Preparing Mathematics teachers for holistic education
Departamento de Matematicas
Facultad de Ciencias
Universidad de Los Andes
October 15, 2004
Among the new challenges in the teaching of Mathematics at basic and middle school levels, is certainly the requirement of integrating the subject with knowledge acquired in other subjects or fields of thought. This is an official requirement now in Venezuela, where the curriculum for the preparation of teachers of Mathematics has not yet included specific features that could enable teachers to respond adequately to this huge challenge.
In this work, we make a proposal for a curriculum, based on personal experience, in which the preparation of Mathematics teachers includes special training in artistic activities, mainly theatre, designed to meet specific goals such as improving teachers’ creativity and their physical as well as psychological preparation for the art of teaching Mathematics. Also, courses in History of Science , connected to the evolution of philosophical , religious and aesthetic ideas are included in this proposal. These courses would offer opportunities to reflect upon ways to use historical events in the presentation of certain mathematical topics to primary, middle or high school students and would stimulate the curiosity of the future teachers around the topic of History, which naturally connects different fields of knowledge and thus provides teachers with basic and solid tools for the holistic teaching they are expected to offer as professionals.
Preparing Mathematics teachers for holistic education
Departamento de Matematicas
Facultad de Ciencias
Universidad de Los Andes
October 15, 2004
Among the current curricular tendencies for Basic and Middle School Education, the proposal for an integrating approach of the different areas of knowledge is presented with and large consensus. In Venezuela, since several years, the official syllabi for Basic Education, in the first and second stage (ages between 7 and 12), are centered in the elaboration of “investigation projects” carried out by the students. Through these projects, it is expected that the students will acquire the skills and knowledge of diverse areas of the syllabus: Geography, History, Mathematics, Languages, Natural Sciences, etc. More recently, the same curricular model has been approved in Merida to be applied in the third stage of Basic Education (ages between 13 and 15).
The best intentions are behind the defense of the integrating curricular plan. However, the syllabi of the Schools of Mathematical Education in Venezuela, until now, do not include tools for confronting this new challenge. Success in carrying out a curriculum with such characteristics requires teachers with a genuinely integral education, very different to the one they currently receive. Those of us who are responsible for preparing the future teachers must take on the task of providing alternatives to the current curricular models and make special efforts for cultivating in our selves this holistic vision of knowledge that we expect to develop in our students.
Within this paper, some ideas about this situation are presented, with special emphasis on the areas of teacher preparation that should complement their specific mathematical and pedagogical knowledge. These ideas are product of many years of experience, as a student, as a researcher in pure Mathematics and more recently in Mathematics Education, teacher of pure Mathematics students, and Mathematics teachers in practice. Furthermore, mother of three children, singer and amateur directress of an early music choir. This experience has shown the potentialities of enrichment that these artistic activities, in this case, musical activities, and the fondness of History can contribute to the work of teaching Mathematics.
Beyond the need to respond to official requirements regarding the integration of different subjects of the syllabus, we may accept that the art of teaching requires, as any art does, of vocation, passion, devotion, a rigorous technical training and a holistic personal development that will allow the flourishing of creativity. It is true that some individuals are naturally endowed with personal gifts that make it unnecessary to look for ways to stimulate their creativity. But those who are not, and nevertheless choose teaching as a career, should be supported by the best resources that society may offer for their preparation. It is not enough to offer to future Mathematics teachers a solid preparation in undergraduate Mathematics and a detailed knowledge of the pedagogical theories that were developed in the 20th century. In Venezuela, at least, these are the two main fields of training for future Mathematics teachers.
The art of teaching requires well developed skills in the art of communicating. Teaching Mathematics particularly requires efforts to achieve the goal of making communication tend to communion of interests. The teacher must always revive his or her own love for mathematical knowledge and be able to express it, to make it evident in every contact with the students. Such as an actor would proceed, as he prepared for the interpretation of a role in a play .
The special effort that is required of the Mathematics teacher in this sense is maybe greater than for teachers in other fields of knowledge, because of the essentially abstract quality of its nature. A great dose of creativity is required to communicate Mathematics to young students effectively, especially if it is to be presented in connection to other subjects.
In the following, I will present the basic elements I believe should be included in the preparation of a Mathematics teacher, in order to allow him or her to cultivate sistematically these aspects which are complementary to the mathematical training.
Besides the knowledge of pedagogical theories that were developed in the 20th century and continue to rise in our days, the student who is getting prepared for teaching Mathematics must have some space for the reflection and group discussion about his or her own experience in learning undergraduate Mathematics. The aim is to create awareness of the nature of the difficulties that are inherent to the process of learning Mathematics, and possible ways of overcoming them. This awareness, coming from reflection upon experience differs greatly from encyclopedic knowledge of other researchers’ findings. In relation to this, Romulo Lins has done very interesting work recently . Furthermore, due to the deteriorated quality of the teaching of Mathematics in basic , middle and high school in Venezuela, today, the future Mathematics teacher in our country must have the opportunity to take courses where basic Arithmetic, Algebra and Geometry are revised, and pedagogical strategies specifically designed for teaching them are discussed. This will avoid having these teachers repeat the same mistakes that Mathematics teachers have been making for years.
In order to strengthen an integrating vision of knowledge, courses of History of scientific and technological ideas will be included, in connection to the mathematical ideas mainly, but also in connection to the evolution of religious and philosophical ideas, as well as of aesthetic tendencies in arts, architecture, literature and music. Since the goal is not to prepare a specialist in these disciplines, it is not convenient to focus on technical details in these courses. The main goal will be to cultivate the student’s curiosity and sensitivity towards the diversity of intellectual and artistic creations of human beings throughout History. In these courses also should be given the opportunities to recognize episodes of the History of Mathematics that can be used in the Mathematics classroom as a pedagogical resource, or as means for connecting to other fields of knowledge. In relation to this aspect of teacher preparation, the ideas of Man-keung Siu, Fung-kit Siu and Ngai-ying Wong are an excellent reference. 
