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Objetos de aprendizagem multimodais e ensino de cálculo : uma proposta baseada em análise de erros / Multimodal learning objects and teaching calculus : a proposal based on error analysisMüller, Thaísa Jacintho January 2015 (has links)
Esta tese teve como objetivo analisar dificuldades de aprendizagem apresentadas por alunos de Cálculo Diferencial e Integral, bem como testar possibilidades de superar tais dificuldades por meio de recursos tecnológicos. Na primeira fase da pesquisa, foram realizadas análises de erros cometidos por estudantes de Cálculo, inicialmente de uma turma de Sistemas de Informação e, na sequência, de uma turma de Engenharia. Em ambos os testes identificou-se que as maiores dificuldades se referiam a conteúdos de Matemática Básica, pré-requisitos para o Cálculo. O trabalho teve como pressupostos teóricos as ideias de Ausubel, Tall, Vinner e de autores que discutem aprendizagem de Álgebra, visto que os erros mais encontrados nas análises se referiam à aplicação da propriedade distributiva da multiplicação sobre a adição. A metodologia de investigação é quanti-qualitativa e está baseada nos pressupostos da Pesquisa Baseada em Design. Foi aplicado, também, um teste de estilos de aprendizagem, a fim de identificar quais os estilos preferenciais dos estudantes, o que guiou a construção de um Objeto de Aprendizagem voltado para a propriedade distributiva. Na segunda fase da pesquisa, foram realizadas atividades na Plataforma MOODLE, com alunos de Cálculo Diferencial e Integral I. Inicialmente, os estudantes responderam a um questionário que envolvia conteúdos de matemática básica, a fim de que fossem identificadas suas dificuldades. A partir delas, os grupos de alunos foram direcionados a objetos de aprendizagem, dentre os quais se tem o objeto construído na primeira etapa. Após o estudo com os objetos, os estudantes foram desafiados a discutir em fóruns, nos quais lançaram-se novas questões sobre as dificuldades encontradas. Nessa discussão, observou-se que muitas das considerações feitas nos pressupostos teóricos foram confirmadas. Por fim, foi aplicado um segundo questionário, semelhante ao primeiro, com fins de comparação do desempenho dos alunos envolvidos na pesquisa. A partir da análise estatística dos resultados, pode-se afirmar que houve uma melhora substancial no desempenho do grupo, o que indica que o trabalho realizado cumpriu com os objetivos propostos. Ainda, foi realizada uma entrevista com uma das professoras responsáveis pelo Laboratório de Aprendizagem da Instituição onde o trabalho foi desenvolvido, na qual foi salientada a importância de realizar uma pesquisa que possa dar subsídios para uso de recursos tecnológicos no Laboratório, para auxiliar os alunos a localizar e remediar suas dificuldades. / This thesis aims to analyze learning difficulties presented by students of Differential and Integral Calculus and test possibilities to overcome these difficulties through technological resources. In the first phase of the research, error analyzes were performed using results from a Calculus test, initially from a group of Information Systems students and, afterward, from a group of Engineering students. In both tests, it was found that the main difficulties refer to Basic Mathematics content, prerequisites for the Calculus discipline. The work is based in conceits of Ausubel, Tall, Vinner and other authors who discuss learning Algebra, since the most common errors referred to the application of the distributive property of multiplication over addition. The research methodology is quantitative-qualitative and is based on assumptions of Research-Based Design. It was also applied a learning style test in order to identify the preferred styles of students, which guided the creation of a Learning Object directed to the distributive property. In the second phase of the research, activities were carried out in the MOODLE platform with students from Differential and Integral Calculus I. Initially, students answered a questionnaire involving basic math content in order to identify their difficulties. From these results, groups of students were directed to Learning Objects, among which is the object constructed in the first stage. After studying with these objects, students were challenged to discuss in forums in which were launched new questions about the difficulties encountered. In this discussion, it was noted that many of the considerations made in the theoretical assumptions were confirmed. Finally, a second questionnaire was applied, similar to the first, in order to compare the performance of the students involved in the research. From the statistical analysis, it can be said that there was a substantial improvement in performance of the group, indicating the work complied with the proposed objectives. An interview was conducted with one of the teachers responsible for the Learning Laboratory where the research was developed, in which was highlighted the importance of conducting a study to sustain the use of technological resources in the Laboratory, in order to help students locate and remedy its difficulties.
