The teaching of mathematics frequently comes in the line of fire due to under achievement and a lack of critical thinking. Accordingly educationists and mathematicians continually seek ways to overcome this hurdle. Against this backdrop, this study attempts to determine if the acquiring of learning-functions will improve academic achievement as well as critical thinking in mathematics. By means of a literature study the nature and importance of learning-functions for the development of critical thinking skills and the improvement of academic achievement are highlighted. The literature shows that critical thinking skills such as reasoning, analysis, hypothesising, making of decisions and problem solving are important skills for the mastering of mathematics. The learning-functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflection have been identified as the learning-functions which can develop the necessary skills for the mastering of mathematics. As the research stems from a combined interpretivist-positivist paradigm, the researcher used a combined qualitative and quantitative study. As part of the qualitative research, observation has been used. For the quantitative research the true experimental research method with a post-test control group design was chosen. The focus was on the qualitative collection of data, supported by the quantitative data. Twenty-three first year education students, with mathematics as major subject were used for this study. By means of systematic random sampling the students were assigned, as participants to an experimental and a control group. During contact sessions the participants of the experimental group were subjected for a period of eight weeks to an intervention programme with the focus on guided learning of the learning - functions decoding of knowledge, synthesis and integration of knowledge, comparisons, application of knowledge, generation of hypotheses and reflection. The control group received normal classroom instruction with no focus on guided learning of learning - functions. With the implementation of the intervention programme the experimental group was observed with regard to their progressive development of the application of these learning - functions. To determine any signs of progressive improvement of achievement and critical thinking skills in the experimental group during the implementation of the intervention programme, class tests and assignments were completed. Both the experimental- and the control group wrote the same tests and completed the same assignments. The post -test was a final examination paper which was written after the completion of the intervention by both groups to determine to which extent achievement and critical thinking skills improved within the experimental group. It can be inferred from the results of the empirical research that the guided learning of the learning -functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflective thought in the course of teaching mathematics, appeared to have enhanced learners' academic achievement and critical thinking. From a combination of the prominent findings of the empirical research, together with the knowledge gained from the literature study, justified recommendations were made regarding the learning of learning -functions in order to promote critical thinking and achievement in the teaching of mathematics. / Thesis (M.Ed.)--North-West University, Vaal Triangle Campus, 2009.

The teaching of mathematics frequently comes in the line of fire due to under achievement and a lack of critical thinking. Accordingly educationists and mathematicians continually seek ways to overcome this hurdle. Against this backdrop, this study attempts to determine if the acquiring of learning-functions will improve academic achievement as well as critical thinking in mathematics. By means of a literature study the nature and importance of learning-functions for the development of critical thinking skills and the improvement of academic achievement are highlighted. The literature shows that critical thinking skills such as reasoning, analysis, hypothesising, making of decisions and problem solving are important skills for the mastering of mathematics. The learning-functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflection have been identified as the learning-functions which can develop the necessary skills for the mastering of mathematics. As the research stems from a combined interpretivist-positivist paradigm, the researcher used a combined qualitative and quantitative study. As part of the qualitative research, observation has been used. For the quantitative research the true experimental research method with a post-test control group design was chosen. The focus was on the qualitative collection of data, supported by the quantitative data. Twenty-three first year education students, with mathematics as major subject were used for this study. By means of systematic random sampling the students were assigned, as participants to an experimental and a control group. During contact sessions the participants of the experimental group were subjected for a period of eight weeks to an intervention programme with the focus on guided learning of the learning - functions decoding of knowledge, synthesis and integration of knowledge, comparisons, application of knowledge, generation of hypotheses and reflection. The control group received normal classroom instruction with no focus on guided learning of learning - functions. With the implementation of the intervention programme the experimental group was observed with regard to their progressive development of the application of these learning - functions. To determine any signs of progressive improvement of achievement and critical thinking skills in the experimental group during the implementation of the intervention programme, class tests and assignments were completed. Both the experimental- and the control group wrote the same tests and completed the same assignments. The post -test was a final examination paper which was written after the completion of the intervention by both groups to determine to which extent achievement and critical thinking skills improved within the experimental group. It can be inferred from the results of the empirical research that the guided learning of the learning -functions decoding of knowledge, synthesis and integration of knowledge, comparison, application of knowledge, generating hypotheses and reflective thought in the course of teaching mathematics, appeared to have enhanced learners' academic achievement and critical thinking. From a combination of the prominent findings of the empirical research, together with the knowledge gained from the literature study, justified recommendations were made regarding the learning of learning -functions in order to promote critical thinking and achievement in the teaching of mathematics. / Thesis (M.Ed.)--North-West University, Vaal Triangle Campus, 2009.

