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PRACTISING CRITICAL THINKING SKILLS WITH SIEVE OF ERATOSTHENES
ANALYSISI OF THE NUMBERS IN MATHEMATICS CLASSES
Samandarov Toji Normurodovich
The Mathematics teacher of the UNIVERSITY OF BUSINESS AND SCIENCE,
Tashkent, Uzbekistan
https://doi.org/10.5281/zenodo.15671689
Abstract:
This thesis depicts that implementing ‘‘sieve of Eratosthenes” approach can
be highly effective for fostering critical thinking skills of the language learners. In
mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime
numbers up to any given limit.
Keywords:
sieve of Eratosthenes, Critical thinking, math analysis, Math classes,”
Socratic questions”, approach, JASP.
While fluency and accuracy are indeed crucial aspects of math, it is also essential to
foster higher-order thinking skills (HOTS) in the mathematics classroom. By promoting
critical thinking and encouraging students to engage in meaningful communication, we can
help them become more proficient math users in a variety of contexts.
When students activate their critical thinking skills in the mathematics learning process,
they go beyond rote memorization and passive comprehension. They learn to analyze,
evaluate, and synthesize information in the target ideas, enabling them to use it effectively
and creatively. Two groups were involved for the pilot study as treatment group and
comparison group. All the calculations were transformed to special statistical program for
further descriptions.
Paired Samples T-Test
Measure 1
Measure 2
t
df
p
Cohen's d
simple prime numbers
analysis
-
analysis Soc questions_
100
37
23
37%
Note.
For all tests, the alternative hypothesis specifies that simple prime numbers
analysis_CT is greater than gr analysis Soc questions_CT.
Note.
Student's t-test.
Assumption Checks
Test of Normality (Shapiro-Wilk)
W
p
simple prime numbers analysis_CT
-
gr analysis Soc questions_CT
38%
62%
Note.
Significant results suggest a deviation from normality.
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Descriptives
N SD SE
Coefficient of variation
simple prime numbers analysis_CT
100
38
62
0.38
gr analysis Soc questions_CT
100
39
61
0.39
Descriptives Plots
simple prime number analysis_CT - gr analysis Soc questions_CT
Prime
numbers
are
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97, ….
Example 2
To find all the prime numbers less than or equal to 30, proceed as follows.
First, generate a list of integers from 2 to 30:
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Density Plot
As shown in figures, in density plot bell curve was formed which emphasizes that the
tasks were normally distributed. The treatment group outperformed the comparison group in
the sieve of Eratosthenes analysis tasks. The treatment group showed a mean score of 3,9
whereas the comparison group had a mean score of 2,6. The independent samples
t
-test
revealed that there is a statistically significant difference between the two groups.
References:
Используемая литература:
Foydalanilgan adabiyotlar:
1.
de Bruijn, N.G. (1950): On the number of uncancelled elements in the sieve of
65
Eratosthenes. Proc. Konink. Nederl. Acad. Wetensch. 53, 803-812 Indag. Math. 12, 247-256
2.
Brun, W. (1920): Le crible d'Eratosthene et le théorème de Goldbach. Videnskaps. Skr.,
Mat.-Naturv. Cl. Christiania. No. 3. 36pp.
3.
Buchstab, A.A. (1937): An asymptotic estimate of a general number-theoretic func-tion
(Russian). Mat. Sbornik (2) 44, 1239-1246
4.
Buchstab, A.A. (1938): New improvements in the method of the sieve of Eratos-thenes
(Russian). Mat. Sbornik (2) 4 (46), 375-387
5.
Buchstab, A.A. (1965): A combinatorial intensification of the sieve of Eratosthenes.
Uspehi Mat. Nauk 22, 199-226 (Russian). [English transl.: Russ. Math. Surv. 22, 205-233)
6.
Browne, M. N., & Keeley, S. M. (2012). Asking the Right Questions: A Guide to Critical
thinking.
