Bernardo Alfaro

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Bernardo Alfaro Sagot and Mathematics Education in Costa Rica


by Angel Ruiz Zúñiga[i]









Some Biography


Dr. Bernardo Alfaro Sagot was born on 28 September 1913 in San Ramon de Alajuela, the son of Gerardo Alfaro Salas and Angela Jenkins Sagot.  Had a primary in Tres Rios (province of Cartago) and the Republic of Mexico School in San Jose, where he finished in 1926 as the best student of the School. The high school's place in the Liceo de Costa Rica, where he graduated in 1930 as a Bachelor of Science and Letters, as well as the best student of the institution.  In 1936, he obtained a degree in pharmacy.  He received the First Prize for Physics in the School of Pharmacy (1933), awarded by the Professor of the Robert Campabadal.  In 1933, began as a temporary lecturer at the Liceo de Costa Rica, first as professor of Castilian. Then in 1935 as professor of mathematics and in 1940 as professor of.  In 1943 he won the state title of Professor of Physics and Mathematics, presenting an original thesis about Numbers Heronianos .  In 1944 the University of Costa Rica it beco for studies of "Teacher Trainer" in "Sciences and Mathematics" at the School of Education, London University.  In 1945, he was appointed Professor of General Mathematics, Faculty of Economics and Social Sciences at the University of Costa Rica.  In 1946 is appointed as Senior Lecturer in Higher Algebra, General Mathematics and Financial Mathematics.  In 1957 he joined as a full professor at the University of Costa Rica. 

His mathematical training was essentially self-taught, because the country did not exist in university-level institutions where studies; as there were some groups of intellectuals who were concerned about implementing their own knowledge about a field that interested them, with the help of texts they got friends.  Within this framework we locate training Sagot Professor Alfaro who managed, as a result of their investigations, some original results in areas hitherto untouched in Costa Rica, as were his studies on heronianos numbers, the nth roots of approximations and in the field of geometry, Theorem BAS.





A Bit of History of Mathematics in Costa Rica


Before the creation of the University of Costa Rica in 1940 in Costa Rica mathematics were developed mainly in secondary schools and the Normal School (an institution to train teachers), founded in 1915, although some people so self - , conducted further studies, either as a supplement to their training abroad or just for the pleasure.  In the period from 1940 to 1957, mathematics were associated with schools and faculties of the young University of Costa Rica that they needed: Engineering, Science and Social and Economic Sciences.  In that first moment, the new institution was practically a federation of professional skills and not a structural unity and uniform academic standards, so that apart from the weakness that Costa Rica had the discipline itself was perfectly natural subordination that mathematics then displayed.  The highest academic standards and the depth of the issues depended on the needs of the training given by these faculties, the Faculty of Science, for example, the level was lower than in the other, had the highest engineering although Economics Social had math teachers with special training.

The turning point for the University of Costa Rica and it was mathematics university rector Reform Rodrigo Facio and the creation of the Department of Physics and Mathematics in 1957.  It is unclear why he chose mathematics and physics together in an apartment and not, say, physics and chemistry, some people say it was almost accidental fortuitous.  The truth is that this decision marked the fate of mathematics for many years.  During these years, are for the entire University, strengthened academic disciplines as such independently of the old powers: a powerful Faculty of Arts and Sciences was the executive unit of the policy.  He grew mathematics: the race progresses, the foreign teachers nurtured his progress, students were motivated to study abroad, and soon began graduates in the Faculty and a few in the Degree in Physics and Mathematics.  The mathematics and physics were strengthened and in ten years the conditions were created to operate separately.

Between 1957 and 1971, the development of mathematics outside the professional schools was essential for defining their own perspective, if it had maintained the subordination of these powers would have impeded scientific progress and the quality of mathematics received by those same powers.  However, this detachment, historically necessary and appropriate, with other factors, paid a distancing of mathematics in relation to those powers and-also-with what we believe are the same fonts for mathematical construction.  The creation of the Department of Mathematics was a natural consequence of the positive development of academic forces created within the old Department of Physics and Mathematics.  This new unit, which by reason global university is called School, has provided the framework which has formed the majority of mathematicians and math teachers in the country.

