast använder utanför och efter skolan. Därför är det ur ett samhällsperspektiv viktigt att alla skolelever får lära sig huvudräkning. Studiens syfte är att undersöka hur elever i åk 8 gör när de löser additions- och subtraktionsuppgifter med huvudräkning samt hur de kommunicerar om sitt arbete med huvudräkningen. Empiriska data samlades in genom intervjuer med 11 elever där eleverna fick lösa 11 huvudräkningsuppgifter och svara på frågor om hur de upplevde arbetet med att lösa uppgifterna. Huvudräkningsuppgifter kan lösas med hjälp av talfakta, uppräkning, visualiserad uppställning eller en sekvens av åtgärder, ofta kallat att använda strategier. Flexibel huvudräkning består av talfakta, förmåga, förståelse och attityd. Intervjudata sorterades och analyserades utifrån dessa fyra komponenter. Resultaten från studien visar att alla eleverna har tillräckligt god kunskap om talfakta för att lösa uppgifterna under intervjun. Förmåga består av kunskap om metoder och procedurer samt kommunikativ förmåga. Eleverna visade olika grad av procedurförmåga. De använde mellan fem och nio olika strategier för att lösa de 11 uppgifterna. Den kommunikativa förmågan var avsevärt lägre än procedurförmågan hos alla elever. Det märktes inte minst av att eleverna hade svårt att hitta rätt begrepp när de skulle berätta om sina lösningar. Förståelse har i det här arbetet brutits ner i taluppfattning, flexibelt eller mekaniskt val av strategi, mentala bilder och medvetenhet i val av strategi. Vissa elever väljer strategi efter talens beskaffenhet och numeriska relationer, medan andra i möjligaste mån håller sig till de bäst inövade strategierna oavsett talen i uppgiften. Under intervjuerna framkom att de flesta eleverna hade någon form av mentala bilder till hjälp när de räknade. Ingen av eleverna förklarade hur de gjorde när de bestämde vilken strategi de skulle använda, vilket tolkats som att de valde strategi undermedvetet. I komponenten attityd ingår tillit till sin egen förmåga och hur ansträngande huvudräkningsuppgifterna i intervjun upplevdes. Ansträngningen skattades av eleverna på en skala 1-10 och svaren varierade mellan 1-8. Flera elever uppgav en skattning för själva arbetet att räkna och en högre skattning när momentet att förklara sina beräkningar inkluderades. Ett problem ur ett samhällsperspektiv är att drygt två tredjedelar av eleverna i studien har så låg tillit till sin förmåga att räkna huvudräkning. Komponenten attityd befanns vara den svagaste delen i elevernas huvudräkning, följt av förståelse. För att stärka elevernas självförtroende är det viktigt att de får känna att de lyckas. Ett sätt att uppnå det är att arbeta mer med muntlig kommunikation, så att idéer får prövas och tankar utvecklas. / Arithmetic is one of the mathematical skills we learn in school, which we most frequently use outside and in our grown up life. Therefore, from a societal perspective, it is important that all school students learn arithmetic. The purpose of the study is to investigate how students in year 8 do when they solve addition and subtraction problems with mental arithmetic and how they communicate about their work with mental arithmetic. Empirical data were collected through interviews with 11 students where the students had to solve 11 mental arithmetic problems and answer questions about how they experienced the work of solving the problems. Mental arithmetic can be done using number facts, counting, a mental representation of a written procedure or by constructing a sequence of transformations, often called using strategies. Flexible mental arithmetic consists of four components: number facts, ability, understanding and attitude. The interview data were sorted and analyzed based on these four components. The results from the study show that all students have sufficient knowledge of number facts to solve the problems presented at the interview. Ability consists of knowledge of methods and procedures as well as communicative ability. The students showed different degrees of procedural ability. They used between five and nine different strategies to solve the 11 problems. The communicative ability was significantly lower than the procedural ability of all students. It was not least noticed that the students had difficulty finding the right concepts when they had to talk about their solutions. Understanding has here been broken down into number perception, flexible or instrumental choice of strategy, mental images and awareness in choice of strategy. Some students choose strategy according to the nature of the numbers and numerical relations, while others, as far as possible, stick to the best practiced strategies regardless of the numbers in the problem. During the interviews, it emerged that most students had some form of mental pictures to help when they calculated. None of the students explained how they did when deciding which strategy to use, which was interpreted as them choosing strategy subconsciously. The attitude component includes confidence in one's own abilities and how strenuous the interview tasks were experienced. The effort was rated by the students on a scale of 1-10 and the answers varied between 1-8. Several students stated one estimate for the actual work of calculating and a higher estimate when the element of explaining their calculations was included. A problem from a societal perspective is that just over two thirds of the students in the study have such low confidence in their ability to do mental arithmetic. The attitude component was found to be the weakest part of students' mental arithmetic, followed by comprehension. To strengthen students' self-confidence, it is important that they feel that they are succeeding. One way to achieve this is to work more with oral communication, so that ideas can be tested and thoughts developed.

