Mathematics in the Elementary Grades: The Soviet ExperienceAuthor(s): Maria MoroSource: The Arithmetic Teacher, Vol. 32, No. 5 (January 1985), p. 26Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41192523 .

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Mathematics in the Elementary Grades:

The Soviet Experience By Maria Moro

In the Soviet Union, a complete ten-year education is free and compul- sory for everyone. All Soviet schools teach the same mathematics curricu- lum for all ten years. The first three years comprise the primary schooling with classes conducted by one teach- er. Teaching is done by subject spe- cialists beginning in the fourth grade.

The current elementary school mathematics curriculum was first in- troduced in Soviet schools more than ten years ago. It retains the arithmetic of natural numbers but includes some elements of algebra and geometry.

By tradition, the curriculum con- sists of problems chosen according to the degree of difficulty. The textbooks enable the pupil to assimilate the basic concepts, ideas, and methods of mod- ern mathematics beginning in the first grade. This approach has considera- bly reduced the time required to study certain topics. For example, a knowl- edge of the properties of multiplica- tion and division has reduced by 75 percent the amount of material to be learned by rote. We have also consid- erably improved the system of learn- ing algorithms.

By using generalizations, gradually we have been able to teach fifth and sixth graders such concepts as the "mathematical expression," "equali- ty," "inequality," and "equation." They also use equations to solve word problems. This approach to solving problems in primary grades avoids the cumbersome, difficult, and sometimes

Maria Moro is an author on pedagogical sub- jects for the Novosti Press Agency in Moscow, USSR.

26

artificial arithmetic techniques of old- er materials.

Modern Soviet mathematics text- books are written to help children develop an ability to compare facts, make and confirm hypotheses, and use and discern regularities in various contexts. For example, in the first grade, before they study how a sum changes when one addend is changed, children are asked to compare such expressions as 5 + 4 and 5 + 3 and "guess" which result will be greater. Students must offer a reason for their answer and then check their hunches by computing the result. Such exer- cises, which are based on children's experience and intuition, always ex- cite lively interest and help students to mature mathematically. Such as- signments are gradually made more sophisticated. In the second and then third grades students might be asked to estimate numerical answers and then to replace asterisks with the signs >, <, or = in such examples as

8-7*8-6 + 8, 8-7*8-6 + 7, (15 + 16) • 8 * 15 • 8 + 16,

and 9-5*5-9.

Another sample assignment would be to complete tables (see table 1).

Developmental exercises are also included. For example, students com- plete a pattern of results to derive a formula for calculating the perimeter of any rectangle. Children are taught to recognize different polygons. These figures are shown by themselves as well as imbedded in more complex figures. For example, children are

asked to show all triangles formed after drawing all diagonals in a quad- rangle.

The focus of the initial course in mathematics is the cultivation of cal- culating skills. This goal is achieved through the system of increasingly difficult exercises. From lesson to les- son in the textbook, the teacher rein- forces new knowledge and reviews old material at the same time.

Toward the end of the third year of school, children are able to solve oral- ly problems with answers less than 100. They can also calculate answers to problems with larger numbers that are reducible to operations within 100, for example, 720 + 210 and 36 000 н- 4. Written work can involve the four arithmetic operations with figures up to 1 million followed by checking of results. Students can read, write, and evaluate expressions like (a + b)/4 and £/(32 + s) and can solve equations like

32 + x _

and 570 - (x + 247) = 16.

Measurements are made using units of mass, time, length, and area, and the relationships among these units are discussed. Simple drawings can be made. Children can use their knowl- edge to solve two- or three-step tex- tual problems that require a good knowledge of relationships among quantities (e.g., among time, speed, and distance traveled by a body in uniform movement). Table 1 Complete the table

a 8 12 32

b 15 10

a + b 25 42 12 93 32

The present system of mathematics teaching in elementary grades in Sovi- et schools has streamlined primary education- and made it possible to re- duce it from four to three years. This gain at the beginning of the curriculum has enabled us to teach mathematics in senior classes more effectively.

Mathematically gifted children at- tend special schools. Their curriculum is the same as in other schools, but learning mathematics is a priority, w

Arithmetic Teacher

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