The Pedagogical Work of Puig Adam

At the Centennial commemoration of the birth of Don Pedro Puig Adam, held at the Spanish Royal Academy of Sciences on 7 June 2000, Joaquín Hernández Gómez delivered the address 'The Pedagogical Work of Puig Adam', a version of which we give below:


Members of the Academy, Ladies and Gentlemen,

Although the feeling that prevails in me at the moment is a certain bewilderment, that of an Institute professor talking from a rostrum to renowned scientists, I must not fail to show my gratitude, first to the Academy of Sciences that provides this incomparable framework for this event, and secondly to the lecturers who have spoken and will speak at this rostrum who have allowed me to address the pedagogical work of Puig Adam, all of us, they and I, aware that any one of them could contribute more, and above all much better, than I in this aspect. Be that as it may, in any case, I will try to make the figure of my political grandfather better known from this year 2000, the centenary of his birth.

A little more than fifteen years ago, in this building and possibly in this same place, an eminent scientist, now unfortunately no longer with us, Professor Mariano Yela, professor of Psychology and member of the Academy of Moral and Political Sciences, delivered a speech from which, because of its beauty and emotion, I would like to extract the following paragraph:

We are in 1940. In a cold and shabby classroom of the San Isidro Institute, a hundred boys of the sixth grade are waiting for our first class on Mathematics. Don Pedro enters ... and you can see, behind his glasses, the sparkling, ingenious, welcoming, naive, almost childlike look.

The class starts. First surprise: Don Pedro does not explain anything, he does not write any formula on the board. He talks to us as an older friend. He asks several of us what is Mathematics. He asks someone to collect together and summarize the answers. Others review and discuss them. Little by little, the class is encouraged; we all intervene. We forget that we are in class, we joyfully think. Suddenly Don Pedro launches a surprising question: Do you think that there are two Spaniards with the same number of hairs on their heads? We all want to talk. We do not think so; some believe that could be the case, but that would be highly unlikely. Then Don Pedro helps us to reinvent mathematics, to realize what it is and what it is for. Slowly at first, dizzily afterwards, ideas are being proposed ... The class is over. Will they all be like this? With a thousand variants, they were.

His appearance is sparkling, ingenious ... In all likelihood, this witty glance had to be reflected very directly from time to time: one day, in class at San Isidro, I was recently with Joaquín Crespo, a retired industrial engineer and student of Don Pedro from San Isidro and from the School of Industrial Engineers, says Don Pedro goes and draws on the board a perfect circle. The "oh" of admiration that escapes from some students thus reflects it.

"What is the name of this bone," Don Pedro asks, pointing at his forearm?

"The radius," a boy responds a little stunned.

"Well, lad, you should not be surprised that with a tool like that, you get a circle like this."

The ingenuity of which Professor Yela spoke was sometimes reflected in a different way: in a lecture to teachers he would be enthusiastic about his heuristic method, and one of the assistants, Santiago Gutiérrez, a former pupil of his, probably not much of a friend of this method, at question time, commented to him: That is, your students, in class, do what you want, to which Don Pedro responds: No, they do what they want to do.

But Puig Adam, as well as his wit, must have had a tremendously jovial character - an almost childlike look, said Professor Yelalo - which undoubtedly helped his students in class "want what they were doing."

Let's listen to one of his classes, for children from 10 to 11 years old. He is talking about the decomposition into prime factors, l.c.d. and g.c.d. After proposing various decomposition exercises he says:

We have, as you see, a new code to describe numbers in a different way. This code is unknown by the enemy. From my command post, the blackboard, I will send you orders and numerical data in the new code and you, from your planes, the tables, you will also answer me in code.

Crew A: Multiply all 23 × 32 × 5 × 7 by 23 × 3 and give the result in code to crew B from your plane.

Crew B: Transmit the result obtained in code.

One of them wanted to give him the numerical result of the product but he interrupted him, following the game, warning him: "In code, in code, or the enemy is finds out."

But all this ingenuity, all this jovial character, would remain as a simple anecdote if it were not united to an impressive capacity to transmit ideas; and this ability he develops using the most diverse of strategies: "I wanted to keep this operation intact on the board - he tells his students one day, showing them the remains of a polynomial multiplication operation - but the janitor has come and erased almost all of it; I just arrived in time to stop him deleting the multiplicand and the product. Let's see, if between us, we reconstruct this operation". The boys, almost without realizing it, are learning, by themselves, the algorithm for the division of polynomials.

Again he invents a puzzle to talk about the irrationality of π.

But not only did he have an extraordinary ability to convey mathematical ideas: One day, Fernando Arce, a former student of his class at San Isidro, was delayed somewhat at the entrance to the classroom, and saw the fifteen-sixteen-year-olds were doing their own thing at their own pace without a teacher - today, sometimes, doing their own thing with a teacher, but it is neither bad luck, or good, as we shall see later, that Don Pedro's entrance coincided with some swear words, clearly out of place, that someone had spoken. Don Pedro appeared and the class was, as expected, in the most absolute of silences. Don Pedro made no allusion to what he had just heard, and a few minutes before finishing the class, he says: "Wait for a moment and I'll be back soon," he leaves the classroom, makes a quick phone call, comes back instantly and tell them: "Tomorrow, at school, instead of waiting for me here, we'll meet at the entrance of Alonso Martínez's Metro."

