Current issues in mathematics education

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  • Current Issues in Water Quality Management from A to Z A
  • current issues IN ECONOMICS AND FINANCE
  • CURRENT ISSUES IN MATHEMATICS EDUCATION

CURRENT ISSUES IN MATHEMATICS EDUCATION

CURRENT ISSUES IN
MATHEMATICS EDUCATION
MATERIALS OF
THE AMERICAN-RUSSIAN WORKSHOP
MOSCOW STATE PEDAGOGICAL UNIVERSITY
TEACHERS COLLEGE, COLUMBIA UNIVERSITY
NOVEMBER 18-20, 2016
CURRENT ISSUES IN
MATHEMATICS EDUCATION
MATERIALS OF
THE AMERICAN-RUSSIAN WORKSHOP
MOSCOW STATE PEDAGOGICAL UNIVERSITY
TEACHERS COLLEGE, COLUMBIA UNIVERSITY
NOVEMBER 18-20, 2016
Edited by Alexander Karp
Articles by the following contributors
work is copyright ? 2017
Alexander Karp
Vladimir N. Dubrovsky, Vladimir A. Bulychev
Sol Garfunkel
Irina Ovsyannikova
Sergei A. Polikarpov
Aleksey L. Semenov
Vladimir Z. Sharich
Dmitry E. Shnol
Erica N. Walker
Nicholas H. Wasserman
Printed in the U.S.A.
ISBN-10: 1-933223-01-4 ISBN-13: 978-1-933223-01-8
Supported by the United States Department of State
This publication was funded by a grant from the United States Department of State.
The opinions, findings and conclusions stated herein are those of the authors and
do not necessarily reflect those of the United States Department of State
Supported by the Eurasia Foundation
This publication is made possible by the support of Eurasia Foundation. The
contents are the responsibility of the authors and do not necessarily reflect the
views of Eurasia Foundation
Published by
170 Middlesex Tpke., Suite 3B, Bedford, MA 01730

Contents
Preface ........................................................................................................................v
Reflecting on the Current Issues in Mathematics Education......................................1
Alexander Karp
MathKit and Math Practicum ..................................................................................13
Vladimir N. Dubrovsky, Vladimir A. Bulychev
Making Cultural Change ..........................................................................................29
Sol Garfunkel
Using Technology in Mathematics Education ..........................................................39
Irina Ovsyannikova
Mathematical Education in Russia: Modern Approaches to Math
Teacher Preparation ..................................................................................................45
Sergei A. Polikarpov
Implementation of the Conceptual Framework for Russian
Mathematical Education............................................................................................61
Aleksey L. Semenov
Goals and Challenges of Mathematical Olympiads of Today:
Science, Sport, University Admission, or Status? ....................................................67
Vladimir Z. Sharich
Mathematical Research Problems in Russian Schools ..............................................79
Dmitry E. Shnol
Some Political, Sociological, and Cultural Issues Related to Mathematics
Teaching and Learning in the United States ............................................................95
Erica N. Walker
The Dilemma of Advanced Mathematics: Instructional Approaches
for Secondary Mathematics Teacher Education ......................................................107
Nicholas H. Wasserman
Notes on Contributors ............................................................................................125
iii
Preface
The present publication comprises a collection of articles by the participants in the
Russian-American workshop "Current Issues in Mathematics Education," which
took place on November 18-20, 2016 in New York. The workshop was organized
with support from the Eurasia Foundation in the form of a grant presented to the
Moscow State Pedagogical University and Teachers College, Columbia University.
Participants in the workshop included faculty from both institutions, as well as in-
vited guests and colleagues, and doctoral and masters students of Teachers College,
Columbia University. The collection opens with an introduction by A.P. Karp, fol-
lowed by the articles in alphabetical order. Articles written in Russian were trans-
lated into English for this publication (conversely, for the Russian edition, articles
originally in English were translated into Russian.)
The materials presented here mirror to a large extent the events of the workshop.
They cannot, however, capture the extensive discussions of the papers and the
problems they raised, which followed each of the presentations. A video recording
of the workshop is available for those interested in that aspect of the proceedings.
At the same time, publication of the papers delivered by the principal participants
will likewise permit the reader to follow the discussion, as it were, by tracing the
similarities and differences in the specific problems encountered in either country.
To be sure, the issues named and discussed here do not make up an exhaustive list.
Mathematics education today faces a host of challenges, and ideas concerning their
origins and remedies are just as numerous. We must continue the discussion, facing
head-on the difficulties and setbacks. Neither shall we attempt to isolate ourselves
from the experiences of other nations, but rather try to use those experiences to our
advantage wherever possible. It is our hope that the materials presented here will
prove useful in that regard.
We would like to extend our sincere thanks to Julia DeButts, Sergey Levchin and
Juliana Fullon for their assistance in organizing the workshop and preparing the
materials for publication.
Alexander Karp
v
1
Reflecting on the Current Issues in Mathematics
Education
Alexander Karp
Teachers College, Columbia University
This article, like the rest of the collection, considers the challenges facing
mathematics education. Education in general and mathematics education in
particular have always faced and will continue to face challenges: indeed, it
could hardly advance save by overcoming difficulties, some of which go back
thousands of years, yet when students complained of the hardships of learning,
and teachers complained of students' laziness. To be sure, every age also ushers
in its own particular problems, its own ways of dealing with problems old and
new, and its own accomplishments. At the same time some problems may be
regarded as universal, not associated with a particular region (even if they are
manifested differently in different parts of the world), while some problems are
endemic to particular regions and countries. In the present volume we intend to
reflect the state of affairs in two countries: the U.S. and Russia. The contribution
of these two nations (despite their many differences) to the international
advancement of mathematics and technology is evident. It seems well
worthwhile, therefore, to compare the different perspectives of people engaged
in mathematics education in these two countries. In this introduction we will
present a general overview of the emerging challenges, which will be discussed
in greater detail in subsequent essays.
It should be noted straightaway that many of today's changes and challenges
manifest itself in many spheres at once, consequently their discussion will
invariably spread to several sections. Two of these changes deserve special
mention: rapid technological advancement and fundamental social change.
The first is obvious. Today's student, whether in Russia or in the U.S., will not be
taking notes in the classroom, preferring instead to record the lesson on his
phone, or she will complain that the lesson does not come with a slide-show

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