The Initial Stage of Teaching Proof in Mathematics Course

This article discusses techniques for organization of propaedeutic stage of teaching proof in mathematics course. It identifies types of tasks that allow students of 5–6 classes to form the ability to carry out simple proofs. This article describes each type of tasks features, it gives some examples.

A critical approach to reading comprehension in english: teaching intervention with group of teenagers at a non-formal education institution [recurso electr?nico]

The following paper is an action research made with a group of 6 teenagers aged 11-13 from the city of Cali. The project was carried out at a non-formal education institution and basically describes the process of a teaching intervention in which the concepts of Critical Pedagogy and Task-Based Learning were the protagonists. The results show first, that students really need to feel motivated in order to accept a critical approach; second, that the role of the teacher in the achievement of the objectives is extremely relevant; it is necessary for them to have a critical perspective before working on this field besides the constant seeking of information in order to innovate in their classes; third, that the TBL (Task Based Learning) and the critical pedagogy are processes that need some time in order to bear fruits; and fourth, that a needs analysis is essential for the quality of the intervention.

Learning strategies implemented by the students of Advanced Intensive English I courses for improving oral discourse in the Bachelor of Arts in English Teaching, Department of Foreign Languages, University of El Salvador, year 2014.

There are many learning strategies some, more successful than others when they are applied in a correct way. “Strategies are most successful when they are implemented in a system that encourages collaboration among staff and students, and in which each is a part of a well-planned whole system” (Johns Hopkins, 2000). Additionally, Learning strategies have become an effective instrument in the field of education because students can make use of several strategies in order to enhance their English level in terms of communication. To communicate in a meaningful way, it is important to express ideas inside and outside the classroom; it is part of the development and improvement of speaking.

The teaching of reading English in a foreign language in Libyan universities: methods and models

This study focuses on the learning and teaching of Reading in English as a Foreign Language (REFL), in Libya. The study draws on an action research process in which I sought to look critically at students and teachers of English as a Foreign Language (EFL) in Libya as they learned and taught REFL in four Libyan research sites. The Libyan EFL educational system is influenced by two main factors: the method of teaching the Holy-Quran and the long-time ban on teaching EFL by the former Libyan regime under Muammar Gaddafi. Both of these factors have affected the learning and teaching of REFL and I outline these contextual factors in the first chapter of the thesis. This investigation, and the exploration of the challenges that Libyan university students encounter in their REFL, is supported by attention to reading models. These models helped to provide an analytical framework and starting point for understanding the many processes involved in reading for meaning and in reading to satisfy teacher instructions. The theoretical framework I adopted was based, mainly and initially, on top-down, bottom-up, interactive and compensatory interactive models. I drew on these models with a view to understanding whether and how the processes of reading described in the models could be applied to the reading of EFL students and whether these models could help me to better understand what was going on in REFL. The diagnosis stage of the study provided initial data collected from four Libyan research sites with research tools including video-recorded classroom observations, semi-structured interviews with teachers before and after lesson observation, and think-aloud protocols (TAPs) with 24 students (six from each university) in which I examined their REFL reading behaviours and strategies. This stage indicated that the majority of students shared behaviours such as reading aloud, reading each word in the text, articulating the phonemes and syllables of words, or skipping words if they could not pronounce them. Overall this first stage indicated that alternative methods of teaching REFL were needed in order to encourage ‘reading for meaning’ that might be based on strategies related to eventual interactive reading models adapted for REFL. The second phase of this research project was an Intervention Phase involving two team-teaching sessions in one of the four stage one universities. In each session, I worked with the teacher of one group to introduce an alternative method of REFL. This method was based on teaching different reading strategies to encourage the students to work towards an eventual interactive way of reading for meaning. A focus group discussion and TAPs followed the lessons with six students in order to discuss the 'new' method. Next were two video-recorded classroom observations which were followed by an audio-recorded discussion with the teacher about these methods. Finally, I conducted a Skype interview with the class teacher at the end of the semester to discuss any changes he had made in his teaching or had observed in his students' reading with respect to reading behaviour strategies, and reactions and performance of the students as he continued to use the 'new' method. The results of the intervention stage indicate that the teacher, perhaps not surprisingly, can play an important role in adding to students’ knowledge and confidence and in improving their REFL strategies. For example, after the intervention stage, students began to think about the title, and to use their own background knowledge to comprehend the text. The students employed, also, linguistic strategies such as decoding and, above all, the students abandoned the behaviour of reading for pronunciation in favour of reading for meaning. Despite the apparent efficacy of the alternative method, there are, inevitably, limitations related to the small-scale nature of the study and the time I had available to conduct the research. There are challenges, too, related to the students’ first language, the idiosyncrasies of the English language, the teacher training and continuing professional development of teachers, and the continuing political instability of Libya. The students’ lack of vocabulary and their difficulties with grammatical functions such as phrasal and prepositional verbs, forms which do not exist in Arabic, mean that REFL will always be challenging. Given such constraints, the ‘new’ methods I trialled and propose for adoption can only go so far in addressing students’ difficulties in REFL. Overall, the study indicates that the Libyan educational system is underdeveloped and under resourced with respect to REFL. My data indicates that the teacher participants have received little to no professional developmental that could help them improve their teaching in REFL and skills in teaching EFL. These circumstances, along with the perennial problem of large but varying class sizes; student, teacher and assessment expectations; and limited and often poor quality resources, affect the way EFL students learn to read in English. Against this background, the thesis concludes by offering tentative conclusions; reflections on the study, including a discussion of its limitations, and possible recommendations designed to improve REFL learning and teaching in Libyan universities.