Art workshops. Much has been said and written about the need to teach youngsters in such a way that they may develop their creativity. The failure to do so is due to many complex reasons, but most of them could be connected to one basic fact: teachers themselves do not cultivate their own creativity. The experience of learning an artistic discipline, well oriented towards the discovery or recovery of transcendental individual and collective values, tends to strengthen certain attitudes which are necessary for the creative process: intuition, self confidence, curiosity, expressive freedom and humility. Moreover, the artistic experience in non-competitive environments fosters self-esteem, and respect and care for others, as well as a joy for living, even under difficult circumstances. Since these are all qualities that enhance the teacher’s personality and youngsters are very sensitive to them, feeling naturally drawn to a person who shines in well- being, much care should be taken to cultivate them. The art workshops should be taken for two years. The first year, the student may choose from diverse options: literature, a musical instrument, singing, dance, theater, painting, etc. In the second year, the student must attend a theater workshop. Among the activities that should be developed, are the following:
Contact with master works of art, with access to relevant information in relation to the historical and aesthetic context in which the work was produced.
Basic, intermediate or advanced training , according to the student’s previous experience. Emphasis should be made in the introspective reflection of the student upon his learning experience. Also, some space for creative activities ( not just technical training) must be given, in order to make it possible for the student to explore, in a supportive environment, aspects of the psyche that are frequently hidden and have a powerful influence in daily performance . Again, the goal is to prepare a teacher who has a knowledge of the psychology of learning that is also based on experience, not only on encyclopedic resources. On the other hand, a special kind of creativity is very much needed in schools that are barely surviving in rural communities in many countries of the Third World. This kind of creativity for solving practical problems of a great diversity is also developed in artistic training, as a new idea is brought to life in spite of (and thanks to) practical difficulties.
The student will receive training in some of the basic technical elements of theatrical performance, such as vocal technique, body expression and other activities which reinforce mental concentration and physical wellbeing. Such practice may bring great benefits to the teacher in his daily practice, as the capacity to communicate grows in effectiveness with less physical strain. Vocal fatigue is common to many teachers and an adequate vocal technique may avoid it. On the other hand, it is a well accepted fact that a speech which is supported by a vital and natural body expression has a great power to attract attention. The best Mathematics teachers, whether consciously or not, play the role of the mathematician who discovers in awe, doubts, delights, makes efforts, questions himself and enjoys. Another aspect of the training that should be cultivated is the capacity to connect to the audience. It is necessary to become “ a real guide , instead of a fugitive”, in words of Gilbert Highet . Some seasons could be devoted to the study and performance of selected classical plays, others to plays by local authors and by the students. In this last group, one could suggest short plays freely based on the dispute between Newton and Leibniz, or the adversity of the professionals of the abacus towards the inevitable penetration of the hindu-arabic system of numeration in Europe. This kind of work would allow the students to internalize important aspects of the social and cultural environment in which these historical events occurred.
Expositions of mathematical topics would be done, incorporating the techniques learned, followed by a critical discussion among students . As in other activities mentioned here, written reports will be required, consisting of reflections upon the experiences . The practice of writing in order to express clearly and formally the student’s own ideas ( as opposed to writing about someone else’s ideas) is a very fruitful one. Good writing skills are very important means for organizing thought , and many schools of Mathematics teacher preparation do not emphasize the need to cultivate these skills, which is a sadly visible weakness in many venezuelan Mathematics teachers.
The difficult and indispensable art of teaching Mathematics creatively at the basic, middle and high school levels, must be trusted to individuals with very special and carefully cultivated characteristics. Part of the challenge of the teacher of Mathematics in our times is to prepare, on one hand, future mathematicians, engineers and technologists who are creative and have a developed sensitivity towards the social and human sciences and arts . On the other hand, to prepare the citizens not related professionally to Mathematics, but with well developed abilities to reason mathematically and an appreciation of Mathematics based on an enjoyable experience. In other words, to prepare individuals for their integral development as humans.
This responsibility, although shared by teachers in all other fields, is significantly important for Mathematics teachers to assume, since this discipline, because of its nature, creates the greatest and deepest divisions: capable and uncapable, lovers and haters, technical experts and complete ignorants prone to all kinds of manipulation in the name of the “holy” number.
The ideas presented here are being incorporated, with certain limitations due to the time available, in a curricular design that is being prepared for a three semester graduate program for Mathematics teachers. This program will be held in the Mathematics Department of the School of Sciences in Universidad de Los Andes, Mérida , Venezuela, in the near future.
 Highet, G. (1982). El Arte de Enseñar. Barcelona: Ediciones Paidós.
 Kline, M. (1985) Mathematics for the Nonmathematician. Dover
 Lins, R., Silva, A., Oliveira, V., Noriega, T. (2002) Of course R3 is blue! Developing an approach to turn a mathematics course into a mathematics education course. Proceedings of ICTM2.
 Porras, O. (2002) Old Ideas: A new tool for teaching basic Mathematics. Proceedings of ICTM2.
 Siu, F.K., Siu, M.K., Wong, N.Y. (1993) Changing times in Mathematics Education:The need of a scholar- teacher. Proceedings of the International Symposium on Curriculum changes for chinese communities in Southeast Asia: Challenges of the 21st century. The Chinese University of Hong Kong.