THE ELEMENTARY MATHEMATICS PROGRAM IN RUSSIA

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80T00246A009700130002-9
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 22
• Document Creation Date: December 22, 2016
• Document Release Date: August 4, 2009
• Sequence Number: 2
• Publication Date: February 26, 1960
• Content Type: REPORT

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etThe .em tt*11 MrW,1 i'09 P e
ftesif
f4nericsn a ,,reness that rent ; oviot achievements in $pa.ae
toehnolo? 9 bespeak a high order of ma.thessatieal o ampeteuuaa has
aroused interest in the teaching of NatbMatias at all ravels in
Soviet ;ichools. The subject is a coasplicated one,, as it is indeed
in our own caastt s and such more detailed study' a suet be r t de before
an7thins like a fully adequate picture can be obtained. As a con-
tribution along these lines the present article offers a translaticet
of the official syllabus for the first four grs6es of ole outer .
school.
As usual with doeaeaent$ of this sort the language in replete
rrith tochniaal jargon and is frequently torso to the point of ambi-
guity* In order that the material may be as meaningful as 1. ,s sable
to the reader I have provided fairl; extensive notes wherever torso
seemed desiraable. The notes are based Uracily on my oxa natiof of
a number of elementary textbooks and works for the training of w;oviet
teachers. The main contents of this article, that is tho three sec-
tions entitled "Explanatory narks," "Methodological In'traactione,
and "?rcasgrruaae," are translated, fror. the official Russian school pro-
grams for IPF#7-
rpsaoW, 1Wa-H i ,
11sbi and their
For i "ur a~ner Aux urw-v s,,, ....~ _ . _
rroaaapr'ent
lrrtionship to the Joviot school aystemm soo I cask ,Arsrup,
caVicrt anion and r Corir u-
`
i
c
n
titls 6urrtcnle
60hc:o itathemeni et 6ountri+e e, t at e e bhoz', fall r OIs?y a ) ,
Via. ': ff.
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XFLk iA`.L OHY
The teaching of srittrsetic in Grades I-IV has as its aim to
teach children eorr,,ctly, knowingly, confidently, and rationally to
perform operations with whole numbers and to apply acquired knawledge
and experience to solving arithmetic problems and perrorring simple
calculations. The teaching of arithmetic must help carry out the
tasks of the eor-uanist upbringing of children.
The study of aritbtsatic in school should be so designed that
number and measurement serve as a tool of cognition of surrounding
re all t-,-7 $
During the instructional period of Grades I?IV the pupils should
ac quire t
A firm knowledge of whole numbers and operations with them and
solid habits of oral and written computation with whole numbers, both
abstract and denom nste$
A firm know,edge of metric m senures and measures of time, and the
ability to use then in measurIngt
ry knowledge of simple fractions;
A knowledge of a few elements of descriptive geometry an the
ability to apply this knowledge in practice;
ability to solve easy arithmetic problems.
ole numbers end operations with them, studied in a definite
order, co prise the basic content of the program of Graces I-IV.
First of all the children study nmeration and the arithmetic
operations (addition and subtrrctim) within the limit of 10, and
then numeration and the four arithmetic operations within the limit
of 0
Next crapes the section "Wixmera
four operations
of 100,
be ins in Grede I and
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is concluded in Grade II, after
begins the stud' of nuereera-
onre within the limit of 1000o From tb4 s :,ec tion
?eretton and the four operations in round hundreds a.re ntu?
died in Orsde Ii,
In Grade III or
Pute ti ones with round
limit
of 10;:0 area studied, and written methods of calculation within t is
limit are introduced.
After the study of the operations within the limit of 1000, nu-
meration and the four arithmetic oporetions involving
within the limit of a million itre studied.
