internalization

nate (schmolze who-is-at students.wisc.edu)
Tue, 23 Dec 1997 08:57:12 -0600

I was checking the links on my Vygotsky page
<http://www.geocities.com/~nschmolze.vygotsky.html> , and found an
interesting article on the best practices website
http://www.bestpraceduc.org/DiscoveryGrants1997/VygotskianMath.shtml. I felt
it related somewhat to the recent threads on internalization. The project
uses a Vygotskian approach to math. What I found interesting was the
students demonstrating proficiency in concepts that go way beyond what the
teacher taught. I have included the article below.

Also, has anyone else heard about this project or have information on
mathmatics instruction in Russia. The results seemed unbelievable.

Nate Schmolze
schmolze who-is-at students.wisc.edu
http://www.geocities.com/~nschmolze/

Vygotskian Math at Susquehanna School, Binghamton, New York
by Nancy A. Ziegenhagen

The Susquehanna School, a 25 year old, independent, not-for-profit,
nonsectarian school for students from Early Childhood through Middle School,
is starting a pilot project that will benefit important aspects of
children's mathematical development in the United States. The pilot project
will enable one or more psychologists from the Russian Academy of Education
in Moscow (formerly Academy of Pedagogical Sciences) to engage in
mathematics curriculum development with elementary school teachers from our
school, from local school districts and teachers-in-training from Binghamton
University. The project would take place under the supervision of Dr. Jean
Schmittau, Associate Professor in Binghamton University's School of
Education and Human Development.

About the Russian (Vygotskian) practice
The practice is a program for teaching mathematics grounded in the
theoretical perspectives of the Russian developmental psychologist Lev
Vygotsky. The method was developed by the Russian psychologist V. V. Davydov
who is vice-president of the Russian Academy of Education and head of the
Russian Institute for General and Pedagogical Psychology.

In 1990, Dr. Jean Schmittau, Associate Professor at the State University of
New York at Binghamton, went to Russia at the invitation of the Academy of
Pedagogical Sciences of the USSR (renamed the Russian Academy of Education).
There she observed classes using materials developed by Davydov and his
colleagues and researched the understandings of students who had been
instructed with these materials. Her research, which replicated with Russian
pupils her dissertation research at Cornell, found the Russian students to
have a profound grasp of mathematical structure, confidence, and the ability
to extend their knowledge well beyond the levels at which they had been
instructed. The Russian children who had just completed three years of
schooling evinced mathematical understandings rarely encountered among
college and high school students (to whom her study was extended) in the
United States. For example, every Russian child who had just completed the
first three years of schooling in Davydov's program was able to multiply
binomials and give a fine grained conceptual analysis of the process,
despite never having been instructed in how to multiply polynomials. This
was in contrast to high school and university students in the United States
for whom polynomial multiplication was conceptually opaque.

Recent data from the US curriculum study of the Third International
Mathematics and Science Study (1996) indicates that US students seldom
explore key concepts in math with any depth, that underlying themes and
principles are either not identified or simply stated but not developed, and
that students spend more time practicing routine procedures than in
conceptual thinking about mathematics. Mathematics pedagogy grounded in
Vygotskian theory approaches mathematics as a conceptual system rather than
a collection of discrete procedures, and provides intense coverage of
advanced topics that in the United States are reserved for students in
higher-level classes. In addition, students in the tenth grade who used
Davydov's materials for the first three years only, with the intervening
years comprised of more or less "traditional" forms of mathematics
instruction, gave evidence that the effects of Davydov's program had
persisted, and continued to influence their mathematical understandings in
profound and positive ways. Dr. Schmittau saw nothing accomplished by the
Russian children that our own children in the United States would not also
be capable of doing and understanding. However, Davydov's program has never
been piloted in the US We propose to pilot Davydov's materials at The
Susquehanna School in Binghamton, New York.

Davydov and his research group have developed and tested a Vygotskian
approach to the development of early mathematics concepts for over 30 years,
creating materials that far exceed the Standards for school mathematics
developed by the National Council of Teachers of Mathematics in the United
States. Davydov's program includes diagnostic tests that are much more
focused in their ability to diagnose students' conceptual knowledge than are
so-called alternative assessments currently being developed in the US. Since
the end of Soviet rule, Davydov's program has been inaugurated in more than
one thousand schools in the former Soviet Union.