The boys are perplexed, arriving the next day, they went to the entrance to the Metro and Don Pedro, without telling them where he was taking them, went with them to the College of Sordomudos, Calle San Mateo. Once in the College he takes them through the various offices, maintaining all the time the most chilling of the silences. At the end, in the hall, he comments: "I hope you have understood the true value of language and, from now on, you will be able to use it when it is convenient. The aforementioned Fernando Arce recalls this lesson sixty years later.

But all this ability to teach is linked to a very clear perception of the difficulty of learning; instead of thinking in the way that so many teachers sometimes think, but "Why can they not understand this given how easy it is?", says the aforementioned Santiago Gutiérrez, when he was already a teacher, who asked him one day:

"And you, in addition to teaching, what do you do?"

"As well as preparing my classes, I go out with my friends, I go to the movies from time to time ..."

That's not what I meant, what do you study, what are you learning now?

Then ... A teacher has to be always learning, he says, and not so much so that they are not being behind in knowledge rather because he has to feel, day by day, how difficult it is to learn, and thus will value his work more, but above all, he will understand a lot better the difficulties of their students. ...

Don Pedro was not a distracted sage. And that, although his daughter Emilia tells us, sometimes he would be at home eating and watching his family while his mind was elsewhere, they would ask at the end of the meal: lets see, Dad, what have you eaten for the first course? And he could not answer.

But in his class, recounts Consuelo de Costa, a former student of his, with 100 other students!, he had the class positioned in a quadrant, knowing the position and name of each, and absolutely controlled the work of each of his students.

Puig Adam was in advance of his time. A person who in 1921, in his doctoral thesis, dealt with problems of the Special Theory of Relativity, when Einstein's theories, although not well understood in many scientific circles, were known by very few in Spain. A person who in his address to the Royal Academy of Sciences, in 1952, quotes Norbert Wiener and gives the first applications of the machines that later we will call computers.

But where you really see that he was a man of another era is in his conception of teaching. All his didactic theory clashed with the pomposity and conservatism of the teaching practice of his fellow teachers.

In 1951, in an article in "Athens. Journal of information and pedagogical guidance," he said:

Let us also always bear in mind that the child is not an empty sack that must be filled with science, but has a potential eager to become active. Let them feel the joy of discovering, of creating, of inventing; that a truth found by their own effort will have more value to their culture and to their morals than a hundred compiled truths.
This lack of synchronicity and some other reason, as we shall see, made him not feel very happy among some colleagues. Let us listen to it him 1953, in the Inaugural Conference of the Mathematics section of the Spanish-Portuguese Congress for the progress of Science held in Oviedo.
After reading the recommendations that UNESCO agreed to take to the Ministries of Public Instruction in July 1950, a reading made at that conference, I verified - joyfully - that Spanish official teaching is not behind in its concerns for mathematical didactics. The spirit that informs them is the same one that guided us more than 25 years ago when writing, in collaboration with my beloved teacher Don Julio Rey Pastor, the books aimed at such didactics, whose later influence in questionnaires and texts both here and in Hispanic America I do not have to faithfully contrast, much less shout about. But I would like to say that when it comes to accounting for the employment of my life, I will count as the most distinguished service I have been able to render to my country, to have collaborated in the task of renewal which, at first received with indifference and scepticism by the offended traditionalists, then ... later it has been shrouded in still more eloquent silences. In reply to them I say what I say, committing a serious sin of immodesty. But I am not referring so much to contemptuous silence as to criminal silence, which accentuates a contempt like that which conceals a plagiarism; that if the first hurts, the second irritates, which is worse.
Let us leave these moments of anger and listen to him, in 1957, with what seem to be words of the most advanced pedagogues of the 21st century. And they were pronounced more than 40 years ago.

It has taken a while to have a clear understanding that the act of learning is much more complicated than the passive reception of transmitted knowledge presupposes; that there is no learning where there is no action, and, in short, to teach well is no longer to transmit well, but to know how to guide the student in their act of learning. This action of the pupil has come to be emphasised over the action of the teacher, conditioning it totally and subverting the initial primacy of its role. The centre of education is no longer the teacher, but the pupil. Emphatic truth that, although simple enough, many teachers have not yet assimilated.

I do not want to extend my address any more, out of consideration for you, since I have already spoken too much out of deference to my colleagues that I have already taken enough of your time and therefore, although I will just mention his "Decálogo de la Didáctica Matemática Media", published in 1955, for being well known, I would like to conclude by saying that all the versatility of Puig Adam - he composed music, painted, wrote verses - forced - according to his daughter Emilia - as a way of facing life. In a talk to his students in the 7th year of the San Isidro Institute, when they left middle school, he told them: "Try to be a little apprentice of everything for your own good, and teachers in something for the good of others."

Many thanks again for giving me the opportunity to contribute to a better knowledge of the figure of Puig Adam in our country. Thank you very much.


JOC/EFR November 2017

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