Pupils learn the reading, and writing of nur t er s and ' rni li rrri se
themselves
o periods w
In grade IV the knowle
no within the
been acquired by
the pupils
In expanded end sya tt+ms ti seed s the 1mvwl*dS* of numeration in expanded
to include the periods of millions and billions; more difficult oases
of multiplication (multiplication of numbers with eeroos at the end)
and division (division with a remainder, etc.) are consolidated; the
relationship between data, and results of arithmetic o rax.ti a is
learned;
"Order
rde$ a and tboir 4.bi s t r ibuMio'j0
last is used for cheekt operations, for solving e.x*
nw er, or ea
of the first order)
the second order # an
groups of three di
a4ussien) are not off
upied b7 the d_i.;ite of 0
a place is ee.llr?d a digit
ent a place is called t digit of
do" refers to the quecessive
,h in our nktiona.l syatom (but not in the
the relationship betee
textbook used in the fifth end
he bnik dl
F;-*
+ye r elegy tionrhtp for eddi-
.udes with the foilo .nL t "in
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i
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with x,, and for solving probleme.4
eve in prime ry
simple fractions in Grade IV.
As a result of their ntu
o ti c concl tdte $
h the C t udy of
totional numbering pu-
pile who complete, Grace IV ehoulda
Rave a. firm grasp of the to r inologg of each ari t;hme ti c opera
ti on;
Have a good command of the technique of written computettems,;
Know the formulatic in which the relationship betwoon the com.
pon.nt parts of operations is expreaeeed, and the rules for checking,.
operations;
Understand the significance of each arithmetic operrition (without
of specific operations) and ?snow the basic eirotrnetances
which each operation is applied to the solution of problems;
Be able to me use o
a properties of operations in oral
and written amputations wi.
with the exception of the. oomutrtiv,
of the se properties,
of adc-A ti on and
order to find an unknown adend it in necessary to subtract the known
addend from the m of the two ad ends. a This in further expro a eed.
with the notation that if a#bec, than &**-a and bac a.
4
't word trenelr ted as "o iea refers to a pure number problem
such an 10*13? whereas '1probieea' refers to what to frequently deals.
nate an "word problem." The expression "'exercises with x" refers
to such exercises as the following, taken from a fourth-.grade Russian
textbooks Find the value of x in M-6 5 1. . (A. 8. Polyak
G* B Polak, rift rtetiice, Uohe bni AM141: n ch
.0 o ecov?
The principle tha
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multiplication,, which pupils should be able to name end formulctol
formation of the fractions (1/2, 1/4, 1/8? 1/10)
and how to add and subtrz'ct fractions having the a den inator and
denominators vhieh are multiples of each other.
rihroughout every year of the pr ry arithmetic source great
ntion is devoted to the study of metric measurement, f" d also
meaeur t of tined
that the students will obtain a concrete idea of all the
measures and learn to use th*n., in every grade, b, in. : . th the
at, the chit ren themselves make up ex p1ee of vrrious meawnwee
and practice .mss
determining appro.,
t of ey'e, and
fight of solids by muscular sonsation of
ht.
6
In Orade IV the operations with compound denominate numbers
should be limited to the simplo s t cases of these operations with
t numbers to whatever extont is reaquired for preparing
to study decimal freotione and for practicaal use in life.
In parti+ ular, operations with n hers r ...Ch express measures of time
should be made easier.
A substantial part of the pro ram of primary arlt:h::t Lie is made
up of goo trio material, the study of which gives some ',n owlet ;e and
experience to the abildron and. develops special concepts in them.
The study of this materi al
the whole course of primary so
teed and closely Interwoven with
in
bec
auce throuk;hout
=ore oorapli ea-
rre e s I ?ia,d II, in
the stue y of nurerati and op+ rations with numbers, sruares, rectangles,
hers refer to ma ,nitudeei oxprossed in units
tion? as maters 1;r, centimeters.
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circles, ctub
didecstie material. The a
and bodies, become father
graph paper, and m,asu,
r solids are employed as
Gb ttLin visual the s of those fi ;sure r
and trree than on
dth of rrcten~,ulr, r figures*
n in the .mer.uremt of
:a exercises are carried out
se rents of a straight line
of distances with the aid
In rade III children obt
ant of segments a
aid of a centimeter ruler and
,or or a tape mea sure.
