It is very unlikely to see at Czech high school in mathematics classes teaching the hyperbolic functions and their inverses. It's a pity, this could be a great opportunity to review and refresh the polynomial, rational, trigonometric and exponential function methods and skills. These functions even set an implicit connection between the exponential and gonio- metric functions, too. The aim of this thesis is to offer an alternative to the usual practice at the ordinary high schools and it is adopted to a limited schooling time available. Our approach has been successfully tested with a group of students at a small high school in the Czech borderland. The thesis also indicates the potential to expand this approach if more schooling time should have been available or more talented students should have been involved.

Made available in DSpace on 2016-06-02T20:29:20Z (GMT). No. of bitstreams: 1 5025.pdf: 1567249 bytes, checksum: c76630986519740d1567022a92b5cf1a (MD5) Previous issue date: 2013-03-28 / Functions represent a very important area of study in mathematics due their wide range of applications in many areas of knowledge. Functions can be approached in concrete and meaningful ways. However, school textbooks often tend to an algebraization of the theme, which hinders students' understanding of the need and importance of studying functions. This work does not focus on formal definitions involved in the teaching of functions. The aim of this work is to present an experiment which allows the development of the concept of functions. The experiment is based on a proposed problem of building a box without a lid using a rectangular sheet of paper, and then calculating its volume. This experiment was carried out in two 8th year classes of a public school in Ribeirao Preto - SP, Brazil. The procedure was carried out successfully and students enjoyed it. This is a low-cost, practical project, feasible to any teacher willing to approach the theme in a practical way. / As funções representam uma parte muito importante da Matemática devido à grande possibilidade de aplicações em diversas áreas do conhecimento. Este conteúdo pode ser abordado de forma concreta e significativa, mas o que observamos, principalmente nos livros didáticos, é que existe uma grande preocupação em algebrizar este assunto. Este processo faz com que os alunos não compreendam a necessidade e a utilidade do estudo das funções. Nosso trabalho não tem o foco nas definições formais que estão envolvidas ao se ensinar funções. O objetivo principal deste trabalho é apresentar um experimento que possibilite iniciar o desenvolvimento do conceito de funções. O experimento usa como base o problema de construir uma caixa sem tampa a partir de uma folha de papel retangular, e de calcular seu volume. Este experimento foi aplicado em duas oitavas séries de uma escola da Rede Municipal de Ensino de Ribeirão Preto. A aplicação ocorreu sem complicações e os alunos gostaram de participar desta aula. É um projeto que não exige muitos recursos materiais e que pode ser usados por todos os professores que pretendam abordar o tema de forma prática.

在台灣，由於中學英語課程的設計大都是考試導向，教學過程中幾乎完全著重於語言形式的教導，而忽略語言使用功能的重要性，所以台灣的英語學習者在中學階段很少有機會接受語言功能教學。本研究主要是要調查間接性以及禮貌性這兩個語用功能對於邀請句式選擇的適當性是否有所影響，進而調查語言功能教學對於本國的中學生學習英語的可行性與成效性。 本研究先分析了20位美國人在間接性與禮貌性的考量之下，對邀請句式的選擇為何，以便建立美國文化在這方面的規範。然後，再以此規範，設計一套四個單元的語言功能教學課程。有135位來自台灣北部兩所高中的高一學生接受了這項課程。這兩所學校的基測成績高低不同；每間學校各有兩班學生分別接受以功能為主的教學和以結構為主的教學。 前測及後測的結果顯示語言功能教學有效地改善了台灣學生的語言功能表現。再者，語言形式選擇的適當性的確受制於間接性及禮貌性的宰制。此外，情態策略也被驗証比直接策略及暗示策略要來得困難及複雜許多。又，基測成績較高的學校的學生比基測成績較低的學校的學生在學習語言功能的過程中表現較好。整體而言，實驗結果顯示，對於以英語為外國語的學生而言，語言功能教學是有效的、可行的，也是必須的。 另外，雖然台灣學生較偏好結構為主的教學法，但是本研究發現功能為主的教學法比結構為主的教學法成效較佳。最後，從學生對於本課程的評量得知，雖然學生們覺得語言功能學習法不是很有趣，但是他們大多認為這樣的教學方法對學習英語是有幫助的，而且是重要的。 / EFL learners in Taiwan are hardly taught language functions in high schools since most of the English courses are designed in accordance with the examination-oriented goal, which is far more focused on teaching language form than on teaching language use. The purpose of the present study is to investigate whether indirectness and politeness would influence appropriate linguistic choice for invitation, and to investigate the effectiveness of teaching language functions to high school students in EFL classrooms. In this study, 20 American subjects’ ratings of eight linguistic forms for invitation by indirectness and politeness were analyzed to obtain the American norm, based on which a four-unit program of teaching language functions was designed. 138 senior high school students from two senior high schools in northern Taiwan took a pre-test before receiving the instruction and a post-test afterwards. Two classes from each school received function-based teaching method and structure-based teaching method respectively. The results of the pre-test and the post-test, in comparison with the American norm, indicate that teaching language functions is effective in improving Chinese students’ competence of the functional aspect of English. Next, the test results verify that the appropriate choice of linguistic forms is indeed influenced by politeness and indirectness, although these two functional factors are not in a systematic relationship. Moreover, Modality strategy is found to be more difficult and more complex than Direct strategy and Hinting strategy. In addition, although the students from the school of high BCT scores tend to perform better than those from the school of low BCT scores, students of both schools made significant improvement in learning the concepts of indirectness and politeness. The findings given above imply that teaching language functions to high school students in EFL classrooms is feasible, necessary, and effective. In addition, according to the results of the general evaluations to this teaching program offered by the students and the English teachers involved, although the Taiwanese students showed preference to structure-based method, function-based method is verified to be more effective. In conclusion, the students’ and the teachers’ evaluations of this program indicate that learning language functions may not be interesting, but it is helpful and important to the students.