Strategies to Promote Research and Logical Reasoning in the Teaching of Mathematics in the Schools

The purpose of this paper is to raise a debate on the urgent need for teachers to generate innovative situations in the teaching-learning process, in the field of Mathematics, as a way for students to develop logical reasoning and research skills applicable to everyday situations. It includes some statistical data and possible reasons for the poor performance and dissatisfaction of students towards Mathematics. Since teachers are called to offer meaningful and functional learning experiences to students, in order to promote the pleasure of learning, teacher training should include experiences that can be put into practice by teachers in the education centers. This paper includes a work proposal for Mathematics Teaching to generate discussion, curiosity and logical reasoning in students, together with the Mathematical problem solving study.

Teaching mathematics using Massive Open Online Courses

Distance learning - where students take courses (attend classes, get activities and other sort of learning materials) while being physically separated from their instructors, for larger part of the course duration - is far from being a “new event”. Since the middle of the nineteenth century, this has been done through Radio, Mail and TV, taking advantage of the full educational potential that these media resources had to offer at the time. However, in recent times we have, at our complete disposal, the “magic wonder” of communication and globalization - the Internet. Taking advantage of a whole new set of educational opportunities, with a more or less unselfish “look” to economic interests, focusing its concern on a larger and collective “welfare”, contributing to the development of a more “equitable” world, with regard to educational opportunities, the Massive Open Online Courses (MOOCs) were born and have become an important feature of the higher education in recent years. Many people have been talking about MOOCs as a potential educational revolution, which has arrived from North America, still growing and spreading, referring to its benefits and/or disadvantages. The Polytechnic Institute of Porto, also known as IPP, is a Higher Education Portuguese institution providing undergraduate and graduate studies, which has a solid history of online education and innovation through the use of technology, and it has been particularly interested and focused on MOOC developments, based on an open educational policy in order to try to implement some differentiated learning strategies to its actual students and as a way to attract future ones. Therefore, in July 2014, IPP launched the first Math MOOC on its own platform. This paper describes the requirements, the resulting design and implementation of a mathematics MOOC, which was essentially addressed to three target populations: - pre-college students or individuals wishing to update their Math skills or that need to prepare for the National Exam of Mathematics; - Higher Education students who have not attended in High School, this subject, and who feel the need to acquire basic knowledge about some of the topics covered; - High School Teachers who may use these resources with their students allowing them to develop teaching methodologies like "Flipped Classroom” (available at http://www.opened.ipp.pt/). The MOOC was developed in partnership with several professors from several schools from IPP, gathering different math competences and backgrounds to create and put to work different activities such video lectures and quizzes. We will also try to briefly discuss the advertising strategy being developed to promote this MOOC, since it is not offered through a main MOOC portal, such as Coursera or Udacity.