? in more dif$'icult neasu
straight line
o: rc? e swing the
and milltereo
roam, but also out in
.re atrai ht
centimotrl'-C,
my in the class-
eloxont of
In Grade IV the pupils become ac min ted with a
with the calculation of arses having ctan~-,ultar form.
For the study of these subjEoetn precties.1 oxercisoc ?;re prov.
in mearturing the area of the el c s ro floor, the i lluninr~ ted area of
the elaer, the area of the ach of j ar en i' and of the as boolyrird, and
no on.
In the fell and sp
t;,i, on
heat*" on to
r a square?
d vi suall >-
d ratio ~s It a. construe
tpb- ?
or learning onus" riousure and cabcul tint-; area t
'to ett * cubic measure and learn to oalcul : to the vole a r~ bc+aA,ion heav
fort! (boxes, rocs). `:WO must be iz itee: ;;c the
f problems in - aich the dinenelons of thO si s i;. "t3 Avon
and it i s nece s nr7. to find the
of d"neions or rmxall objects,
a in
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In the calculation of eron end volume to notation in used which
in besed upon the rethod of meeeu nt of these magnitudes and in
easier for to -:eats in the prcry grtidoe?
notation is 6 sq* ta. x 4 Is 24 so* isa
About half or the time
mot
of the go,
.d be used for
pr-obles n .
The ability
solve
solution of
id speaking,
to doter
life.
(An o ruple of this
voted to erithretic in of acc >ork end.
toeehlnE? children thr solution of t1 rit h
roblems fool
etic pr+ bl~t9 in one of the basic
canoe of the e rlth etie
he development of the stuo
inration:, eru. their ability
Tong m nituder anc: to make correct
i; t solution of problemn helps to p r+ep re stu::~ont - for
The solution of problems hel
concrete meaning of ari th etio o!1ere tlor
e the diverse
eirc> snsts nCon in which they ore op lied, provides ale en L.: practice
pplicatidn o ssssn:.el reie and ?yntheo
B innin with the first steps in vehin and cx w,6An, through-
out the whole pour a of a ri t2r tic, the solution of prr blorre proceeds
parallel
In t
s olu,
hi
s to unc er s tand the
a necee r r ;, ,U.) adhere
in oin#?, 'ron ee.e r pr~obl.emn to rnor0 V ficult
oneey from, the simple
in Credessw I, II,
basic repeats of eim;?:
the pupils boeo ,e F4caut inter.'. v 4th the
ms in each of the four cri ti'mm is
In (trade I imrle probic ores solved. in tindi
zee. in increeein.; nnc7
of' tip ear
given nUnLort, in tindi
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the product (fin a given wriber is an addend several
ti.m aa) rnd in parts vision,,
In Grade II problems are solved in ccx perison by nubtrcteticm,~` in
finditg one of the addends from the Gunn of two .numbers and one of the numbers,
in finding the minuend from r, given *ubtrt9,hend and (1 #' 'o r r-nee, In
scent division, in inorev I2t i ecrr~ lira iven r- r~aere by
a times 0 9
in finding the fractional pe its of a nurnUee r, and in
oa as rison by divisicm.10
Partitive division refers to finding the size of the uxa.it- ;roue
When given the whole group and the number of groups. or ex zr ile,
how may people are tbore in each f;r-Oup if 100 people sro divided
into is groups? It contradte with measurement division, hioh con-
sists of finding the number of j r'oupa when given the whole ;ge p itni
.,a r the size or the amit-t;roup. x or exile, how ean L r
if 100 people are divided into groups of 20 people?
a - __.., 19 rsw..- ~.,? the a "!3rn in .. ,_ ride II
Litarel.ly, "cia< -or'(-ncsV 7 c entimstors lone nd the
a
text depicts two recten:l.ar bane? ot
boi?eters
other 4 eentimeterae with the nc~trtis n that one is 3 ce timete d
longer*" (A. + olko Gy. . Pollak, ri trneti3 ?~.
u%
ts"z
, ,
o kl+aa sa n tc t>'i aaRko ?C.
a ;~ to tv~ of nroblem in
4 th t;
tfini to ?numoerJ