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Dependency Parsing and Dialogue Systems : an investigation of dependency parsing for commercial applicationAdams, Allison January 2017 (has links)
In this thesis, we investigate dependency parsing for commercial application, namely for future integration in a dialogue system. To do this, we conduct several experiments on dialogue data to assess parser performance on this domain, and to improve this performance over a baseline. This work makes the following contributions: first, the creation and manual annotation of a gold-standard data set for dialogue data; second, a thorough error analysis of the data set, comparing neural network parsing to traditional parsing methods on this domain; and finally, various domain adaptation experiments show how parsing on this data set can be improved over a baseline. We further show that dialogue data is characterized by questions in particular, and suggest a method for improving overall parsing on these constructions.
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Language Acquisition and the Errors We Make : A comparison between beginners and intermediate learnersFeltsen, Patrik January 2009 (has links)
The aim of the study was to find out whether or not there is a difference in the type and number of errors made by L2 intermediate learners and beginners of English. Texts were gathered from two age groups, 9-10 year olds and 16-18 year olds, 16 texts from the younger beginner level learners and 9 from the older intermediate learners. From the errors made in the texts five categories were formed (six for the beginners): Grammatical errors, word missing errors, morpheme errors, word order errors and spelling errors that is unique to the beginners. It was found that intermediate learners make fewer errors overall but that they make the same types of errors as the beginners when they do make an error.
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Do Students Who Continue Their English Studies Outperform Students Who Do Not? : A Study of Subject-verb Concord in Written Compositions in English by Swedish University StudentsPreber, Louise January 2006 (has links)
This essay deals with subject-verb concord in written compositions by Swedish students at Uppsala University. The essay investigates the possibility that students who continue studying English beyond the A level at the university make fewer errors than students who do not continue. In order to minimize the influence of the students’ gender and first language, only essays written by female students were included in the study; in addition, all students included had Swedish as their first language, and so did their parents. 25 essays by students who continued their studies and 25 essays by students who may not have done so were chosen. All 50 essays were examined for both correct and incorrect instances concerning concord between subjects and verbs in the present tense. The primary verbs to be, to do and to have were analysed as well as regular and irregular verbs. The results show that the 25 students who continued beyond the A level made fewer errors than the 25 students who may not have continued. The results also indicate that subject-verb concord is not a serious problem for Swedish learners.
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SequÃncia Fedathi e anÃlise de erros aplicadas ao ensino de fraÃÃes / Fedathi sequence and analysis of errors applied to the teaching of fractionsVirlane Nogueira Melo 28 July 2017 (has links)
nÃo hà / O tema desta pesquisa à o ensino de fraÃÃes, um conteÃdo cujo aprendizado à imprescindÃvel para Ãxito na vida escolar quanto à MatemÃtica, visto que ocorre desde o Ensino Fundamental atà o Ensino MÃdio, servindo de base para o aprendizado de muitos outros conteÃdos mais complexos. A anÃlise concentrou-se na aplicabilidade da SequÃncia Fedathi, aliada à metodologia de AnÃlise de Erros no ensino-aprendizagem desse assunto. Objetiva-se com este estudo testar a aplicabilidade das metodologias retrocitadas no que tange ao conteÃdo de fraÃÃes, com vistas a tornar a aprendizagem dos alunos mais eficaz. Quanto à fundamentaÃÃo teÃrica, este trabalho se baseia sobretudo, nos escritos de HermÃnio Borges Neto, (2001) acerca da SequÃncia Fedathi, bem como nos estudos de Helena Cury, (2015) quanto à AnÃlise