Interference of Native Language in English Language Acquisition in Santa Cruz and Calheta Secondary schools

This study analyzes the interference of native language when students are learning a foreign language, in this case English. According to this study, interferences from the native language such as lexical-semantic and phonological are not infrequent. It is one of the main barriers that create difficulties when learning English. The outcome of this study is presented at the end of the Monografia: to provide English-language teachers and students the most significant linguistic interferences that occur during the learning process of English language. Furthermore, some teaching strategies are discussed to avoid the biases that appear due to the interferences of the native language. As a result of this study, I hope to contribute to the learning success among English-language students.

Students’ viewpoint on engineering subjects taught in English

The European Educational Institutions have the challenge and the commitment to enhance multilingual competence and teaching curricular subjects in a foreign language is seen as one of the most promising alternatives. In that context, professors teaching different engineering subjects at the School of Engineering of the UPC at Manresa (EPSEM) have been involved in projects aiming at analyzing the current linguistic situation and developing some on-line open access materials using CLIL as a strategy. They formed the u-Linguatech Research Group on Multilingual Communication in Science and Technology in order to provide such resources in an effective and efficient way. In this paper, we focus on students’ perception of the improvement of their multilingual competence throughout their Engineering degree, by means of subjects taught in English by non-native speakers. Data about the English level of current students are taken into account. We also describe the use of the above resources to improve the quality of subjects learning related to Chemical Engineering curricula.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Teaching and learning english : a guide to recent research and its applications.

Es una síntesis de investigaciones recientes sobre la enseñanza y el aprendizaje del inglés en la enseñanza primaria y secundaria en Gran Bretaña. Incluye un capítulo sobre el significado de la lengua inglesa en la escuela contemporánea, además de otros capítulos sobre conversación y comprensión, escritura, lectura, enseñanza de la literatura, la relación del lenguaje verbal con las imágenes fijas y en movimiento, y tecnologías de la información y la comunicación (ICT) e inglés y alfabetización.

Teaching mathematics creatively.

Texto que promueve la creatividad como elemento clave para el desarrollo del conocimiento, la comprensión y el disfrute de las matemáticas en la enseñanza primaria. Ofrece una gama de estrategias: contar historias , aprender las matemáticas al aire libre, trabajar con una escala mayor, la música, problemas de investigación y resolución de problemas, que permitan a los profesores a adoptar un enfoque lúdico en la enseñanza de esta materia.

Techniques and principles in language teaching.

Esta obra da una visión práctica de las diferentes metodologías y las recientes innovaciones en la enseñanza de idiomas. Ofrece, paso a paso, instrucciones prácticas, nuevos enfoques e ideas de enseñanza para los profesores con menos experiencia.

Attitudes to reading in English primary schools

This article reports on a two-year research project investigating attitudes to reading held by teachers and pupils in a sample of English primary schools. The project draws on international and national surveys of reading engagement and the findings of previous research, but seeks to provide more detailed data relating to the attitudes of individual children and the strategies used by individual schools and teachers whose pupils demonstrate positive attitudes to reading. Written questionnaires for teachers and pupils and oral interviews with teachers are used, generating both quantitative and qualitative data. Results are related to previous research literature in this area which shows a link between reading motivation and attainment, and to motivational theory. In conclusion, it is argued that teaching strategies which promote positive attitudes to reading need to be used alongside the teaching of reading skills in any effort to raise attainment.