Submitted by Rafael Santana (rafael.silvasantana@ufpe.br) on 2017-05-17T19:08:31Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Roberto_Mariano.pdf: 2556716 bytes, checksum: bc04f16516e0632af829880453a025c6 (MD5) / Made available in DSpace on 2017-05-17T19:08:31Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Roberto_Mariano.pdf: 2556716 bytes, checksum: bc04f16516e0632af829880453a025c6 (MD5) Previous issue date: 2015-02-24 / CAPES / Esta pesquisa tem por objetivo analisar a aprendizagem colaborativa suportada por computador no contexto da formação do professor de matemática quanto ao uso de modelagem para o ensino e aprendizagem de funções. A pesquisa fundamenta-se na Aprendizagem Colaborativa com Suporte Computacional (CSCL), Caracterização das Funções e Modelagem Matemática. A metodologia de investigação conta com as fases de elaboração do ambiente virtual CSCL para propiciar: discussão das dificuldades de aprendizagem das funções, discussão e elaboração de simuladores utilizando o software Modellus, exploração da modelagem como metodologia de ensino e aprendizagem, de forma colaborativa. A situação foi estruturada tendo como momento inicial uma instrumentalização dos softwares que suportam a comunicação e interação, além do software de modelagem que permite a exploração de situações envolvendo as funções afim e quadrática, em sintonia com as discussões das teorias da CSCL. O estudo analisa o trabalho colaborativo desenvolvido por 3 grupos de licenciandos em Matemática. Os dados revelam que o grupo menor conseguiu colaborar com mais facilidade que os grupos maiores. Os dados mostram também que as discussões acerca das dificuldades dos estudantes foi onde houve maior colaboração. Além disso, o script elaborado não conseguiu direcionar os participantes sozinhos durante a atividade, precisando sempre de uma intervenção do mediador. Também foram percebidos entraves do ambiente que mostraram a necessidade da montagem de outro espaço, que pudesse oferecer recursos que facilitem a comunicação entre os participantes da sessão. / This research aims to analyze collaborative learning supported by computer in the mathematics teachers trainning course in the use of modeling for teaching and learning functions. The research framework is based on Collaborative Learning with Computer Support (CSCL), Characterization of Functions and Mathematical Modeling. The research methodology includes the design of a colaborative learning environment, preparation of CSCL virtual environment to provide: discussion of the difficulties of learning functions, discussion and development of simulators using Modellus software, exploitation of modeling as a teaching and learning methodology, collaboratively. The situation was structured taking as a starting point the instrumentalization of software programmes, the one which supports communication and interaction and Modellus, the modeling software which allows the exploration of situations involving quadratic and affine functions, considering the discussions of CSCL theory. The study analyzes the collaborative work of three undergraduates groups of students. The data shows that the smaller group collaborated more easily than larger groups. The data also show that discussions about the difficulties of the students was where there was greater collaboration. In addition, the script written could not direct participants themselves during the activity, always in need of a mediator intervention. Also some environmental barriers were showed the need to rethink the virtual space, which could provide resources to facilitate communication between participants in the session.