de Erros, entre outros estudiosos dessas metodologias. Este experimento, desenvolvido ao longo do ano 2017, teve como objetivo aplicar a SequÃncia Fedathi ao ensino de fraÃÃes e fazer a anÃlise das principais dificuldades e erros cometidos pelos alunos, ao resolverem os exercÃcios testes â diagnÃsticos aplicados. Configura uma pesquisa-aÃÃo, de abordagem quanti-qualitativa, cujo levantamento de dados sucedeu mediante aplicaÃÃo de exercÃcios a cada uma das oito aulas ministradas, bem como aplicaÃÃo de questionÃrio na primeira e na Ãltima aula. Participaram da pesquisa dez alunos da rede estadual de ensino do CearÃ, matriculados no 8 ano do Ensino Fundamental na EEFM Professor Paulo Freire. Com amparo na anÃlise dos dados obtidos na prÃpria investigaÃÃo, os resultados apontam que a aplicaÃÃo da SequÃncia Fedathi junto à AnÃlise de Erros nas aulas se mostrou eficaz, visto que os estudantes se mostraram mais confiantes e interessados pelo conteÃdo, destacando, em resposta aos questionÃrios, os benefÃcios dessa mudanÃa de perspectiva no trabalho com o erro e no posicionamento do professor em sala de aula / The theme of this research is the teaching of fractions, a content whose learning is essential for success in school life in Mathematics, since it occurs from Elementary to High School, serving as the basis for learning many more complex content. The analysis focused on the applicability of the Fedathi Sequence, coupled with the methodology of Error Analysis in teaching-learning of this subject. The objective of this study is to test the applicability of the feedback methodologies with respect to the content of fractions, in order to make student learning more effective. As for the theoretical basis, this work is based mainly on the writings of HermÃnio Borges Neto (2001) on the Fedathi Sequence, as well as on the studies of Helena Cury, (2015) on Error Analysis, among other scholars of these methodologies. This experiment, developed during the year 2017, had the objective of applying the Fedathi Sequence to the teaching of fractions and analyzing the main difficulties and errors committed by the students, when solving the tests - diagnostic exercises applied. It sets up an action research, of quantitative-qualitative approach, whose data collection happened through the application of exercises to each of the eight classes taught, as well as the application of a questionnaire in the first and last class. Ten students from the state education network of CearÃ, enrolled in the 8th year of Elementary Education at EEFM Professor Paulo Freire participated in the research. With the support of the analysis of the data obtained in the research, the results indicate that the application of the Fedathi Sequence with the Error Analysis in class was effective, since the students were more confident and interested in the content, highlighting in response to the questionnaires, the benefits of this change of perspective in working with the error and the positioning of the teacher in the classroom.
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Objetos de aprendizagem multimodais e ensino de cálculo : uma proposta baseada em análise de erros / Multimodal learning objects and teaching calculus : a proposal based on error analysisMüller, Thaísa Jacintho January 2015 (has links)
Esta tese teve como objetivo analisar dificuldades de aprendizagem apresentadas por alunos de Cálculo Diferencial e Integral, bem como testar possibilidades de superar tais dificuldades por meio de recursos tecnológicos. Na primeira fase da pesquisa, foram realizadas análises de erros cometidos por estudantes de Cálculo, inicialmente de uma turma de Sistemas de Informação e, na sequência, de uma turma de Engenharia. Em ambos os testes identificou-se que as maiores dificuldades se referiam a conteúdos de Matemática Básica, pré-requisitos para o Cálculo. O trabalho teve como pressupostos teóricos as ideias de Ausubel, Tall, Vinner e de autores que discutem aprendizagem de Álgebra, visto que os erros mais encontrados nas análises se referiam à aplicação da propriedade distributiva da multiplicação sobre a adição. A metodologia de investigação é quanti-qualitativa e está baseada nos pressupostos da Pesquisa Baseada em Design. Foi aplicado, também, um teste de estilos de aprendizagem, a fim de identificar quais os estilos preferenciais