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- The role performed by the teacher’s question in the learning of quadratic function in an exploratory mathemPublication . Silva, Anaís Veloso; Viseu, Floriano; Menezes, LuísCommunication plays a key role in teaching and learning processes. Questions are a communicational act greatly used by teachers to structure their discourse, establish dynamics, and foster interaction between the different participants in the classroom. In view of these potentialities of questions in the classroom context, we have developed a teaching experiment with the aim of understand the role of the teacher's question in the learning of topics on functions. Considering the nature of this aim, a methodology of qualitative and interpretative nature was used. The data collection was based on the students’ written productions and on the audio and video recordings of a mathematics class of a Grade 10 educational group (in northern Portugal). Data analysis is based on content analysis techniques, crossing collected data and categories emerging from the literature. The study revealed that the teacher’s questions alternated between confirmation, focalization, and inquiry, with inquiry prevailing. Questions aimed at testing the student’s knowledge gave both the teacher and actual student important information. Questions that focused the student’s attention on a particular detail enabled the students to organize their reasoning and structure their answer. Questions that required the students to explain or justify their thoughts were those that proved to most contribute to the development of the student’s reasoning process.
- Humour in mathematics teaching: A study in Portugal and SpainPublication . Menezes, Luís; Viseu, Floriano; Flores, Pablo; Amante, Susana; Costa Lopes, Ana MariaThis study analyses humour in a school context in Portugal and Spain. The study aims to respond to the following questions: (1) Do mathematics teachers consider that they have a sense of humour? (2) What conception do they have of humour? (3) Do they consider humour to be compatible with the teaching of mathematics? and (4) If teachers use humour in the teaching of mathematics, how do they use it and for what purpose? To carry out this study, we adopted a mixed methodology. Mathematics teachers, Portuguese and Spanish, teaching from primary school level to higher education, were asked to respond to a questionnaire, comprising open and closed questions. Data analysis combines statistical with content analysis. The main results reveal that most teachers claim they appreciate/value humour and acknowledge its educational relevance. Most teachers claim they use it regularly and present examples of its use. These examples show small differences between Portuguese and Spanish teachers.
- El humor en clases de matemática puede ser cosa seria?Publication . Menezes, Luís; Flores, Pablo; Balula, João Paulo; Ribeiro, António Augusto Gaspar; Gomes, Helena Margarida dos Santos Vasconcelos; martins, ana patrícia; Oliveira, A. M.; Delplancq, Véronique; Matos, Isabel Aires de; Viseu, Floriano; Guitart, MónicaEn este texto presentamos algún trabajo desarrollado en el proyecto HUMAT (Humor in Mathematics Teaching) que se inició con la pregunta que sirve de título a este póster: ¿el humor en clases de matemáticas puede ser cosa seria? Para responder a esta pregunta, se definieron líneas de acción: (1) Conocer el uso que los profesores hacen del humor para enseñar matemáticas; (2) Desarrollar recursos didácticos, en forma de tareas matemáticas, basadas en humor gráfico; y (3) Comprender el impacto en el aprendizaje de las Matemáticas del empleo de tareas matemáticas basadas en humor gráfico. En este póster presentamos algunos de los principales resultados ya obtenidos de los dos primeros.
- Humor in mathematics teaching: tasks for the classroomPublication . Menezes, Luís; Gomes, Helena Margarida dos Santos Vasconcelos; Ribeiro, António Augusto Gaspar; martins, ana patrícia; Flores, Pablo; Viseu, Floriano; Oliveira, Ana Maria; Matos, Isabel Aires de; Balula, João Paulo; Delplancq, VéroniqueThis book, Humour in Mathematics Teaching: tasks for the classroom, is a corollary of HUMAT Research Project (Humour in Mathematics Teaching), developed by the Higher School of Education of Viseu (Portugal), in partnership with the University of Minho (Portugal), the University of Granada (Spain) and the University of Mendoza (Argentina), with the support of the Polytechnic Institute of Viseu (Portugal) and of the CI&DETS. The project rests upon two fundamental assumptions. On the one hand, it assumes that humour plays a crucial role in creating a learning environment that can boost the students’ motivation and encourage them to learn mathematics. On the other hand, it assumes that the understanding of humour and the learning of Mathematics are two activities that require a good reasoning capacity. It also recognises that the inquiry-based mathematics teaching, grounded on the work of the students leading to the completion of challenging mathematical tasks, provides a high potential for learning. All those considerations led to the birth of this book that offers mathematical tasks with a humorous twist and whose main goal is to fulfil these two functions: to persuade students to learn and make them think about humorous situations that involve mathematical concepts. To achieve this goal, the book is organised into two sections. The first is devoted to a brief introduction to the concept of humour and the other concepts that are associated to it approaches the concept initially in a broader sense, then focusing on the teaching of Mathematics. The largest section of the book, the second, is devoted to the presentation of mathematical tasks that are based on panels or comic strips involving humorous and witty content.
