# Alexander Karp and Bruce R. Vogeli (eds): Russian mathematics education: history and world significance. Series on mathematics education

## Authors

This book is the fourth volume in the mathematics education series of World Scientific edited by Mogens Niss of Roskilde University (Denmark), Lee Peng Yee of National Institute of Education (Singapore) and Jeremy Kilpatrick of the University of Georgia (USA). The editors of this volume, Alexander Karp and Bruce R. Vogeli of Columbia University (USA) are both well known in mathematics education in the US and around the world. They have numerous publications between them particularly of mathematics textbooks. In 1992–2000, Karp was involved in the reform of the system of Russian mathematics examinations (including the revision of their content). He was chairman of the Mathematics Department of the St. Petersburg City Independent Examination and Assessment Board. Karp is particularly interested in the history of mathematics education. This book indulges that interest and draws on his former experience in the Russian mathematics education community.

The book supplies background to researchers, educators and students of international mathematics education with an understanding of Russian mathematics education. The authors examine the history of Russian mathematics education, explore the development of teaching methodology in Russia, and compare the impact on mathematics education to and from other nations such as France, Poland, Hungary and Cuba.

Tatiana Polyakova begins the book by emphasizing on the history of the development of mathematics education in Russia in the first chapter. The discussion of “the first stage” occurring in the tenth to twelfth centuries, and teaching strategies from the twelfth century to the early 1900s, is insightful. A thorough and detailed account and narration of the evolutionary process of mathematics education during these times, especially the process of development of effective mathematics textbooks are helpful to mathematics educators. Under the patronage of Peter the Great Magnitsky wrote his famous *Arithmetic* (Apифмeтикa) in 1703 and this was used as the principal textbook for mathematics in Russia until the middle of the eighteenth century.

“Education was free, but at the conclusion of study, before issuing a certificate a teacher had the right to collect a rubble for each student. Without this certificate it was forbidden to marry” (Kostamarov, 1995, p. 351). American readers will clearly sense that the Russian mathematics education system had several similar “growing pains” to those the US system has undergone such as the movement away from corporal punishment and the discovery of student learning differences.

Extensive historical information is provided in this book. The method of development is a clear narration as the author tells the history of education by outlining a series of events spanning decades and continents. Karp begins the second chapter with thoughts from Ivan Tolstoy (2002) and discusses the Soviet system of mathematics in the first half of the twentieth century. The author outlines various changes made in an attempt to improve the quality of the school systems. He also evaluates coercive collectivization and the purges of the Communist Party, and their damages. During the decades of 1940s–1950s, Russian mathematics teachers stuck to the curriculum (Karp, 2007) which was less affected by the so-called “cosmopolitan campaign.” The achievements and problems of reforms and counter reforms supply unique models and lessons for future Russian mathematics education, as well as mathematics education of other nations. Karp gives a systematic description and practical guidance that mathematics educators can use to improve practice.

The consequent discussion of the reform of mathematics education in the next chapter gives the analysis of the origin and development of mathematics education in Russia. Alexander Abramov highlights the so-called “Kolmogorov Reform” of the 1960s–1980s by Andrey Kolmogorov who composed his humorous “Plan for Becoming a Great Man If One Has Enough Will and Energy” (Shiryaev, 2003) for his 40th birthday. The detailed and thorough information in this chapter has been gathered from a plethora of educational books and journals. Abramov delves into the history, follows events in order, and describes the whole process backtracking from the current curriculum to the implementation of the reform, with the reform process broken down by grade level. Every piece of information follows the correct timeline. The author tells an entertaining and educational story without any need for embellishment.

An analysis of the recent history of Russian mathematics education is delivered by Mark Bashmakov with an illustration of key challenges facing the system at present. Russia’s reform deals with government standards and book company competitions. A uniform standards system was set up much like those in the US. In the 1990s, Russia started to give more freedom to educators. Teachers were allowed to arrive with their own curriculum. The same freedom was given to teachers with regards to textbooks as well. As in the US, Russian students were also given state examinations for an assessment such as the Uniform State Examinations or USE. In Russia, the use of a textbook was seen as vital in education. A textbook was meant to jumpstart students’ thinking and then let them solve it for themselves. The author concludes that it is important to maintain a balance between old and new educational ideas: Do not fix what is not broken. In fact, the development of fundamental ideas is central to school mathematics.