dos estudantes, o que guiou a construção de um Objeto de Aprendizagem voltado para a propriedade distributiva. Na segunda fase da pesquisa, foram realizadas atividades na Plataforma MOODLE, com alunos de Cálculo Diferencial e Integral I. Inicialmente, os estudantes responderam a um questionário que envolvia conteúdos de matemática básica, a fim de que fossem identificadas suas dificuldades. A partir delas, os grupos de alunos foram direcionados a objetos de aprendizagem, dentre os quais se tem o objeto construído na primeira etapa. Após o estudo com os objetos, os estudantes foram desafiados a discutir em fóruns, nos quais lançaram-se novas questões sobre as dificuldades encontradas. Nessa discussão, observou-se que muitas das considerações feitas nos pressupostos teóricos foram confirmadas. Por fim, foi aplicado um segundo questionário, semelhante ao primeiro, com fins de comparação do desempenho dos alunos envolvidos na pesquisa. A partir da análise estatística dos resultados, pode-se afirmar que houve uma melhora substancial no desempenho do grupo, o que indica que o trabalho realizado cumpriu com os objetivos propostos. Ainda, foi realizada uma entrevista com uma das professoras responsáveis pelo Laboratório de Aprendizagem da Instituição onde o trabalho foi desenvolvido, na qual foi salientada a importância de realizar uma pesquisa que possa dar subsídios para uso de recursos tecnológicos no Laboratório, para auxiliar os alunos a localizar e remediar suas dificuldades. / This thesis aims to analyze learning difficulties presented by students of Differential and Integral Calculus and test possibilities to overcome these difficulties through technological resources. In the first phase of the research, error analyzes were performed using results from a Calculus test, initially from a group of Information Systems students and, afterward, from a group of Engineering students. In both tests, it was found that the main difficulties refer to Basic Mathematics content, prerequisites for the Calculus discipline. The work is based in conceits of Ausubel, Tall, Vinner and other authors who discuss learning Algebra, since the most common errors referred to the application of the distributive property of multiplication over addition. The research methodology is quantitative-qualitative and is based on assumptions of Research-Based Design. It was also applied a learning style test in order to identify the preferred styles of students, which guided the creation of a Learning Object directed to the distributive property. In the second phase of the research, activities were carried out in the MOODLE platform with students from Differential and Integral Calculus I. Initially, students answered a questionnaire involving basic math content in order to identify their difficulties. From these results, groups of students were directed to Learning Objects, among which is the object constructed in the first stage. After studying with these objects, students were challenged to discuss in forums in which were launched new questions about the difficulties encountered. In this discussion, it was noted that many of the considerations made in the theoretical assumptions were confirmed. Finally, a second questionnaire was applied, similar to the first, in order to compare the performance of the students involved in the research. From the statistical analysis, it can be said that there was a substantial improvement in performance of the group, indicating the work complied with the proposed objectives. An interview was conducted with one of the teachers responsible for the Learning Laboratory where the research was developed, in which was highlighted the importance of conducting a study to sustain the use of technological resources in the Laboratory, in order to help students locate and remedy its difficulties.
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RAZÕES TRIGONOMÉTRICAS NO TRIÂNGULO RETÂNGULO: UMA ANÁLISE DE ERROS NO ENSINO MÉDIOFortes, Adriana Wachtmann Borges 06 January 2012 (has links)
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Previous issue date: 2012-01-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research aimed to analyze errors made by high school students to solve problems
involving trigonometric reasons in the rectangle triangle and plan activities to remediate them.
