ERG SES E 04, Mathematics Education Research
While participating in the discussions at the doctoral seminar from 2014, I noticed that the majority of research projects are focused on the pejorative aspects of education and upbringing. Negative factors are constrained to support the development of mathematical aptitude gains in children, shortcomings in school education blocking their development, and finally, life events that interfere with mathematically talented individuals to achieve academic success in mathematics.
While studying pedagogical and psychological literature, I noticed that no aptitudes have been tried so far from specific events and situations that have started the career path and have contributed to achieving extraordinary achievements. The exceptions are the studies of Howard Gardner and Joseph Walters (Walters & Gardner, 1986, as cited in K. J. Szmidt, 2012) described in the article: "The Crystallizing Experience: Discovering an Intellectual Gift". The authors defined experiences crystallizing as such events "that involve a person with an unusual talent or potential abilities with a given field in which the talent can be revealed" (Szmidt, 2012, p. 77)
According to Gardner and Walters, the crystallizing experience is an extraordinary meeting - usually in adolescence - with authority in a given field of creativity or with its characteristic material, or even hardware and instrumentation, which becomes a breakthrough in its further life. The course of the fact of this meeting results in the fact that the creative person begins to concert his life on a chosen problem, material or experience. (Szmidt, 2012, p. 77)
The authors suggest (Walters & Gardner, 1986, as cited in K. J. Szmidt, 2012) that in the case of the greatest talents, crystallizing experiments are inevitable, and most importantly, they happen more often in the case of musicians and mathematicians.
These views were an inspiration in establishing the purpose of my research. However, I decided that it is worth considering what other factors could have influenced the development of mathematical aptitudes or whether it was just a stroke of luck (M. Shermer 2018, p. 2) or other factors. In the development of the research program, I was helped by the publication of Charlotte Bühler (Buhler, 1999) and the methodological concept of conducting research into the course of human life.
Speaking about aspects of human life according to Ch. Buhler opens the perspective of three problem areas that I will distinguish in the overall course of human life. These three problem groups are: first, the course of human life as a biological process, as the development and destruction of the body and its functions; secondly, the course of life as individual behavior and personal experience, studied on the basis of biographical data and subjective experience; third, the course of life in its objective results, its impact on others, its production and its historical role in the broadest sense of the word. (Buhler, 1999, p. 34).
Milestones in my understanding are: "determined by me (or indicated by the interested) key events and moments in their history of reaching the highest dignity and recognition in the field of mathematics". For example, these are important experiences in a person's life that played a huge role in choosing mathematics as a direction for further development or confirmed in the belief that mathematics is the right choice.
The choice of a group of outstanding mathematicians was determined by the fact that I was already relatively familiar with the problems of mathematical aptitudes and also in what is not conducive to developing talents. I, therefore, considered it attractive to consider the course of the life of mathematicians in terms of what favors the development of talents.
In this situation, I have chosen an inductive research strategy, which is a way of reaching new scientific assertions and checking them. It involves the generalization of unitary empirical facts according to the principle "observe and generalize the results of observations - first observation, then theory". That is why I have formulated goals and distinguished research tasks from them, which are precisely defined by the selected fragment of pedagogical reality. Next, I have chosen research methods, ensuring that each of them provides information about the variables studied. (Such, 1969, p. 140) . I used the biographical method narrative interviews and analysis of documents (journals, diaries, autobiographies). When I was analyzing the results, I used Charlotta Buhler's research findings (The course of human life).
My research on "Milestones in the course of the life of outstanding mathematicians and mathematically talented youth" covers the last period of about eighty years. Research has shown that changes have taken place over the years: • during the beginning of a scientific career: deceased Professors of mathematics began their scientific activity after the age of 20, living professors - a few years later, contemporary Ph.D. students do not start their scientific activity until the age of 30 (they do not say anything about important milestones in their lives) publications and articles). • The time to start a scientific activity is very important if it is considered psychologically in terms of the stages of cognitive development of the mind. Period conducive to the development of scientific activities in exact sciences is 20-30 years. If by that time a man did not it will undertake scientific activities in exact sciences, it is very likely that it will not take it anymore. • Changes in the master-student relationship. Already during the interviews with mathematicians, I noticed some differences in the fragments concerning the statements in which the respondents explained to me who contributed to the development of their talents. Dedications posted in mathematical works are also important because in these dedications one can read a close relationship between the master and the student. To my surprise, Ph.D. students and doctors only pointed to the closest family and teachers from primary or secondary school. They focused more on institutions that enabled study visits, while mathematicians from the first group entirely referred to valuable scientific authorities. Young adults, while studying or even traveling abroad, had to meet outstanding personalities, although they did not consider it appropriate to talk about them.
The paper presents a study about milestones (i.e. significant events, critical points, crystallizing experiences) in the life course of distinguished mathematicians and mathematically gifted adolescents. It focuses on presenting people, things, situations in the whole context, which has a direct relationship with the directing of one’s mind towards mathematics. An interesting and important point for mathematical education and mathematical abilities can be an agreement that the milestones are either constant or inconstant depending on the time. This consideration will be based on a humanistic and holistic attitude connected with Charlotte Buhler’s method.
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