March 9, 2011
15:1
9in x 6in
Russian Mathematics Education: Programs and Practices
b1073-ch02
64
Russian Mathematics Education: Programs and Practices
One of the peculiarities of Ivashova et al. (2009) is psychological
differentiation. Exercises intended for students with different styles
of perception and information processing are marked accordingly:
sign
stands for kinesthetic perception (exercises dealing with
movements and notions about movement), sign
stands for visual
perception (exercises involving images and diagrams), aural perception
(listening), and sign
stands for verbal representation. Here are some
exercises for the derivation of the number 5 (first grade):
Lay out four circles. Add one more. How many circles are there?
Examine the drawing and explain how the number 5 was derived.
Name four girls, then name another one. Now say the five names
all together.
Typically, textbooks break down the material into discrete lessons;
the exceptions are Alexandrova (2009), Istomina (2009), and Rud-
nitskaya and Yudacheva (2009), where the material is presented
thematically. Rudnitskaya and Yudacheva (2009) include a review
section after each theme, while Davydov et al. (2009) and Alexandrova
(2009) gather all the review materials into a single section at the end
of the textbook, titled “Check your skills and knowledge” or “Check
yourself!”. In providing review sections, textbooks encourage self-
monitoring by students.
Several sections are aimed at broadening or deepening the students’
mathematical skills, e.g. “This is interesting!” (Alexandrova, 2009;
Rudnitskaya and Yudacheva, 2009), “Problems for those who like to
work hard” (Alexandrova, 2009), “For the math enthusiast” (Demi-
dova et al., 2009), “From the history of mathematics” (Bashmakov and
Nefedova, 2009; Ivashova et al., 2009; Rudnitskaya and Yudacheva,
2009), “Let’s play with the kangaroo” (Bashmakov and Nefedova,
2009), and so on. Here is a sample exercise from the third-grade
textbook of Bashmakov and Nefedova (2009):
Which number matches the following description? It is even, none of
its digits are the same, and the digit in the third position is double
that in the first position. (A) 1236, (B) 3478, (C) 4683, (D) 4874,
(E) 8462.
March 9, 2011
15:1
9in x 6in
Russian Mathematics Education: Programs and Practices
b1073-ch02
The History and the Present State
65
We should note that for the enrichment of their courses, teachers
of elementary mathematics frequently make use of the publication by
Kalinina et al. (2005), which essentially doubles as an encyclopedia for
the elementary school, written in accessible language.
Many textbooks include group exercises, aimed at developing
communication skills in children. Working in dialog, the students
acquire new skills and knowledge and learn to accept another’s point
of view. For example, Istomina (2009), Ivashova et al. (2009), and
Rudnitskaya and Yudacheva (2009) make use of recurring characters
with competing viewpoints, which are sometimes correct and some-
times incorrect.
A number of texts include reference materials (such as average
speeds of various types of transportation and animals, or weights of
various types of objects and materials), which train the students’ ability
to work with data and promote interest in mathematics and creativity
in composing one’s own exercises.
Many of the “complexes” place special emphasis on the cultural
aspect of mathematics through word problems (including problems
with interdisciplinary content) and calculation exercises that require
students to decipher certain names, terms, etc., contextualize numerical
data, and identify geometrical figures in their immediate surroundings
or in architectural structures. In certain textbooks, entire lessons are
structured around a narrative. For example, the review sections in
Bashmakov and Nefedova (2009) for the second and third grades have
unifying themes: “Little Boy and Karlsson” (recalling Astrid Lindgren’s
story), “A Flight to the Moon,” and “The Golden Fleece.”
For example, a calculation exercise in “A Flight to the Moon” asks
the student to decipher the name of the first astronaut to step on the
surface of the moon, which requires a series of calculations to determine
the correspondence between numbers and letters.
Overall, many of the “complexes” in elementary mathematics may
be characterized as “next generation.” Their content is primarily
scientific, personalized, and aimed at general development, follows the
“active” approach to elementary education, and generally conforms to
current standards (Uchebnye standarty, 1998) and forthcoming edu-
cational standards (http://standart.edu.ru/catalog.aspx?CatalogId=
531).
March 9, 2011
15:1
9in x 6in
Russian Mathematics Education: Programs and Practices
b1073-ch02
66
Russian Mathematics Education: Programs and Practices
Do'stlaringiz bilan baham: 