We also seek to collect the opinions of teachers about such errors, through a questionnaire
applied to them. The investigation was carried out with students from second year of high
school in the city of Quevedos, RS. The errors made by the students in response to a test were
categorized separately for each question. We analyzed 11 public school teachers and 58 high
school students. Thirty-three students answered these questions and, further, 25 other students
made some activities on Trigonometry, in order to verify if these students also had difficulties
in solving such issues. In the final stage of this research participated 12 students of the Youth
and Adults Education (EJA) who tested the activities that had been proposed as final product
of this dissertation. By the number of occurrences in each class of errors, it was noted that the
students have many difficulties related to the identification of the names of the sides of a
triangle and to the knowledge of trigonometric relationships defined therein. Teachers who
responded to the survey have generally considered that the difficulties of the students are
related to the lack of attention and knowledge prerequisites. All the teachers work in public
schools in Quevedos as well in the neighboring city, Santa Maria, RS. Based on the opinions
and suggestions made by the teachers, we created a Webquest as final product of this
research, with a sequence of activities that aim to overcome the difficulties presented by the
students. / Esta pesquisa teve como objetivo analisar os erros cometidos pelos alunos do Ensino Médio
na resolução de problemas que envolvem razões trigonométricas no triângulo retângulo e
planejar atividades para remediá-los. Também procuramos coletar as opiniões de professores
sobre tais erros, por meio de um questionário a eles aplicado. A investigação realizou-se com
estudantes do 2º ano do Ensino Médio de uma escola pública, no município de Quevedos, RS.
Os erros cometidos pelos alunos nas respostas a um teste foram categorizados separadamente
para cada questão. Participaram desta pesquisa 11 professores de escolas públicas e 58 alunos
de Ensino Médio. Trinta e três desses alunos responderam às questões e, posteriormente, 25
realizaram algumas atividades sobre Trigonometria, com intuito de verificar se esses
estudantes também tinham dificuldade para resolver tais questões. Na etapa final da pesquisa,
também participaram 12 alunos da Educação de Jovens e Adultos (EJA) que testaram as
atividades que foram propostas como produto final desta dissertação. Pelo número de
ocorrências em cada classe de erros, notou-se que os alunos têm muitas dificuldades
relacionadas à identificação da nomenclatura dos lados de um triângulo retângulo e ao
conhecimento das relações trigonométricas nele definidas. Os professores que responderam à
pesquisa consideraram, em geral, que as dificuldades são relacionadas à falta de atenção e de
conhecimentos pré-requisitos. Todos os professores trabalham em escolas públicas de
Quevedos, bem como no município vizinho, Santa Maria, RS. A partir das opiniões e
sugestões apresentadas pelos docentes, foi elaborada uma Webquest como produto final desta
pesquisa, com uma sequência de atividades que visam superar as dificuldades apresentadas
pelos estudantes.
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Análise de erro de funções de pedotransferência na estimativa de retenção de água no solo por meio de árvore de decisão / Error analysis of pedotransfer functions in estimating soil water retention by using decision treeBoschi, Raquel Stucchi, 1982- 25 August 2018 (has links)
Orientadores: Luiz Henrique Antunes Rodrigues, Maria Leonor Ribeiro Casimiro Lopes-Assad / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agrícola / Made available in DSpace on 2018-08-25T00:51:45Z (GMT). No. of bitstreams: 1
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Previous issue date: 2014 / Resumo: O conhecimento das propriedades hidráulicas do solo é indispensável para modelagem do sistema solo-planta-atmosfera. A determinação destas propriedades de forma direta é problemática: ¬exigem métodos caros, laboriosos e grandes demandantes de tempo. O uso de funções, que estimam estas propriedades a partir de outras, facilmente obtidas, tem sido objeto de várias pesquisas. Estas funções são denominadas de funções de pedotransferência (PTF). As PTF são normalmente avaliadas em função dos valores observados e estimados; pouca atenção tem sido dada à análise do erro em função das propriedades do solo. Este tipo de análise pode revelar detalhes importantes sobre o desempenho de uma PTF, podendo contribuir para melhorar sua capacidade preditiva. A hipótese científica deste trabalho foi que é possível identificar e avaliar padrões nos erros das PTF utilizadas para estimar a retenção de água no solo, por meio de modelos baseados em árvore de decisão. Outra hipótese é que a identificação dos padrões nos erros das PTF