Thesis (Ed.D.)--Liberty University School of Education, 2009. / Includes bibliographical references.

The whole thesis has been the view on the level of the understanding to the number among children at first grade of the elementary school. The beginning part focuses on the general summary of the points related to the main subject. This means the developing of cognitive functions at the time when children start attending school, summary of the technical terms connected with mathematical abilities and describing the development of the mathematical abilities at the first grade. The research applies to the topics in the field of mathematical abilities, which are relatively new in the Czech Republic. I tried to describe the number sense among children at the first grade, their strategies during solving the tasks and also to describe the measure of their math anxiety. Another outcome is finding out the dependence of results of the powers of intellect test, number knowledge test and the math anxiety measure. My research was realized under the patronage of the research realized at the Australian University, Sydney. The conclusion of the thesis focuses on the suggestions how to support the children's mathematical abilities development before they start attending school. The translation of two research methods is also the partial result. Key words: number sense, math anxiety, mathematical abilities

The purpose of the study is to support a younger mathematically gifted student to develop his problem solving ability in mathematics. The study was based on a micro-ethnographic study through participatory observations, where the analysis was based on Krutetskii's eight mathematical abilities. The result of the analysis shows that even younger, especially talented students in mathematics demonstrate Krutetskii's thoughts on mathematical abilities. The specific child in the study shows that there are several mathematical abilities within him. The problem is that the child does not get enough management and stimulation to develop his or her abilities. The child in the study needs adequate support to be able to reach full potential. Problem solving has been the focus of our meetings in order to develop the ability to motivate mathematical problems. The study has focused on two different types of problems, both closed and open issues. The result of the analysis also shows that the special education teacher needs to guide teachers in rich mathematical problems and treatment for particularly talented students in mathematics.

Läraren fyller en viktig roll för att elever ska utveckla sina matematiska förmågor som bland annat innefattar att tillhandahålla eleverna med återkoppling som syftar till att ta elevernas lärande vidare. Syftet med denna studie är att utifrån ett lärarperspektiv undersöka hur lärare som undervisar i matematik i årskurs 1-3 beskriver att arbete med återkoppling sker vid bedömning för att bidra till att elever utvecklar sina matematiska förmågor. För att kunna uppnå studiens syfte och frågeställningar har tre fokusgruppintervjuer genomförts med lärare som undervisar matematik i årskurserna 1-3. Det insamlade materialet har analyserats utifrån ett fokus på olika sorters återkoppling som förkommer i matematikundervisningen samt olika fokus som dessa kan ha. Resultatet visar att olika sorters framåtriktad återkoppling, målinriktad återkoppling och återkoppling förekommer i matematikundervisningen för att på olika sätt bidra till elevers utveckling av de matematiska förmågorna. Vidare visar resultatet att återkopplingens fokus har betydelse för hur återkopplingen bidrar till att utveckla elevers matematiska förmågor. De slutsatser som har dragits utifrån studiens resultat är att återkoppling som ges på ett medvetet och effektivt sätt är av stor vikt för att bidra till elevers utveckling av matematiska förmågor. / <p>Matematik</p>

The purpose of this study is to see how some teachers in primary school creates and adapts their mathematics teaching for students with special mathematical abilities. It also aims to identify opportunities and challenges that teachers see in creating a teaching adapted to these students. In this study, qualitative interviews has been done to collect data. The interviews were conducted with five teachers who all are active in the primary school. The study results show that there is great variation in how the interviewed teachers create their mathematics teaching for students with special mathematical abilities. The use of mathematics book proved to be significant for how this adaptation took place. The result also shows that the teachers’ explanations for the choice of the adaptations that they make in teaching vary. Some of the teachers stressed that the teaching they were carrying made it possible for adaptation in the normal teaching while others stressed that they made adjustments to fit the current student best. The result showed two challenges that many of the teachers saw in the creation of a teaching adapted for students with special mathematical abilities. These challenges were time and group.

The school is in the social, cultural and political contest which is complexical and changeable. Our society’s democratization and education reforms obligate us to look at the education aspects newly. One of them is the students abilities’ diagnostic. There are talking about mathematical abilities in this work. But, of course, such diagnostic principles can be used in other subjects, too. The main education’s mission is to develop the person’s forces, to formulate a human for the life in the society which is changing very fast in the sociocultural condition. The training is becoming orientated into the process but not into the results. But it’s very important to reach positive changes in each student’s studies. So, it’s very important to know every pupil, to understand his/her person’s features, addictions and faculties. The primary school had refused to value students’ knowledge and abilities in marks. But after some time there had risen necessity to create a new estimation system, which can mach purposes and goals in the training. The teachers need objective and reliable estimation’s instrument. Such instrument can be the standardized learning gains’ tests. There are talking about the tests’ information (which is necessary), perfection, administration, the forthcoming results’ interpretation in this work. The subject of the research is primary class pupils’ mathematical abilities as the diagnostic construct. The aim of the research is to open methodological, theoretical... [to full text]