The project at Susquehanna
For the proposed project at our school, we anticipate the participation of
L. K. Maksimov, Doctor of Science, of the Pedagogical Institute of
Nizhnevartovsk. Maksimov is a senior researcher with Davydov's group with
whom Dr. Schmittau worked closely while in Russia and with whom she has
continued to collaborate. In November 1992, Dr. Schmittau was co-organizer
of a conference that brought together American and Russian scholars. This
conference was attended by both Davydov and Maksimov who were among the
featured speakers.
Recently Dr. Schmittau has been adapting some of the Russian materials for
use by teachers in the Binghamton area, with excellent results. Many have
reported breakthroughs in understanding obtained with ordinary students they
had all but "written off." The aim of Davydov's work is to render
mathematics as accessible to the majority of students as it
presently is to the few. As an independent school, The Susquehanna School
affords an opportunity for innovation that makes it an ideal site in which
to pilot curriculum materials and assessment methods based on Vygotskian
perspectives in mathematics. At the same time The Susquehanna School offers
multi- aged grouping which provides a context for introducing materials to
children ages 4- 14, from pre-K students to those who are already working on
the first two years of high school mathematics, all of whom have been
exposed to more or less "traditional" methods of mathematics instruction.
First, however, the Russian materials will have to be translated into
English and adapted for use in American schools. For this purpose, we would
hire Olga Matyash, a native Russian and doctoral candidate in residence at
Syracuse University, who has already worked with Dr. Schmittau on projects
involving text and teacher education materials produced by Davydov's
research group.

We anticipate that the piloting process itself will result in further
refinements since we plan ongoing assessment as we use the materials for the
first time in the US setting. We know of no prior use of this method in the
United States.

Best Practices in Education grant
The Discovery Grant from Best Practices in Education will help the
Susquehanna School is seeking Best Practices in Education support to adapt
mathematics curriculum materials based on the work of Russian psychologist
V. V. Davydov and to bring one or more psychologists from Davydov's senior
research group to Binghamton, New York to assist in training teachers and
piloting these materials at our school.

The project will start in September 1997 and end September 1998. We will
request curricular materials prior to the psychologists' arrival, so that
Dr. Schmittau and Olga Metyash can begin work on translation. Upon their
arrival, we anticipate working together for two months on the initial
teacher training effort, as this will require nothing short of a paradigm
shift on the part of teachers. Afterwards, Dr. Schmittau will continue
working with teachers and will place one of her graduate students at our
school to assist us with continued implementation of the program.

We plan to provide videotape documentation of children interacting with the
instructional materials. We will have a field test of how they actually work
in practice, observations and feedback from teachers that will help us
refine the materials for future use in a Binghamton public elementary
school, where 20% of students have limited English proficiency, and in
programs, activities and exhibits at the Discovery Center, a children's
museum and regional attraction located in Binghamton that serves 60,000
visitors annually. We will use some of the Russian diagnostics to test
students' knowledge and assess understanding. Since the Binghamton City
School District ranks in the bottom 1 per cent of the 735 school districts
in New York State with respect to poverty, we feel that the challenge of
implementing Davydov's program here would be eminently worth undertaking.
The Susquehanna School, in collaboration with Dr. Schmittau, has applied for
a New Connections grant from Apple Computer to provide us with training and
multimedia computers so that we can put these curriculum materials and
segments of video studies on CD-ROM for classroom use, dissemination and
publication on the World Wide Web. We are also interested in using
technology to set up problem solving traces to do more fine-tuned assessment
of students. Documentation from this pilot project would enable us to seek
further funding.

At the completion of the project The Susquehanna School will have imported a
program that's been scientifically tested and refined for more than three
decades, translated it into English, adapted it for use by American
students, trained teachers in its implementation and field-tested it with a
small but varied segment of the US student population.

(A follow-up report will be produced by November, 1998, a portion of which
will be made available here).

Nancy A. Ziegenhagen, May 1997

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