The book presents a purely Russian experience—the far-reaching influence of research mathematicians into school mathematics education. Russian mathematicians are not only involved with research and problem solving but also with teaching and observing in classrooms, organizing mathematics clubs, or writing problems for mathematical Olympiads, amongst other things. The problem-solving section of the *Kvant* magazine is still available to this day. The author of this chapter, Alexey Sossinsky, also examines the often strained relationship between secondary educators and mathematicians or college professors.

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This book presents the appealing idea that the Russians produced mathematical problems that required little to no background knowledge so that mathematics was available to all students.

Jean Schmittau illustrates interesting mathematics examples in the next chapter and discusses the program of mathematics teaching in elementary schools, developed by the outstanding psychologist, Vasily Davydov. Davydov’s teaching program has helped many students excel in mathematics. The author explains how the Davydov teaching method focuses on teaching mathematics as a whole not as separate parts and teaches abstract ideas in early elementary education not waiting until secondary school as in the US.

Natalya Stefanova writes about the history and practice of pre-service mathematics teacher education with a very concise and coherent style. A surplus of information about becoming a mathematics teacher in past and present Russia is provided. The author outlines the old methods of training and certifying mathematics teachers in Russia and then continues through the years until current times, describing the changes in mathematics teacher preparation over the years. The author is careful to define terms and provide the sources dealing with teacher certification in Russia. The preparation of mathematics teachers in Russia requires students to make use of high-school textbooks (Karp and Werner, 1999) and take the course “Methodology of Mathematics Education in Specialized Schools.” The author concludes by outlining the new demands placed on the modern mathematics teacher and new organization of the education process.

Antoni Pardata, Katalin Fried and Orlando Alonso discuss Russia’s influence on the development of mathematics education in three countries of the former so-called socialist block: Poland, Hungary, and Cuba. The story of each country is explained from the point of view of what education in the particular country was like prior to Russia’s involvement and then what it was like during and/or after. Pardata examines the involvement of the government in educational reform in Russia, France, and eventually Poland which had a large effect on Poland’s mathematics development. Poland’s openness to incorporate the methodology from different countries has largely influenced its mathematics education. Fried discusses how mathematics teachers were in demand and Hungary provided a “fast track” education to teaching after World War II by using all resources possible including Russian textbooks due to limited availability of their own textbooks. Alonso points out that Russian involvement in Cuban mathematics education did not occur until 1959. The combination of study and work, intellectual preparation and scientific formation promoted Cuban school community and relations (Cruz-Taura, 2003).

In the final chapter, Jeremy Kilpatrick focuses on the influence of Soviet psychological studies in the US following translation and publication of Soviet studies in English. The author compares Soviet psychology with that of the US. The Soviet researchers studied in actual classrooms and schools instead of laboratories, which made their research results more applicable in reality. US mathematics education researchers have since attempted to follow the Soviet model (Lester, 1985). This mathematics education research made the socio-cultural phenomena of learning, teaching and thinking visible.

Many American researchers began research programs adopting the Russian ideas. Norton and D’Ambrosio (2008), for example, examined students’ mathematical development as the teacher worked within the students’ zones of proximal development (ZPD) and students’ zones of potential construction (ZPC). Such an approach was typical of the research spawned by the publication of the Soviet studies. The ZPD, almost a household word today in mathematics education, had its roots in the social constructivist perspective on learning and was originally proposed by the Russian psychologist, Vygotsky. On the other hand, the ZPC was proposed by the American Steffe, and was grounded in a radical constructivist perspective on learning. Working with individuals, pairs, or small groups was found to be better than adopting the then “new form” of teaching and learning for an entire class approach when it came to aspects of the ZPD and teacher intervention that fostered development of mathematical concepts (Norton and D’Ambrosio, 2008). This melding of Russian and Western ideas was to create a groundswell of similar research in the English speaking world which continues to this day.

The thesis articulated in this book is that the excitement and encouragement passed down from mathematicians to their students were driving forces towards the overall development of effective teaching methods and curricula in Russian mathematics education. Undeniably, Russian mathematics education has had an absolute and significant impact on methodology innovations in mathematics education all over the world as I have just exemplified. “Russian Mathematics Education: History and World significance” is an informative resource book that is both authoritative and evidence-based. It could play an important role in the mathematics education of current and future teachers at all levels.

## Acknowledgments

Special thanks go to Andrew McCaffery, Brandon Budd, Brian Jonas, Cassandra Depew, Christopher Rezykowski, Gina Gliniecki, Heather Yonkin and Mallory Pencek who contributed to the chapter reviews of this book in the Mathematic Education and Methods class at Keystone College in November 2010.