Presentation

By Mariya Boyko —  What were the causes of each reform? —  What were the legacies of each reform? —  What pedagogical and methodological ideas are being implemented now? COLD WAR And Education US USSR Khrushchev’s Education Reforms Kolmogorov’s reforms in math education —  Background information Ø  Education reforms in US and USSR during the cold war period —  Kolmogorov`s ideas in pedagogy Ø  Education for mathematically gifted youth Ø  General education —  Modern applications of Kolmogorov`s ideas —  1930’s: —  Professor of pedagogy William Kilpatrick (Columbia University) declared that learning mathematics is "harmful rather than helpful to the kind of thinking necessary for ordinary living.” —  Psychologists supported his statement. They asserted that mathematical skills are NOT transferable —  Activity Movement emerges. Their goal is to “teach children, not subject matter” —  1940’s —  It is clear that the youth educated in progressivism traditions lacks basic mathematical skills —  Life Adjustment Movement emerges. Its proponents insist that secondary schools are “ too devoted to an academic curriculum” What caused the youth’s mathematical abilities to decline? “mathematical education had failed because the traditional curriculum offered antiquated mathematics, by which they meant mathematics created before 1700.” Pronounced as [Spootnik] —  Mathematicians were exploring various topics in set theory, group theory, topology and number theory —  Educators wanted to close the gap between the ‘school mathematics’ and the ‘modern mathematics’ —  This decision was independent of the geopolitical situation. —  Cold War period was a convenient time to re-­‐form the math curriculum because enormous amounts of funding were allocated to the studies of sciences —  Deductive logical approach —  Learning axioms and deriving theorems —  Usually used in geometry, but the “New Math” movement introduced this method into the studies of algebra, trigonometry and arithmetic —  Set theory —  Defining all mathematical concepts in terms of sets —  Too many unnecessary words and too little substance —  On the surface it looks like the situation is similar —  Set theory and deductive approach are being emphasised in the math curriculum But… They are emphasised for different reasons —  USSR`s education is undergoing a major Khrushchev`s education reform where mathematics is a part of a large plan —  And the plan was to defeat the enemy (USA) by winning the `arms race` and the `space race`. —  Hence, USSR needed engineers, scientists and mathematicians immediately —  The more the better! —  Increase the minimum education to 8 years —  Provide an opportunity to finish their education to the youth who were unable to go to school during the war —  Modify the mathematics curriculum…. —  But why??? What was wrong with the old math curriculum? —  Classic gymnasiums —  Sciences, mathematics (algebra, geometry, trigonometry), arts with theoretical emphasis —  Pathway to university —  Careers: educator, politician, lawyer, doctor. —  ``Real Schools`` —  Science, mathematics (algebra, geometry, trigonometry), arts with practical applications —  Careers: banker, engineer —  No university acceptance though —  Communist government insisted on making education available to the general public —  Requirements of the classic gymnasiums were NOT lowered. —  The presentation of the material was adjusted to suit the general public —  This curriculum proved to be so effective that there were no drastic changes until the 195o`s. —  Some new textbooks were written but the community of educators realized that in order to execute a global education reform, sporadic effort will not suffice —  Mathematics needed to be integrated in the new curriculum seamlessly —  Central Committee for Developing the Content of School Education was formed in 1965. It consisted of educators, professors, teachers —  Professor A. Kolmogorov gets involved … —  Born 1903, died 1987 —  Professor of mathematics at the Moscow State University —  Probability theory, topology, logic, etc —  Took interest in history of mathematics —  Enthusiastic educator! —  Got interested in gifted and general — 
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mathematical education at the school level at the end of 1950s Got involved with the Central Committee for Developing the Content of School Education Believed that rigorous and `non-­‐
rigorous` concepts should not be distinct in the students` minds. Kolmogorov wanted his students to become so familiar with advanced mathematical concepts that they would use them as freely as they use other daily common sense notions 1970 – Kolmogorov is appointed as a head of the math committee of the Scientific Methodological Council —  Co-­‐authored and edited numerous textbooks —  Encouraged the production of methodological literature for the math teachers —  Promoted the search for gifted students and created various educational programs for them —  Specialization is necessary to produce highly qualified specialists —  Specialization should start in high school —  In addition to the compulsory courses, extracurricular courses in mathematics, sciences, technology, arts and languages should be introduced —  Mathematics should be studied throughout the entire school year —  Olympiads and competitions should serve as a motivational tool for the students —  Winning gold in an Olympiad is a pleasant experience, but winning does NOT ensure one`s extraordinary mathematical abilities or deep understanding of all the concepts —  3 compulsory lessons and 2 optional lessons every day —  Physical education every day —  Art and literature lessons —  Music lessons —  Emphasis on the sense of `adventure` -­‐ mental and physical —  Extended trips on boats —  Hikes and scavenger hunts —  Created in 1963 —  Support of the Moscow state University —  Mathematics education needs to start as early as possible —  Physical education and arts are just as important as mathematics and physics —  Set theory and deductive — 
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approach may deter the students from further exploration of mathematics Students are unfamiliar with technical aspects of some mathematical problems Boarding schools may have a negative effect on child`s emotional development due to prolonged separation from patents Textbooks and methodological literature were published in a rush Authors of textbooks often had a different academic background than high school teachers —  Kolmogorov`s Boarding School (Specialized Education and Research Centre of the Moscow State University) —  Textbooks are used at the university level and at high school level in Russia and abroad —  Physical education is a compulsory subject at the Moscow State Mathematics undergraduate program —  Reasoning Mind Software: —  http://
www.reasoningmind.org/ —  Students develop at their own rate —  Lesson plans are structured according to some of the methodological publications suggested by Kolmogorov —  Software provides the variety of mathematical problems to keep the students engaged for the entire class time