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Nikolai Lobachevsky The Great Mathematics Educator 1792 – 1856 Maryam Vulis Norwalk CC Nikolai Ivanovich Lobachevsky Biography • November 20, 1792 - Born in Niznenovgrod Region or Nizny Novgorod • Had two brothers • 1802 – 1807 - Attended Kazan Gymnazia • 1807 - 1811 - Kazan University student, graduated with MS in Mathematics in 1811 • 1814 – Adjunct, Kazan University • Taught pure mathematics, physics, astronomy, hydraulics • 1816 – Extraordinary professor • 1822 - Ordinary professor Biography • 1820-21 and 1823-25 – Dean of Math and Physics Department • 1825 – 1835 – Head of the University Library • Feb. 11, 1826 – Lecture on his new, non-Euclidean geometry • 1829-30 – published an article on his new geometry in Kazan Journal (“Vestnik) • 1832 – Marriage to Varvara • 1827 – 1846 –President (Rector of Kazan University) • Declining health, blindness, lack of recognition • Feb.12, 1856 – died in Kazan Kazan Kazan University \ Lobachevsky’s House Older Lobachevsky 1896 Medal in Honor of Lobachevsky 1896at the University Lobachevsky’s1896 Monument Wife Varvara Moiseeva Mysteries Around Lobachevsky’s Biography • Two different dates of birth: 1793 and 1792 • Birth records : • Father : Ivan Maksimov (no last name) • Who was the real father? Ivan Maksimovich Lobachevsky Sergei Shebarshin More Confusion • Information taken from family’s confession records, but the name Lobachevsky is omitted • Professor Gudkov (Kazan University) demonstrated in his book “Mysteries of the Biography” that the biological father of the three Lobachevskys brothers was S.S Shebarshin, a land surveyor. • Church confessions records stated the Lobachevsky’s children Shebarshin’ “wards” (out of wedlock children according to the 1744 law) • Mother Praskovya lived with Lobachevsky for a short period of time Biography • This would explain how the brothers were prepared to sit and successfully pass gymnasia’s entrance exams • The brothers were well prepared and given full room and board at the Gymnazia • Even the famous portrait by Shchegolkov was not Lobachevsky’s portrait! “Not” Lobachevsky Lobachevsky’s Critics • Notably, the Kazan Mathematical School was not even mentioned in the 1948 Great Soviet Encyclopedia and Lobachevsky, the great Geometer was “not understood” , and thus “did not create any kind significant school” • Lobachevksy’ geometry was not accepted, and he was considered to be “not well” • 1834 article in “Sons of the Nations” Was Ostrogradsky was behind the article on Lobachevsky? Character Shaping • Childhood • Sent to live-in gymnazia , along with two brothers • Very good math education, but stifling atmosphere, lack of privacy • Prankster, but forgiven because of his math abilities • Protective of his family and close to brothers • Fair person, teacher, administrator Mathematician • • • • • 1805 –Kazan University founded as part Kazan Gymnazia Lobachevsky was as an excellent student Stayed to teach Since 1818 – member of the Education Board of Kazan region Later on while Kazan U President was a also the head of Education Board of Kazan region • Supervising educational process, textbooks selection • Member of the Committee on Entrance Examination Preparation Approach to Teaching • The methods of teaching mathematics were of the highest importance • Lobachevsky's writings were compressed, “dense”, but the lectures were very well presented and clear, with details so the students could study for the exams. He would consider some problems, then would move to generalization , mostly concerned with the ideas, rather then mechanics. • During an examination, expected deep understanding from the students • Had very convincing manner in a conversation Teaching • Lobachevsky was well regarded and liked by the students He was strict but fair, always listened to students’ problems “No one did not like him” • Son Nikolai : the father was extremely strict with his children as students, came every day to the room to listen today’s preparation • Told his wife: “I am Professor Lobachevsky first” Pedagogical Views • Notions (ideas) must be clearly explained and not come from experience only, so that they can be used in further studies • Abstraction should be taught, and the children should not be taught how to solve problems using examples only and discern notions from examples • The difficulty of mathematics lies in the methods of teaching • “While I did not achieve perfection, I have chosen a straight path towards my goal, and let others confirm this” Contributions to Mathematics Education • 1830 composed “Instructions for Gymnazia Mathematics Teachers” • “General View on Teaching Physics”, “Instructions for teaching Physics in a Gymnazia” • His idea was to teach about the phenomena, about the applied laws, who studied them, and then state the purpose of studying the mathematical theory of physics • 1836 – visited St. Petersburg’s schools and Simbirsk Gymnazia, had a clear picture of teaching mathematics at secondary school. Submitted the written report. Contributions to Mathematics Education • At some point, taught at Kazan Gymnazia • Preface to his “Algebra“ book reflects his secondary level teaching experience • Instructions for Gymnazia Mathematics Teachers • Applied similar ideas to university level teaching • 1828 – Lecture on “Important Aspects of Upbringing”: • Role of learning in the progress of mankind • Emphasized the importance of learning mathematics to develop the ability of making decisions using giving conditions Contributions to Mathematics Education • Lobachevsky's approach : • Learning through “feelings”, then confirmation by abstraction - this method provides a better understanding of the subject • The level of the student determines the time abstraction is introduced • Against overly emphasizing concrete examples • “Strict “ thinking vs. intuition • Important that students enjoy intellectual activity , and do not cultivate subject interest only Contributions to Mathematics Education • In lower classes, the teacher must combine teaching mechanical calculations with again, clearly stated rules • Teaching general concepts through examples, then when the theory is established, go back to illustrations • The same method applied to foreign language studies • In teaching Russian language, for example, he emphasized on the historical approach of language development, in foreign languages studies - the method of comparison Contributions to Mathematics Education • Importance of introducing initial concepts . This provides further deep understanding of the subject. • In the preface to “Algebra” (textbook): • “Algebra is taught in Kazan Gymnazia under my supervision for two years. I admire children success and convinced that the concepts cannot be acquired by skills, but must be initially clearly and definitely stated, then easily memorized , and them applied in further studies. Such rule was not followed before.” Contributions to Mathematics Education • Protested plans to cut math in favor of languages, and thus the transition to “classical education” was not fully competed in Kazan region • Stated that mathematical talent of a student had to be cultivated in the sense one should not overburden the student with studying many languages • However, made great emphasis on Russian language and literature, writing essays as a way of learning to think critically and precisely express thoughts Contributions to Mathematics Education • Lobachevsky saw the lower school as a step to the middle, then the high school (in modern terms), making education available to all population strata • Saw a gymnazia a step to a higher education institution, • Thus the in general school had to have a “common program” • On the contrary, the government supported dividing the lower, middle, and high schools into separate units and education by “classes” • 1840- The Decree of the Education Minister meant to “keep in classes in mind” Educational Innovations • He also abolished “internship” - instead, a student would go on to teach in a gymnazia for several years, then after learning more mathematics and obtaining educational experience, the student could obtain a “Master’s Degree” • Then the student could return to the University to teach • It was a complete system of preparing professors • Lobachevsky’s student Popov, who was the Chair of the Pure Mathematics Department, kept the system, and only later on the candidates and the teachers were on their own to pursue of self-education Teacher Education • From the very beginning, the Kazan University graduates who became math teachers, had to continue selfimprovement • The University itself “was learning” the practical side of teaching, learning from mistakes, and using in further assisting the Kazan Region Department of Education • First attempts were just stories from the classroom, then they would become more scientifically founded Conclusion • Nikolai Lobachevsky’s contributions to Mathematics Education • Principles used in Russian Math Education • Methods of Teaching