Nikolai Lobachevsky and Russian Mathematics - HPM

Nikolai Lobachevsky
The Great Mathematics Educator
1792 – 1856
Maryam Vulis
Norwalk CC
Nikolai Ivanovich Lobachevsky
• 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
• 1820-21 and 1823-25 – Dean of Math and Physics
• 1825 – 1835 – Head of the University Library
• Feb. 11, 1826 – Lecture on his new, non-Euclidean
• 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 University
Older Lobachevsky
1896 Medal in Honor of Lobachevsky
1896at the University
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
• 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
Character Shaping
• Childhood
• Sent to live-in gymnazia , along with two brothers
• Very good math education, but stifling atmosphere, lack of
• Prankster, but forgiven because of his math abilities
• Protective of his family and close to brothers
• Fair person, teacher, administrator
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
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
Lobachevsky was well regarded and liked by the students
He was strict but fair, always listened to students’
“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
• 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
• “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
• “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
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
• 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
• 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
• Nikolai Lobachevsky’s contributions to Mathematics
• Principles used in Russian Math Education
• Methods of Teaching
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