My carreer as a professor of Mathematics started early with my graduation and has been active until today. I have experienced several levels of Education that permit me a wide angle on the innovative approaches and techniques. I present bellow my teaching statement according to this.
1. Experience. I have been a teacher of Mathematics at several levels of Education, from Middle School to Graduate level. In the summer semester of 2012 I taught, in Slovene language, a course of Probability and Statistics at the Computer Science Faculty of the University of Ljubljana, under Aleksander Jurišič. Between 2010 and 2012 I was pedagogical collaborator and erasmus tutor at the Faculty of Mathematics also at the University of Ljubljana, under Jaka Čimprič and Sergio Cabello. During this period I have been successfully assisting students enrolled in this exchange program. While I was in Portugal I have been a teacher of Mathematics at Escola Secundária de Bocage, in Setúbal. During two school years I have teached on the several levels of high school education, being involved mostly with pedagogical and organizational tasks as well as related european projects. This teaching time was a natural consequence of my graduation in education of mathematics where I achieved pedagogical skills of great quality. Right after my graduation I was invited to take the responsibility over the module of Mathematics for the graduation of Multimedia at Escola Técnica de Comunicação e Imagem, in Lisbon, to which I prepared the learning program, notes and exams under Sandra Pinheiro. While I still was an undergraduate student of Mathematics, I was invited by the coordinator of this course, Teresa Almada, to assist her on several Algebra and Algebraic Topology courses at Universidade Lusofona, in Lisbon. I participated on the preparation of several lectures and exams, was responsible for all the exercises of those courses, the reinforcement of weaker students and the correction of exams. I also have been involved with several professional mathematics teachers associations. Since 2012 I have been a collaborator of Mathema, the Slovenian Institute for promotion of Mathematics, under Mateja Budin. Between 2005 and 2007 I was a collaborator of Project Gripenet, at Instituto Gulbenkian de Ciencia, a multidisciplinary science project that aimed to construct a forecast for the virus of flu in Portugal with international collaborators. It was closely related with high schools and teachers for whom educational materials were produced. I am also a certified teachers trainer with experience in the area, having prepared courses for teachers on Experimental Mathematics. In this context I collaborated with the Portuguese Mathematics Teacher’s Association and with the teachers training center of Seixal, collaborating at the present time with CREF Education, in Sesimbra, Portugal.
2. Methodology. Research activities in the classroom have taken in recent years, a fundamental role in view of the profound changes in the curricula of mathematics that points for innovation in the purposes and objectives, contents and methodologies, and evaluation of teaching and learning. In that it allows the exchange of ideas between students, as well as exploration of tasks and materials in the classroom, the implementation of exploration activities within an innovative curriculum perspective. Knowledges are constructed from experience, the reflection and evidence, gradually deducting up to intuition. The focus is communication and research, and not only for getting routine tasks. In short, it is, also, to tailor schooling to the evolution of society. However, often the space management, educational materials and resources in schools and universities is not the most appropriate. Still prevails space at the math class, only with tables, chairs and chalkboard, in the traditional way, and (not always) an overhead projector. Increasingly asserts its importance, these days, feature new technologies at all levels of education. With the introduction and right exploration of IT resources, conditions are created so that each, in its own way, take advantage of the best tools available for the benefit of students and their learning in the classroom. The use of technology, although recommended in all levels of education, is still also embryonic. The need to find connections and produce tasks to apply to classroom encourages the use of new technologies and manipulatives, a universe of interdisciplinarity, standardizing and optimizing the various material resources. The Moodle platform and other such resources are essential tools in the process of teaching and learning at a distance, as shown by Coursera, maximizing the advantages of using this together with other tools of dynamic geometry as Geometer's Sketchpad or similar. Not only allows the creation of multiple workspaces, discussion forums and conducting small ratings, and also facilitates the exchange among students towards their own development.
3. Vision. The Mathematics Education must contribute to developing advanced aspects of mathematical training of students as the aptitude to formulate and solve problems or to make and test conjectures. The objectives to achieve this can not be confined to the acquisition of knowledge, but should cover the development of capabilities/skills and attitudes/values. The school mathematics can take this challenge if it is able to operate a significant change in the nature of the activities that have been dominant in the classroom. It is necessary to provide students with experience in appropriate activities. Research has revealed that the acquisition of knowledge, so by itself, as well as the domain of simple techniques of calculation, do not guarantee recognition of its applicability in new situations. Mathematical investigations (such as with the problem-solving activities) involve complex processes of thought and require the involvement and creativity of the students, but are characterized as being from statements and objectives and vague structured and require that students define the purpose, conduct experiments, formulate and test conjectures. As the mathematician George Cantor once said, "the art of proposing a question must be held of higher value than solving it".