Between 1972 and 2003, higher mathematics have had their development and not only at the University of Costa Rica but also in the new colleges were created: the National University (1973), the Technological Institute of Costa Rica (1972) and State Open University (1979).  However, the main burden has been, for many reasons, the University of Costa Rica.




Alfaro as Administrator


In 1957, following the reform that was given at the University of Costa Rica, driven mainly by Mr. Rodrigo Facio, specifically the departmentalization of the University, Professor Alfaro became the Coordinator of the Department of Physics and Mathematics Institution, a position he held from 1957 to 1958.  Professor Jose Joaquin Trejos was the Director of the Department, as a surcharge to its position as Dean of the Faculty of Science and Letters, however, recognize that Alfaro, although the position of Coordinator for almost all practical purposes was the first director of the department.  The office of Director is held for two consecutive terms, then was reelected at the end of the first period.
Alfaro continued working as a full professor at the University until May 4, 1978, when he retired.

Alfaro was editor of several chairs and even Director of Teaching Mathematics in 1976.  In 1968, the University conferred the rank of Professor, the highest distinction offered by this institution.  Subsequently, on 29 May 1978, according to trade VD-362-78, the Vice-Rector of Teaching at the University of Costa Rica, he was appointed Professor Emeritus of the institution.  The Rector ai, Luis Fernando Mayorga, in a letter to Janina Del Vecchio, then Chief of the Evaluation Section, 2 June 1978 slogan: 

"I inform the Assembly of the School of Mathematics, in session 67, agreed, after fulfilling all the formalities set out in Academic Regulation Scheme, to appoint Prof. Bernardo Alfaro Sagot, Professor Emeritus of that academic unit. This appointment follows the spirit and the rules of procedure, so I am happy to officially notify the corresponding effects ... "[xi]

We now turn to describe several aspects of the work of Dr. Alfaro Sagot.






Let's start with his work in developing and writing textbooks.  Being a teacher at the Liceo de Costa Rica, Alfaro Sagot worried about the printing of texts for use by their students (especially in physics) in mimeograph (printing in color, transcription of figures and drawings, etc.)..  When such texts were sold in bookstores, Prof. Alfaro succeeded, perhaps unwittingly-unify the teaching of physics throughout the Republic, which had not been achieved with the provisions and resources of the Ministry of Education.

At that time, when a teacher wanted to print a text, the publishers required a minimum number of copies which costs should provide the author, this meant a great risk to the author and something out of reach for most.  Dr. Alfaro Sagot used the cross print style duplicator, which allowed encuardernar sheets in the form of an ordinary book.  Thus, many of his fellow professors at the university were motivated to write texts that were printed by Dr. Alfaro, which assumed the risk and, if the book was sold, the author received a cut on the sale of it.  That was how books were published Castilian (Isaac Felipe Azofeifa), Geography and History (Carlos Monge) Etymology (Victoria Garron), Biology (Joaquin Vargas Mendez), Mineralogy and Geology (Ramiro Montero), Modern Algebra (José Joaquín Trejos Fernández ), Economics (Rodrigo Facio), Administration (Fidel Tristán), Geometry (Manuel Thebes), Statistics (Wilbur Jimenez).  Besides the books of Prof. own Alfaro: 

•   Mathematics for First Year
•   Physics lessons (three volumes, for first, second and third years)
•   Mathematical Problems
•   Problems of Application of Trigonometry
•   Analytic geometry
•   Euclidean geometry (several volumes)
•   Projective Geometry
•   Ruler and compass constructions,
•   Elementary Theory of Numbers
•   Heronianos numbers
•   Infinitesimal  Calculus
•   General Mathematics for Biologists I and II

He also published many booklets with original presentations on common topics (partial fractions, trigonometric equations, algebraic number system, review of geometry, significant ratios, matrices, geometric constructions, financial mathematics for secondary schools, high schools logarithmic theory, nth roots by approximations.).

Now to the participation of Dr. Alfaro on reform in the Teaching of Mathematics: the "modern mathematics".



Reform in Modern Mathematics


In 1961, was held in Bogotá the First Meeting of Mathematics Education.  This was primarily aimed at implementing the Secondary Education for all American countries, the new currents on mathematics and its teaching was brewing worldwide.  A Sagot Alfaro attended this conference as a representative of Costa Rica and was appointed to represent management in Central America until 1966.

