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5
First Results of Teaching the Experimental
Curriculum
Because a stochastics curriculum is only now beginning to make its way
into the general school, while in high schools it is still at the pilot stage,
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Russian Mathematics Education: Programs and Practices
available only in certain regions, problems in probability and statistics
have not yet appeared on the State Exams taken after the 9th year (basic
school) or the 11th year (complete school).
Nevertheless, those regions that have introduced elements of
combinatorics, probability, and statistics into the general curriculum
do hold regional tests after each year of study. The content of these
tests accurately reflects performance expectations at every level of study;
thus, by looking at student performance, we can judge to what extent
these expectations are being met. In conclusion, let us consider a
test (Vysotsky and Borodkina, 2009) for the seventh grade, given
in Moscow schools in 2009, along with some statistics on student
performance.
Students have 45 min to complete their work. All necessary calcula-
tions may be carried out without a calculator; however, the students
are permitted to use calculators.
Grading criteria:
The highest mark (“excellent”) is given to students successfully
completing four problems of their choice; the mark “good” is given
to students successfully completing three of the problems below
(a calculation error should not be penalized when it is evident that
the student’s reasoning is correct); “satisfactory” is given to students
successfully completing two of the problems below, with a possible
calculation error.
Problems:
1. The following table shows the duration of different vacation
periods throughout the school year.
Fall
Winter
Spring
Summer
Days (total)
4
22
7
87
120
Which of the pie charts below accurately represents the distribu-
tion of vacation days as given in the table?
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Fig. 2.
2. The diagram below gives the total number of factory workers in
the Russian Federation in 1927 (numbers represent thousands of
workers). Use the diagram to answer the following questions:
Fig. 3.
(a) Which month saw the sharpest rise in the labor force?
(b) Compare the number of factory workers in July with that
in May. Give the approximate difference (in thousands of
workers).
(c) Which months in the latter half of the year saw a drop in the
number of workers?
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Russian Mathematics Education: Programs and Practices
3. The table below gives the number of Internet users in the 10
countries with the largest land areas in the world.
Country
Number of users (mln)
Russia
30
Canada
24
USA
220
China
213
Brazil
68
Australia
15
India
81
Argentina
11
Kazakhstan
2
Sudan
4
(a) Find the arithmetic mean of the total number of users.
(b) Find the median of the total number of users.
(c) Which of the two values better represents the number of
Internet users in these countries? Briefly explain your logic.
4. Swiss watchmakers use a special procedure to test the accuracy of
their watches. The test measures errors in time-keeping (in seconds
per 24 h period) at different temperatures, humidity levels, and
positions of the mechanism. A watch receives a certificate of
accuracy if the range of error does not exceed 4.5 s per 24 h period,
with a dispersion less than 3 s. If the mean error in either direction
exceeds 2 s, the watch must be recalibrated.
The following table gives the results of five tests of the same
mechanism.
Test number
1
2
3
4
5
Error(s)
−1.1 −2.7 −0.8 −5.5 −2.9
(a) Find the mean error, range, and dispersion of error.
(b) Determine whether this watch will receive a certificate of accu-
racy.
(c) Determine whether the watch must be recalibrated.
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5. The mean value of a set of numbers is 4; dispersion equals 18.
Each number in this set was replaced by its opposite. Find:
(a) the mean value of the new set;
(b) the dispersion of the new set.
We can gauge the success of teaching this material — new for
students and teachers alike — by performance statistics (Vysotsky,
Borodkina, 2009, p. 50):
Number of classes taking the exam: 2,538
Number of schools administering the exam: 1,193
Number of students taking the exam: 52,900
Grades
5 (excellent)
4 (good)
3 (satisfactory)
2 (poor)
Number of students
10,239
19,805
20,316
2,540
Percentage of students
19%
37%
38%
5%
The same data represented in a diagram:
Fig. 4.
The following table shows to what extent each problem was solved.
Problem No.
1
2a
2b
2c
3a
3b
3c
4a
4b
4c
5a
5b
Problem solved
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
(%)
Fully solved
82
75
76
67
90
83
68
40
45
47
29
24
Solved with minor
deficiency
1
2
4
10
3
3
5
12
3
3
1
1
Partly solved
1
2
3
6
1
2
4
12
3
3
1
1
Incorrectly solved
13
20
15
13
5
9
14
18
17
14
7
9
Not attempted
3
1
2
3
2
3
10
17
31
34
60
64
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Russian Mathematics Education: Programs and Practices
The same numbers represented in a diagram:
Fig. 5.
The following table and diagram show the breakdown by test score
of the total number of participating students.
Breakdown by score
Score
[0:1]
(1:2]
(2:3]
(3:4]
(4:5]
% solved
(0–20)
(20–40)
(40–60)
(60–80)
(80–100)
Number of students
1067
2821
16,013
18,794
14,205
% of students
2%
5%
30%
36%
27%
Fig. 6.
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