Made available in DSpace on 2016-03-15T19:41:17Z (GMT). No. of bitstreams: 1 Daniel Sa Roriz Fonteles.pdf: 13600013 bytes, checksum: 81f3daa37d6065256402cd59e9bdad6c (MD5) Previous issue date: 2012-10-03 / Fundo Mackenzie de Pesquisa / Currently, there are studies which advocate higher mathematical abilities in individuals with Autism Spectrum Disorders (ASD), namely Asperger Syndrome/High Functioning Autism, sometimes even declaring that these individuals do have an above average performance when compared to neurotypicals. When Hans Asperger first described the syndrome that takes his name, he observed that some of his patients exhibited some difficulties concerning the ability to perform arithmetic operations. The present research aims to better understand mathematic abilities of people with ASD, mainly because this area is still open and yet little explored, especially in Brazil. In order to do that, mathematical abilities of 20 ASD students, aging from 7 to 23 years, were investigated using an Arithmetic Test validated for children from 1st to 4th grade of the Brazilian school system (SEABRA et al., 2009). An exploratory study of qualitative and quantitative nature was performed, with detailed written record of each Arithmetic Test session, and the use of non-parametric statistics to verify possible interactions between variables. Comparison between Autism, Asperger and Normal Students groups were made, besides other variables taken from students files considered during this research. Results suggest that ASD students had similar performance to 1st graders of a public school in the State of São Paulo; and that ASD students who have had inclusive experiences in regular schools tend to get higher scores in the Arithmetic Test. Other considerations indicate that further research is needed to accomplish better ways to Mathematics teaching. / Na atualidade existem estudos que defendem a ideia de que os indivíduos com Síndrome Asperger/Autismo de Alto Funcionamento apresentam certas habilidades matemáticas acima da média das pessoas com Transtornos de Espectro do Autismo (TEA) ou mesmo das pessoas sem deficiência. Hans Asperger, quando descreveu a síndrome que hoje leva o seu nome observou que seus pacientes apresentavam certas dificuldades nas capacidades relacionadas a cálculos aritméticos. A presente pesquisa buscou conhecer melhor as habilidades matemáticas de indivíduos com TEA, tendo em vista tratar-se de uma área ainda pouco explorada, sobretudo no Brasil. Para isso investigou-se as habilidades matemáticas de 20 pessoas com TEA, com idades entre 7 e 23 anos. A medição das habilidades em pauta foi feita através da utilização de instrumento de uma Atividade de Matemática validada para crianças da 1ª à 4ª série (Seabra et al., 2009). Um estudo de natureza qualitativa e quantitativa foi conduzido, no qual houve registro detalhado, por escrito, das sessões de aplicação da Atividade de Matemática, assim como foram conduzidos testes estatísticos não-paramétricos para a verificação da interação entre as variáveis do estudo. Procedeu-se a comparação dos grupos Autismo, Asperger e Sem Deficiência, dentre outras variáveis obtidas a partir do estudo dos prontuários. Os resultados sugerem que o desempenho dessas pessoas foi compatível com o nível de desempenho de crianças da 1ª série de uma escola pública de São Paulo; e que os alunos com Transtornos do Espectro do Autismo que frequentaram escola regular tenderam a apresentar melhores resultados na Atividade de Matemática. Outras considerações apontam para novas pesquisas a serem desenvolvidas visando métodos promissores de ensino de Matemática.