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.

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Mathematics has always been a problem at schools, colleges and universities and to address this problem the South African government has introduced a new subject called Mathematical Literacy into schools and colleges. Since this subject places the emphasis on real-life contexts, there has been a special focus on its management at schools and colleges so that its implementation is done in an efficient way. This study therefore focuses on the experiences and interactions of managers of this new subject and how their leadership can improve performance in it. In addition to the literature review, an empirical investigation based on a qualitative approach and involving semi-structured interviews with managers of three public TVET colleges in the Western Cape was conducted to collect data. The other method used was the analysis of documents relevant to the study. The research found that managers of Mathematical Literacy have varying experiences in both their roles and the implementation of the subject. They also face varied challenges in relation to lecturers and students although there are also similarities regarding these at the different colleges in the study. The strategies of instructional leadership in intervention methods to improve performance in the subject which are encouraged by managers also differ, and some have better results than others. Various methods to empower lecturers are recommended. Recommendations are also made on what was found in this study, as are recommendations for further study. / Educational Leadership and Management / M. Ed. (Education Management)

Made available in DSpace on 2016-04-04T18:33:12Z (GMT). No. of bitstreams: 1 Ana Cristina Fonseca.pdf: 1411916 bytes, checksum: 430c126b2ad1fac0272c3fa9e10e205c (MD5) Previous issue date: 2013-10-04 / This study aims to analyze and understand the pedagogical practices of early childhood education related to the development of mathematical concepts to children five years of a municipal public school Campinas and reflections and approximations of these practices in the 1st year of elementary school . We present first a theoretical approach on child development , conceptions of childhood and play. Also our studies on mathematics in early childhood and the difficulties encountered in working on mathematical literacy and inclusion of meaningful activities that allow the construction of the concept of number by children . This study attempts to print meaning to the knowledge needed for school children , in the relations of learning mathematical concepts and implications for the continuity of the same in the early years of elementary school. Participated as research subjects a teacher Cluster III Childhood Education and her students , a teacher of 1st year of elementary school and curriculum coordinator of the Municipal Education Campinas . Observed episodes of the work of a group of cluster III School of Early Childhood Education . The research problem thus announces : How knowledge / knowledge related to mathematics are developed in early childhood education rooms and how they are perceived by elementary school teachers ? The methodology was qualitative , which were used as methodological resources : 1 ) interviews about the participants' understanding of the work with mathematics in kindergarten , about the contributions of this work for the students of 1st year of elementary school and prospects that such work offers classes for 1st year . ; 2 ) observations of episodes of work with mathematics classroom grouping III . The analysis is given from three categories : Working with mathematics in kindergarten - conceptualization and planning ; Playing in Early Childhood Education - contributions to literacy ; Initial and continuing the teachers of kindergarten and the early years of elementary school - the challenges of mathematics . As a result of this investigation it is possible to say that the actions developed in early childhood education , specifically those related to mathematics , are still poorly considered in the work of the early years of elementary school and that there is still a lot to make efforts with regard to training teachers of kindergarten and the early years of elementary school in order to better prepare them to work with mathematics in these stages of basic education. / Este estudo tem como objetivo analisar e compreender as pr?ticas pedag?gicas da educa??o