THE LONGEST CHILDHOOD IS THAT OF CIVILIZATION REALIZING THAT IT CANNOT LIMIT THE IMAGINATION OF THE YOUNG.
"KNOWLEDGE IS NOT A LOOSELEAF NOTEBOOK OF FACTS. ABOVE ALL, IT IS A RESPONSIBILITY FOR THE INTEGRITY OF WHAT WE ARE. PRIMARILY OF WHAT WE ARE AS ETHICAL CREATURES...THE COMMONPLACE OF SCHOOLBOOKS OF TOMORROW IS THE ADVENTURE OF TODAY, AND THAT IS WHAT WE ARE ENGAGED IN."
J. BRONOSKI
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ENRICHMATH.COM
PUT THE PROPER SPIN ON HIGH SCHOOL MATHEMATICS
"...In a world in which illiteracy is the shame of societies where it is found, science illiteracy is increasingly disastrous. And wherever it is measured, this illiteracy rate is 90 to 95 percent...Can we modify our educational system so that all high school graduates emerge with a scientific way of thinking?...Galileo and his followers for the past 400 years have demonstrated how scientists must construct new intuitions in order to know how the world works.
But let us all realize that to change ways of thinking by students, we must first change the ways of thinking by teachers...For teachers who love children and who love teaching, it is still a major problemchanging culture is extraordinarily difficult..." This excerpt of an article by Leon Lederman titled "Science education and the future of humankind" ( p.36, Science News May 10, 2008) follows 12 years after his call ( in Discover magazine) for students to understand the concept of the scientific method and which I quote in the introduction. Math teachers can help in this quest by linking math and science.
The following excerpts from a lecture by Apostolos Doxiadis clearly describe the essence of the direction that I feel mathematics education must take in order to truly succeed. The enrichment of our curriculum that I developed over my 30 years of teaching and described in Mathematics and The Human Condition, along with the opportunities for students to write about mathematics can only serve to bring the subject to life and into their lives permanently.
'Mathematical narrative must enter the school curriculum, in both primary and secondary education. The aim is: a) to increase the appeal of the subject, b) to give it a sense of intellectual, historical and social relevance and a place in our culture, c) to give students a better sense of the scope of the field, beyond the necessarily limited technical mathematics that can be taught within the constraints of the school system... This is the meaning of paramathematics; this is the need for it: for a field, literally, on the side of mathematics... This will of necessity be cross and interdisciplinary, drawing on mathematics itself but also on logic, philosophy, epistemology, the history of ideas, cognitive psychology, sociology, anthropology, education theory. And, of course, mathematics education. Of paramathematics we require that it provide mathematics as we know it with context and thus meaning, extramathematical meaning and thus criteria, distance, clarity, bird's eye view, integration with thought, history and society... I believe that they point to a new and original way to look at mathematics itself. This is a crucial point to which I shall return, as it sets the basis for a nonformalist, nonPlatonist a view, a view of mathematics not as something pinned like a dead moth for Euclidean purists to examine — and in this form taught to our unprepared children —, but mathematics as it is lived by human beings, as it is loved, as it is explored, feared, created, dreamed of... By human beings. This new mathematical storytelling is inspired — in my view — by a rebel spirit. And I believe it is about time that this rebel spirit begin to infest mathematics education... If people were logical machines & education the equivalent of programming them, like computers, what I have to say would be irrelevant. Yet, as every teacher can tell us, these hypotheses don't apply. On the contrary, education is — should be, at its best — a process involving the complete human being. And as the wise always knew, and the philosopher — and also, incidentally, exmathematician — Edmund Husserl told us, human beings do not perceive passively, but with intention. We see more when we want to see more, we learn more when we are eager to learn more. Our cognitive processes are guided by our motives, our reasons for wishing to make sense of this world... Mathematical narrative must supplement and interact with technical mathematics teaching. But a substantial amount of time now given to technical mathematics — the only kind that is taught —, should, according to the age and the level of the students, be taken over by narrative mathematics. It is a certain fact that at least 90% of the students will forget at least 90% of the technical mathematics they are taught anyway, before the end of their education. So, use some of the time to make sure what they are taught sticks. Save time for narrative, use it to embed mathematics in the soul. Of course, if it is to come to fruition, both you, the specialists and researchers in mathematics education and we, the storytellers, have a daunting task. Even an experimental application of such a program, needs planning, hard work, both in the way of concrete research and in the preparation of the teaching material, in whatever form. This is not a case of going down to the level of the students, but changing the paradigm, to provide a worthy context for a great and glorious subject — and by this change all will profit, even the subject itself.
I ask you: Which are the best teachers? Those that love their students. Which are the best students? Those that love their subject. So, you should work on the love — this is where the problem lies. Embed mathematics in the soul by embedding it in history, by embedding it in story. By showing how it is lovely and adventurous — the stuff of the best quest myths. By showing how it was created by complex, adventurous, brave, struggling human beings. If you cannot teach or even show much of its beauty directly, for technical reasons, show it by showing the light it reflected on the faces of its discoverers.'
Doxiadis, Apostolos. Embedding Mathematics in the Soul: Narrative as a Force in Mathematics Education. Opening address to the Third Mediterranean Conference of Mathematics Education. Athens, January 3, 2003
Reference: http://www.apostolosdoxiadis.com/files/essays/embeddingmath.pdf
