7. About Current Teaching

I often think about how the true liberal attitude in the western world is becoming increasingly difficult. The basic knowledge of the civilizations that have preceded us begins to be outdated. Now it prevails over the acquisition of bits of information, from any source, together with speaking and writing without thinking and without assuming any responsibility, particularly in social networks. I am deeply concerned about current teaching both for the deterioration that I seem to see and for its inability to respond to the changes we are experiencing.

Unfortunately, I don’t speak by ear. For 50 years I taught, or tried to guide, students of all levels, from elementary to graduate, in three different countries. The last 31 years doing research and teaching at the graduate level in the United States. Over the years, I have had the opportunity to visit, and offer workshops and lectures as a visiting professor, and speak with professors from many countries around the world, while analyzing the basic teaching of mathematics, and seeing the resistance to carrying out changes that responded to the technological advances we were experiencing, as well as the positive results of research on the appropriate implementation of these in the classroom.

At a time when technology allows us, like never before, to increase our emphasis both on the development of analytical skills and on the use of exploration as a basis for problem solving – essential skills that are transferable to any other area of knowledge- we continue to insist on the teaching of algorithms as the fundamental nucleus of mathematics. Many teachers never learn that mathematics is the art of solving problems, discovering patterns, and making logical inferences. And unfortunately, no one can teach what they don’t know.

I should clarify that, for 20 years, I was part of the pioneering group that initially experimented with the integration of technology (initially the Casio 7000 and TI-81 calculators from the late 1980s) in the teaching of mathematics, and shared the results of our research, not only in publications and conferences, but also by providing several years training to different teams of teachers from around the world. To give you an idea, in the summer of 1995, we had about fifty teams from as many countries at Ohio State University. It seemed so obvious to us, and the statistical results backed us up, that if instead of only thinking algebraically, we also exposed our students to graphical and numerical thinking, their comprehension would improve drastically. Suffice it to say that many of the ideas we tested and proposed have not yet been implemented, to show how difficult it is to introduce changes in teaching.

My perception is that the teaching of the other basic areas of knowledge is not much better, although I admit that I rely only on what I observe and what I read. At a time when electronics facilitate access to information automatically, I do not conceive how, as far as I have observed, everything that is taught does not seem to have been reconsidered, both in content and in approach, to reestablish in the light of the new advances which should be not only the objectives but also the pillars that support each of the different disciplines as a basis for their teaching. I remember starting to ask that question in my lectures around 2010. I foresaw then that, with the content of the curriculum necessarily limited and the increasing number of relevant topics that technology makes accessible at all levels, we would eventually stop teaching part of the curriculum traditional content while incorporating innovative ideas and reconsidering the fundamental bases of each discipline. I certainly hoped that the usual and, in my opinion, excessive emphasis, given in mathematics to the mastery of algorithms and memorization, would be disappearing.

In the US, all I observed while I was active, was a curriculum that seemed to grow without limit and without particularly coherent changes. It was not easy to find answers to crucial questions such as:

1.    Who establishes the curriculum and what principles are
used to update it? Are real specialists on the subject?

2.    Are the positive results clearly established by educational
research, analyzed and integrated?

3.    When and how are the new proven innovative ideas
introduced?

4.    Are the new needs of industry, commerce, and society in
general considered in light of the changes of recent technologies?

5.  Who and at what level teaches the new methods, advances,
and content?

6.    What training is provided to teachers, both during
their studies and throughout their career?

7.    Is the education that students receive accurately assessed?
When problems are detected, how are they addressed?

8.    Do college professors receive any pedagogical training or
is it assumed that if knowing the content is enough properly teach it? Are they
keep abreast of new positive pedagogical research results on their subject?

The responses I heard to these questions were not encouraging, as they often did not come from staff with the necessary training to give them. Often it was the text authors who, little by little, in light of the comments that circulated, introduced some of the latest ideas in the basic courses of mathematics at the university level. To my surprise, the mathematical preparation of the university professors of pedagogy was oriented towards elementary and intermediate students, this together with the fact that the college professors of mathematics or of other disciplines, have not taken any pedagogical courses nor did they keep informed of the pedagogical research results, did not favor a coherent and updated teaching.

The problem that I point out is accentuated if we consider that Buckminster Fuller, creator of the curve that shows how long it takes for human knowledge to double, estimated in 2013 that, on average, human knowledge doubles every 13 months. At the same time, IBM predicted that year that the Internet would cause it to double every 12 hours. Considering this, it is difficult to understand that memorization, as a fundamental element of learning, continues to play a much greater role than reading, as well as the search and analysis of ideas in any discipline, followed by the development of the ability to coherently express what was found.

The reality is that less and less is being read and written. This, together with the fact that both the school demands and the respect for teachers and for the education of the mind and spirit seem to be decreasing dramatically, explains that the result of these approaches is a widespread lack of culture at all levels. As far as traditional culture is concerned, there is no depth at all, truly little is known about many historical, philosophical, and cultural ideas that used to be universally accepted as relevant, while many specialists, seem to know a lot about almost nothing.

If we add the above to the general lack of values, other than the economic one, we have conditions that facilitate the demagogy of a large part of the population. Freedom is confused with licentiousness, the social responsibilities that we all have are ignored, and the essential goal of the majority that strives is material wealth at all costs. From what I read, in some countries, many of those who do not work and are in good health also expect everything to be given to them.

As I am an optimist, I am confident that we are hitting rock bottom and that we will soon begin to recover, but I must confess that it is increasingly difficult for me to think like this.

Por Antonio R Quesada

A esta altura de mi vida reconozco que lo que creo saber es ínfimo comparado con lo que desconozco. Usando mis experiencias, trato de profundizar en algunas ideas espirituales básicas que comparto con toda humildad a fin de animar a otros a que hagan lo mismo. Agradezco de antemano cualquier sugerencia o corrección que reciba. ________________________________________________________________________________ At this time of my life, I acknowledge that what I think I know, is minimal compared to what I don’t know. Using my experiences, I try to deepen on some basic spiritual ideas that I share with all humility, with the purpose of encouraging others to do the same. I thank you in advance for any suggestions or corrections that I receive. ________________________________________________________________________________ Dr. Antonio R. Quesada, Professor Emeritus of Mathematics at The University of Akron. Ohio Teaching Fellow. Director of Project AMP. T^3 International Emeritus Professor.

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