fornecerá subsídios para o uso de tais funções de forma mais confiável e precisa. O objetivo geral deste trabalho, portanto, foi obter árvores de decisão capazes de auxiliar na compreensão de quais atributos do solo afetam o desempenho das PTF na estimativa de retenção de água no solo. A metodologia foi baseada no modelo CRISP-DM e foram avaliadas PTF disponíveis na literatura, com base na análise do erro, por meio de árvore de decisão. A metodologia foi dividida em duas partes. Na primeira parte, a PTF desenvolvida por Vereecken e colaboradores em 1989, foi avaliada no próprio conjunto de dados utilizado para sua geração. Na segunda parte, as PTF desenvolvidas por Vereecken e colaboradores em 1989, van den Berg e colaboradores em 1997 e Lopes-Assad e colaboradores em 2001, foram avaliadas em um conjunto de dados diferente do utilizado na sua geração. Os resultados mostraram que os erros inaceitáveis a -10 kPa (CC) se deram para as mesmas condições de erros aceitáveis a -1500 kPa (PMP) ; por outro lado, os erros inaceitáveis na estimativa de PMP, de modo geral, se deram para as mesmas condições de erros aceitáveis para estimativa de CC. A diferença entre o conjunto de dados utilizado para desenvolver uma PTF e o conjunto de dados utilizado para avaliá-la é um importante fator na incidência de erros. Na seleção de uma PTF deve-se considerar o maior número de fatores possíveis e não somente a distribuição granulométrica e a proximidade geográfica dos conjuntos de dados. A técnica de indução de árvore de decisão apresentou-se como uma alternativa complementar à avaliação da PTF, uma vez que permitiu uma avaliação detalhada dos erros nas estimativas. Este tipo de avaliação é interessante, pois permite a identificação de erros sistemáticos na aplicação destas funções. Pode, ainda, ser usada como uma forma de diagnóstico a ser explorada por desenvolvedores de PTF / Abstract: Knowledge of the soil hydraulic properties is essential for modeling the soil-plant-atmosphere system. Direct determination of these properties is problematic: the methods are expensive, laborious and time consuming. Therefore, the use of functions that estimate soil hydraulic properties from other more easily measurable soil properties has been the subject of several studies. These functions are called pedotransfer functions (PTF). Most studies have focused on the development of these functions; however, few have attempted to improve their implementation. PTF are usually evaluated in terms of the measured and predicted values; less attention has been given to the analysis of the error term in relation to soil properties such as texture, bulk density and organic matter. This type of analysis may reveal important details about the performance of PTF including options to improve their predictive capability. The hypothesis of this study was that it is possible to identify and evaluate patterns in the errors of PTF used to estimate soil water retention by using decision tree models. Another hypothesis is that the identification of PTF errors patterns will provide subsidies for the use of such functions more reliably and accurately. The objective of this study was to obtain a decision tree that can assist in understanding what soil properties affect the performance of PTF in estimating soil water retention. The methodology was based on the CRISP-DM model and refers to the evaluation of PTF available in the literature, based on an error analysis by means of decision tree induction. The PTF developed by Vereecken and coworkers in 1989 was evaluated the same data set as used for their development. Next, the PTF developed by Vereecken and coworkers in 1989, van den Berg and coworkers in 1997 and Lopes-Assad and coworkers 2001, were evaluated on a different dataset than the one used for their development. Results indicate that unacceptable errors at -10 kPa (CC) occurred for the same conditions that lead to acceptable errors at -1500 kPa (PMP); on the other hand the unacceptable errors at -1500 kPa (PMP) occurred for the same conditions that lead to acceptable errors at -10 kPa (CC). The difference between the data set used to develop a PTF and the data set used to evaluate is a factor of error incidence. In selecting a PTF should be considered the largest possible number of factors and not only the particle size distribution and the geographical proximity of the datasets. The decision tree induction technique provides a complement for evaluation of PTF, since the method is efficient in the detailed evaluation of PTF. This type of assessment is interesting because it allows identifying systematic errors in PTF applications. It can also be used as a diagnostic tool to be explored by PTF developers / Doutorado / Planejamento e Desenvolvimento Rural Sustentável / Doutora em Engenharia
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Learner mathematical errors in introductory differential calculus tasks : a study of misconceptions in the senior school certificate examinationsMakonye, Judah Paul 28 August 2012 (has links)