This thesis reports on two different investigations. The first is a systematic review of pedagogical and organizational practices associated with gifted pupils’ education in mathematics, and on the empirical basis for those practices. The review shows that certain practices – for example, enrichment programs and differentiated instructions in heterogeneous classrooms or acceleration programs and ability groupings outside those classrooms – may be beneficial for the development of gifted pupils. Also, motivational characteristics of and gender differences between mathematically gifted pupils are discussed. Around 60% of analysed papers report on empirical studies, while remaining articles are based on literature reviews, theoretical discourses and the authors’ personal experiences – acceleration programs and ability groupings are supported by more empirical data than practices aimed for the heterogeneous classroom. Further, the analyses indicate that successful acceleration programs and ability groupings should fulfil some important criteria; pupils’ participation should be voluntary, the teaching should be adapted to the capacity of participants, introduced tasks should be challenging, by offering more depth and less breadth within a certain topic, and teachers engaged in these practices should be prepared for the characteristics of gifted pupils. The second investigation reports on the interaction of mathematical abilities and the role of mathematical memory in the context of non-routine problems. In this respect, six Swedish high-achieving students from upper secondary school were observed individually on two occasions approximately one year apart. For these studies, an analytical framework, based on the mathematical ability defined by Krutetskii (1976), was developed. Concerning the interaction of mathematical abilities, it was found that every problem-solving activity started with an orientation phase, which was followed by a phase of processing mathematical information and every activity ended with a checking phase, when the correctness of obtained results was controlled. Further, mathematical memory was observed in close interaction with the ability to obtain and formalize mathematical information, for relatively small amounts of the total time dedicated to problem solving. Participants selected problem-solving methods at the orientation phase and found it difficult to abandon or modify those methods. In addition, when solving problems one year apart, even when not recalling the previously solved problem, participants approached both problems with methods that were identical at the individual level. The analyses show that participants who applied algebraic methods were more successful than participants who applied particular methods. Thus, by demonstrating that the success of participants’ problem-solving activities is dependent on applied methods, it is suggested that mathematical memory, despite its relatively modest presence, has a pivotal role in participants’ problem-solving activities. Finally, it is indicated that participants who applied particular methods were not able to generalize mathematical relations and operations – a mathematical ability considered an important prerequisite for the development of mathematical memory – at appropriate levels. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: In press.</p>

The study aims to describe variation in the expression of students’ mathematical ability and the various ways in which their mathematical aptitude is acknowledged and supported by their teachers, parents and peers in a Swedish context. Ability is defined as a complex of various abilities each of which may be more or less pronounced in a given individual. The study is based on ten case studies of highly able students (ages 6-19). Six of the studies are longitudinal, ranging from three to six years. In order to validate the results of the case studies, two survey studies were carried out involving 180 teachers (preschool to Grade 9 in Swedish compulsory school) and 284 mathematics developers from 229 Swedish municipalities. The survey studies raised questions concerning the teachers’ personal experience of identifying and supporting highly able students, the nature of their everyday teaching, and the support given to able students. The results show that mathematical abilities can take many different forms and there is great need for pedagogical support for this group of students. Since extra resources are rarely available for the benefit of nurturing talent and since there are, as yet, no Swedish national or local policy documents that specifically address the support of talent in students, teachers are on their own in figuring out how to best help able students develop mathematically. The study points to the importance of the social norms that influence the interaction between teacher and student(s): everyday social norms as well as socio-mathematical norms, i.e. norms specific to the subject of mathematics. The latter place considerable demands on the teachers’ mathematical knowledge and competence. The benefits of early interventions, of supportive teaching environments, and of providing the students with challenging tasks and questions are also discussed.

Made available in DSpace on 2016-04-27T16:59:07Z (GMT). No. of bitstreams: 1 Rogerio Giorgion.pdf: 2816091 bytes, checksum: 1fdcae05b78c48f1a3c3dff99f540152 (MD5) Previous issue date: 2010-06-02 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This piece of work aims to identify mathematical abilities present in middle school students who participate in the Science Fairs. In order to research the relationship between the process of carrying out the work for Science Fairs and the development of mathematical abilities we use the mathematical ability categories made by Krutetskii (1976) and the concepts of the learning theory by Vigotski. Some aspects of the history of the Science Fairs and the teaching of mathematics, including an analysis of curricular changes made in the last few years explain the scenario of the research. The methodology chosen was qualitative and exploratory, since the objective was to identify and analyze what mathematical abilities were present in the subjects of the research: three finalists of the national Fairs with unsatisfactory performance in the regular mathematics course. The tests were inspired in those developed by Krutetskii (1976) and the analysis made confirmed the presence of some of the abilities investigated: perception, spatial perception, mental representation and flexibility / Este trabalho visa identificar as habilidades matemáticas presentes em alunos do ensino médio participantes de Feiras de Ciências. Para pesquisar a relação entre o processo de realização dos trabalhos para Feiras de Ciências e o desenvolvimento de habilidades matemáticas utilizamos as categorias de habilidades matemáticas feitas por Krutetskii (1976) e os conceitos da teoria de aprendizagem de Vigotski. Alguns aspectos da história das Feiras de Ciências e do ensino de matemática, incluindo uma análise das mudanças curriculares dos últimos anos explicam o cenário da pesquisa. A metodologia escolhida foi exploratória qualitativa, visto que o objetivo foi identificar e analisar quais eram as habilidades matemáticas presentes nos sujeitos de pesquisa: três estudantes finalistas de Feiras nacionais com desempenho insatisfatório no curso regular de matemática. Os testes foram inspirados nos desenvolvidos por Krutetskii (1976) e a análise realizada confirma a presença de algumas das habilidades pesquisadas: percepção, percepção espacial, representação mental e flexibilidade