infantil relacionadas ao desenvolvimento de conceitos matem?ticos com crian?as de cinco anos de uma escola publica municipal de Campinas e os reflexos e aproxima??es dessas pr?ticas no 1? ano do Ensino Fundamental. Apresentamos inicialmente uma revis?o te?rica da abordagem sobre o desenvolvimento infantil, as concep??es de inf?ncia e do brincar. Tamb?m nossos estudos sobre ? matem?tica na inf?ncia e as dificuldades encontradas no trabalho relacionado ao letramento matem?tico e ? inser??o de atividades significativas que possibilitem a constru??o do conceito de n?mero pelas crian?as. Este trabalho buscou imprimir significado aos saberes necess?rios para a escolariza??o infantil, nas rela??es de aprendizagem de conceitos matem?ticos e as implica??es para a continuidade do mesmo nos anos iniciais do Ensino Fundamental. Participaram como sujeitos da pesquisa uma professora de Agrupamento III da Educa??o Infantil e seus alunos, uma professora de 1? ano do Ensino Fundamental e o coordenador de Curr?culo da Secretaria Municipal de Educa??o de Campinas. Observamos epis?dios dos trabalhos de uma turma de agrupamento III da escola de Educa??o Infantil. O problema de pesquisa assim se anuncia: Como os conhecimentos/saberes relacionados ? matem?tica s?o desenvolvidos em salas de Educa??o Infantil e de que maneira s?o considerados pelos professores do Ensino Fundamental? A metodologia utilizada foi de car?ter qualitativo, onde foram utilizados, como recursos metodol?gicos: 1) entrevistas a respeito da compreens?o dos participantes sobre o trabalho com a matem?tica na Educa??o Infantil; sobre as contribui??es desse trabalho para os alunos do 1? ano do Ensino Fundamental e as perspectivas que tal trabalho oferece para as turmas de 1? ano.; 2) observa??es de epis?dios de trabalho com a matem?tica em sala de agrupamento III. As an?lises se deram a partir de tr?s categorias: O trabalho com matem?tica na Educa??o Infantil concep??es e planejamento; O brincar na Educa??o Infantil contribui??es para a alfabetiza??o; Forma??o inicial e continuada das professoras da Educa??o Infantil e anos iniciais do Ensino Fundamental- os desafios da matem?tica. Como resultados desta investiga??o ? poss?vel dizer que as a??es desenvolvidas na Educa??o Infantil, de maneira espec?fica aquelas relacionadas ? matem?tica, ainda s?o pouco consideradas no trabalho dos anos iniciais do Ensino Fundamental e que h? ainda muito o que empreender esfor?os no que se refere ? forma??o de professores da Educa??o Infantil e dos anos iniciais do Ensino Fundamental no sentido de melhor prepara-los para atuar com a matem?tica nestas etapas da educa??o b?sica.

The purpose of the present study is to gain a more complete understanding of the impact of human and physical resource allocations and their interaction on students&rsquo / mathematical literacy skills across Turkey, member and candidate countries of European Union through the Programme for International Student Assessment (PISA) 2003. Hierarchical linear modeling (HLM) techniques were used separately for three different cultural settings using the database of Programme for International Student Assessment (PISA) 2003. The results indicated that students in Turkey, member and candidate countries of European Union who performed higher on the mathematical literacy assessment tended to have the following characteristics: (1) enrolled at higher grade levels, (2) more educational resources at home, (3) higher levels of mathematics self-efficacy, (4) lower levels of mathematics anxiety, (5) more positive self-concept in mathematics, (6) less preferences for memorization strategies, and (7) more positive disciplinary climate in mathematics lessons. As the performance of schools were considered, the higher average mathematics self-efficacy of students, the higher the mean school mathematical literacy performance. The influence on mathematical literacy assessment varied from school to school with respect to grade level and disciplinary climate in mathematics lessons in Turkey and European Union countries, with respect to grade level, mathematics self-efficacy, and disciplinary climate in mathematics in European Union candidate countries. Moreover, school size and mathematics student-teacher ratio at school influenced the disciplinary climate in mathematics lessons in Turkey / academic selectivity of the school influenced the grade level and mathematics self-efficacy in the candidate countries of European Union.

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