D.Phil. / The research problematised the learning of mathematics in South African high schools in a Pedagogical Content Knowledge context. The researcher established that while at best, teachers may command mathematics content knowledge, or pedagogic knowledge, that command proves insufficient in leveraging the learning of mathematics and differentiation. Teachers' awareness of their learners' errors and misconceptions on a mathematics topic is critical in developing appropriate pedagogical content knowledge. The researcher argues that the study of learner errors in mathematics affords educators critical knowledge of the learners' Zones of Proximal Development. The space where learners experience misconceptions as they attempt to assign meaning to new mathematical ideas to which they may or may not have obtained semiotic mediation. In their Zones of Proximal Development learners may harbour concept images that are incompetition with established mathematical knowledge.Educators need to study and understand those concept images (amateur or alternative conceptions), and how learners come to have them, if they are to help learners learn mathematics better. Besides the socio-cultural v1ew, the study presumed that the misconceptions formed by learners in mathematicsmay also beexplained within a constructivist perspective of learning. The constructivist perspective of learning assumes that learners interpret new knowledge on the basis of the knowledge they already have. However, some of the knowledge that learners construct though meaningful to them may be full of misconceptions. This may occur through overgeneralisation of prior knowledge to new situations. The researcher presumed that the ideas that learners have of particular mathematical concepts were concept images they construct. Though some of the concept images may be deficient or defective from a mathematics expert's point of view, they are still used by the learners to learn new mathematics concepts and to solve mathematics problems. The lack of success in mathematics that results in the application of erratic concept images ultimately leads to unsuccessful learning of mathematics with the danger of snowballing if there are no practicable interventions. Differentiation is a new topic in the South African mathematics curriculum and most teachers and learners have registered problems in teaching and learning it. Hence it was imperative to do research on this topic from an angle of learner errors on that topic. The significance of the study is that this research isolated the differentiation learner errors and misconceptions that teachers can focus on for the improvement of learning and achievement in the topic of introductory differentiation. The research focused on the nature of errors and misconceptions learners have on introductory differentiation as exhibited in their 2008 examination scripts. It sought to identify, categorise (form a database) and discuss the errors and their conceptual links. A typology of errors and misconceptions in introductory calculus was constructed. The study mainly used qualitative methods to collect and analyse data. Content analysis techniques were used to analyse the data on the basis of a conceptual framework of mathematics and calculus errors obtained from literature. One thousand Grade 12, Mathematics Paper 1 examination scripts from learners of both sexes emanating from diverse social backgrounds provided data for the study. The unit of analysis was students' errors in written responses to differentiation examination items.
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The need to sensitize primary schools teachers to the effect of mother tongue interferenceTurner, Norma Estelle 06 December 2011 (has links)
M.Comm. / This dissertation explores the effects of mother tongue interference during the process of the acquisition of English as a second language. The Contrastive Analysis and Error Analysis hypotheses are presented and the concepts of interlanguage explored. The limitations and strengths of Contrastive and Error Analysis hypotheses are highlighted. Research on errors that are caused by mother tongue interference is reviewed. A sample of error analysis in the written work of English second language learners at primary school level is undertaken. Errors resulting from mother tongue interference are identified at lexical, semantic, phonological and syntactical level. Various methods and approaches in the teaching of English are identified in accordance with their relevance to outcomes based education. An Eclectic Solution is suggested to facilitate remedial intervention. The Input Hypothesis validity is explored and related to the communicative approach. Examples of lesson material to address some of the issues are included to assist educators.
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