- Formulação de problemas matemáticos na aprendizagem de números racionais por alunos do 4.º ano de escolaridadePublication . Martins, Bibiana; Viseu, Floriano; Menezes, LuísIn many countries, as in Portugal, Mathematics syllabus at different levels of education highlight problem solving, in some cases as a teaching strategy and in others as a mathematical ability to be developed by students. In addition to this activity, problem posing arises, which has deserved less attention at the level of curricular recommendations, although it may constitute a strategy for deepening mathematical concepts and developing the understanding of procedures. While in problem solving the student has to answer questions, in problem posing the student is challenged to contextualize situations using his language, knowledge and experiences. The formative potentialities of problem posing have led us to investigate how students in the fourth grade use and deepen their mathematical knowledge about non-negative rational numbers in that mathematical activity. In particular, we aim to know what kind of problems students formulate, the strategies of problem solving that they value and the traces of creativity that they identify in this activity. Given the nature of the objective, a qualitative and interpretative methodology was adopted. The collection of data is based on the collection of the written productions of students and the application of a questionnaire. The study reveals that students tend to formulate problems similar to the ones in school textbooks. In this formulation, students use the mathematical concepts relating to the non-negative rational numbers they have learned, creating, in most cases, plausible contexts. The study also reveals that students value the structure, the imagination, the originality, the playfulness and the degree of difficulty as traces of creativity in problem posing.
- Olhares dos professores sobre o valor pedagógico do humor para ensinar MatemáticaPublication . Menezes, Luís; Viseu, Floriano; Flores, PabloThis study focuses on teachers' perspectives on humor to teach mathematics. In particular, it seeks to answer the questions: What happens at school with humor, specifically in the teaching of mathematics? Do teachers consider that they have a sense of humor and appreciate the sense of humor in others? Do teachers recognize the educational value of humor in teaching and learning mathematics? What functions do they associate with instructional humor and what didactical knowledge do they reveal in their justification? To answer these questions, a questionnaire, with open and closed questions, was constructed and applied. The data collected from 601 Portuguese mathematics teachers, at all levels of education, reveals that teachers consider that they have a sense of humor and appreciate it in others, recognize the pedagogical value of humor to teach mathematics, and say they use, regularly, the humor to teach. Invited to comment on a humorous strip about Mathematics, they manifest their didactic potential, highlighting their cognitive function, but also the affective and communicative. In the justification of their options they reveal didactic knowledge regarding Mathematics, combined with the knowledge of the practice.
- Humor para aprender Matemática: Tarefas matemáticas para rir e aprenderPublication . Menezes, Luís; Flores, Pablo; Viseu, Floriano; Gomes, Helena Margarida dos Santos Vasconcelos; Ribeiro, António Augusto Gaspar; martins, ana patríciaA boa disposição e o bem-estar facilitam o trabalho e a aprendizagem. O humor tem essa particularidade, de bem-dispor e fazer rir as pessoas, aliviando situações de stress e facilitando a comunicação. De entre as diversas formas de humor, o humor gráfico, baseado em tiras e cartoons, tem larga difusão em revistas, nos jornais e na internet. No projeto HUMAT: Humor no ensino da Matemática criámos um conjunto de tarefas matemáticas baseadas em diversas situações de humor gráfico que estão disponíveis na internet e em revistas, de diversos autores, e que incidem sobre vários conteúdos matemáticos, que são trabalhados em diversos anos de escolaridade. Este é, portanto, um livro destinado a alunos, tendo como objetivo apoiar a aprendizagem da Matemática, tanto em contextos de sala de aula como extra sala de aula, de uma forma bem-disposta. Em todas as tarefas deste livro, apresentamos uma tira ou um cartoon e colocamos, a propósito dela, um conjunto de questões que estimulam o pensamento matemático dos alunos, ao mesmo tempo que, esperamos, despertem momentos de boa disposição. Em todas as tarefas, a questão inicial procura levar os alunos a descrever a situação e a apreciar o humor nela presente. Para apoiar a resposta a esta questão, propomos o seguinte roteiro, focado em quatro pontos: Ambiente (em que contexto/cenário ocorrem os eventos? quais são os elementos do desenho que nos fazem identificar esse cenário?); Sujeitos (quem são os personagens? o que se sabe sobre eles? o que representam?); Ação (o que acontece?); Choque de expectativas/final inesperado (o que causa humor? qual é a circunstância que torna a situação engraçada?). Para além das tarefas se dirigirem a diferentes anos de escolaridade e de versarem conteúdos matemáticos diversos, têm também uma duração estimada diferenciada. Algumas são curtas, outras são mais longas. Em todos os casos, esperamos que delas resulte um texto escrito. Podendo ser realizadas individualmente ou em grupo, podem depois ser partilhadas e discutidas as suas resoluções. O projeto HUMAT tem um site onde se podem partilhar as resoluções produzidas em sala de aula ou fora dela.