Made available in DSpace on 2016-04-27T16:57:17Z (GMT). No. of bitstreams: 1 Joao Pereira Viana Filho.pdf: 1271947 bytes, checksum: 208d347d897241981c97d9a49aefc09d (MD5) Previous issue date: 2012-06-20 / This has been written to investigate possible contributions of Mathematical modeling to teaching functions on Basic Education. In order to do this, investigations were aimed on answering the main question in the research: what are the contributions from researches which use Mathematical modeling, and what possibilities and difficulties come from this teaching and learning methodology or strategy to introduce or teach functions on both Ensino Fundamental (in Brazil it is from 1st grade to 9th grade) and Médio (10th to 12th grade)? A meta-analysis has been developed for this, and, in this case, we understand it according to Fiorentini and Lorenzato s (2009) proposal: a systematic review of other researches aiming to make a critical evaluation about them, with the intention of making a documental study, to summarize ideas, investigate contributions, classify and find research categories, find similarities and point possible differences or peculiarities between research results. The analysis has been done by following Severino s (2002) guidelines to reading, analyzing and interpreting texts, and it was conducted on seven Master s Degrees produced in Brazil, which have approached the theme learning and teaching functions with Mathematical modeling. Five of those are Professionalizing Masters (Mestrado Profissionalizante) and two of them are Academic Masters (Mestrado Acadêmico). Three of them are focused on Ensino Fundamental and four of them are focused on Ensino Médio. Those researches were found in and selected from the CAPES abstracts database. On research results, we present our identification and classifying criteria: eight categories for conception of Mathematical modeling, eight ways this can contribute to function teaching, six types of possibilities and five types of difficulties found on implementation and development activities and actions in the classroom, and six types of possible contributions that Mathematical modeling, when adopted as a function teaching and learning methodology or strategy in Ensino Fundamental and Médio, can bring. The results from the search and analysis of the theses have also pointed to the necessity of more research on themes related to the approach of functions in Basic Education (Educação Básica, from Preschool to 9th grade), using Mathematical modeling; specially Doctoral degrees (Doutorados) / Este trabalho teve como objetivo investigar possíveis contribuições da modelagem matemática para o ensino de função na Educação Básica. Para atender tal objetivo, as investigações foram delineadas de forma a responder a questão de pesquisa: o que as pesquisas que utilizam a modelagem matemática em sala de aula, trazem como contribuição, e apontam como possibilidades e dificuldades do uso dessa metodologia ou estratégia de ensino e aprendizagem para introduzir ou ensinar função no Ensino Fundamental e Médio? Foi desenvolvida, para isso, uma metanálise que aqui é entendida, segundo propõem Fiorentini e Lorenzato (2009), como sendo uma revisão sistemática de outras pesquisas, visando realizar uma avaliação crítica sobre elas, quando se intenciona realizar um estudo de caráter documental, com o objetivo de sintetizar ideias, investigar contribuições, classificar e encontrar categorias de pesquisa, encontrar similaridades e apontar possíveis divergências ou particularidades entre resultados de pesquisas. A análise seguiu as diretrizes para a leitura, análise e interpretação de textos, propostas por Severino (2002) e foi feita sobre sete dissertações de mestrado produzidas no Brasil, as quais abordaram o tema ensino e aprendizagem de função com modelagem matemática. Dessas, cinco são de Mestrado Profissionalizante e duas de Mestrado Acadêmico, em que três delas dedicaram suas investigações ao Ensino Fundamental e quatro as dedicaram ao Ensino Médio. As pesquisas foram levantadas e selecionadas a partir do Banco de resumos da CAPES. Nos resultados de pesquisa, apresentamos, segundo nossos critérios de identificação e classificação: oito categorias de concepções de modelagem matemática, oito maneiras pelas quais pode contribuir para o ensino de função, seis tipos de possibilidades e cinco tipos de dificuldades encontradas na implementação e no desenvolvimento das atividades e das ações em sala de aula, além de seis tipos de possíveis contribuições que a modelagem matemática, quando adotada como uma metodologia ou estratégia de ensino e aprendizagem de função no Ensino Fundamental e Médio pode trazer. Os resultados da busca e análise dos trabalhos, apontaram, também, para a necessidade de mais pesquisas sobre temas relacionados à abordagem das funções na Educação Básica, por meio da modelagem matemática, em especial, de pesquisas de doutorado