Nikolai Lobachevsky The Great Mathematics Educator 1792

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Nikolai Lobachevsky The Great Mathematics
Educator 1792 1856

• Maryam Vulis
• Norwalk CC

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Nikolai Ivanovich Lobachevsky
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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

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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

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Kazan
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Kazan University
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Lobachevskys House
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Older Lobachevsky
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1896 Medal in Honor of Lobachevsky
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1896 1896
Lobachevskys Monument at the University
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Wife Varvara Moiseeva
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Mysteries Around Lobachevskys 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

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More Confusion

• Information taken from familys 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
  Lobachevskys children Shebarshin wards (out
  of wedlock children according to the 1744 law)
• Mother Praskovya lived with Lobachevsky for a
  short period of time

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Biography

• This would explain how the brothers were prepared
  to sit and successfully pass gymnasias entrance
  exams
• The brothers were well prepared and given full
  room and board at the Gymnazia
• Even the famous portrait by Shchegolkov was not
  Lobachevskys portrait!

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Not Lobachevsky
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Lobachevskys 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?

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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

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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

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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

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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 todays preparation
• Told his wife I am Professor Lobachevsky first

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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

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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. Petersburgs schools and
  Simbirsk Gymnazia, had a clear picture of
  teaching mathematics at secondary school.
  Submitted the written report.

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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

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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

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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

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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.

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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

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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

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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 Masters Degree
• Then the student could return to the University
  to teach
• It was a complete system of preparing professors
• Lobachevskys 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

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Teacher Education

• From the very beginning, the Kazan University
  graduates who became math teachers, had to
  continue self-improvement
• 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

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Conclusion

• Nikolai Lobachevskys contributions to
  Mathematics Education
• Principles used in Russian Math Education
• Methods of Teaching