In 1963, the Ministry of Education commissioned the writing of mathematics textbooks for the Secondary Education; Prof. Alfaro took the opportunity to start implementing modern mathematics in Costa Rica.  This situation was reinforced by the fact that it was restructuring all curricula of Secondary Education, for this purpose were appointed committees in the different disciplines, accounting for Dr. Alfaro participate in the commission that drafted the math programs.  They convey the ideas discussed in this Conference.  Thus, Costa Rica became the first Latin American country to officially "upgraded" their teaching of mathematics.

Furthermore, the National Science Foundation in the United States collaborated in the publication of new texts and these were used in Central America, Colombia and Chile.




Institutional Work


Now continue with the work of Alfaro at the University of Costa Rica.  In his tenure as Coordinator and Director of the Department, Alfaro says that there were two basic ideas.  The first one: the University is committed to return, somehow, to secondary education, human resources that took the time of its creation, that the same or higher quality.  So given a major boost to the career of the Teacher in Physics and Mathematics, aimed at training teachers for high school.  In his opinion, this commitment still valid given the lack of an adequate number of well-trained math teachers.

The other was his idea to form a veritable laboratory of physics at the Department for use by the student community and faculty, so that would meet the condition can be deployed and restored in Costa Rica.

As a professor of mathematics, Alfaro Sagot contributed much in the field of geometry, a contribution that is evident in the textbooks they wrote.  For many years, his writings and his lectures gave a firm footing in this field to students in math and construction workshop organized geometric figures.  Alfaro was a delegate of the UCR in the Higher Education Council from 1957 to 1960.  Alfaro was the representative of the UCR in the National Commission for UNESCO in 1960.  In another matter, Professor Alfaro Sagot made significant actions on the academic organization and union of teachers in Costa Rica.

Until 1940, the only educational institution for the Normal School was founded in 1915.  Teachers of High School consisted of a very particular: Pharmacists taught Biological Sciences, and Social Studies Association.  Also teachers who had distinguished themselves in teaching any subject were called to teach in high school.  All Interim basis for five years.  After these years, were eligible for the title of Professor of State, after presenting an original thesis on some topic in their subject and another on his teaching.  Therefore, it was very frequent at that time that the school teacher only knew what I had to teach. Concerned by this situation, Dr. Alfaro Sagot founded an Association of Teachers of Mathematics to exchange ideas and successes with peers.  Sensing that this was not enough, he proposed the establishment of an association to fight for academic promotion in-service teacher, was born and the Association of Teachers of Secondary Education (APSE).

As a professor at the University of Costa Rica, tried to convince their leaders to authorize secondary teachers to enroll those subjects that would enable them better to carry out their work.  However, it was not until Alfaro came to the Directorate of the Department of Physics and Mathematics, which achieved its purpose, ie, promote the training of Secondary School Teachers in Physics and Mathematics.
In summary, the contribution of Prof. Bernardo Alfaro Costa Rican education is highly valued from different perspectives: teaching, writing and editing texts, forming educators, administrators, and worrying about the academic development of teachers in general.

[i] With the collaboration of Professor Danilo Solano of the University of Costa Rica

[ii] According to the Annual Report of the Liceo de Costa Rica, 1930

[iii] Their studies conducted in the School of Pharmacy of Costa Rica.  File B.  Alfaro, UCR

[iv] In the Liceo de Costa Rica between 1933 and 1934.  According to his Curriculum Vitae in his personal file at UCR

[v] Between 1935 and 1949 and between 1953 and 1956 at the Liceo de Costa Rica, between 1950 and 1952 at Lincoln School

[vi] Between 1940 and 1943 and between 1945 and 1949

[vii] A summary of this is found in the journal Mathematical Gazette, No. 282, pp.  226

[viii] He was Director from 1959 to 1964

[ix] However, as Professor Alfaro used then was pensioned by the Board of National Teachers Pension since 1 October 1962.  As explained in the action plan of the UCR number 102,278 of May 4, 1978

[x] Determination of category of teacher career regulations of April 23, 1968

[xi] Office R-655-78.  the Dean of the University of Costa Rica