| Abstract |
The present research is focused in the investigation of the ability to apply estimation
and checking criteriaof the algorithms of the arithmetic operations. Its aim is: a) to study the
development of the ability to apply estimation and checking criteriaof the algorithms of the
arithmetic operations, b) to examine the relation between the ability to apply estimation and
checking criteria of the algorithms of the arithmetic operations and other mathematical
abilities as well as the ability to apply other type estimation criteria and c) to determine the
characteristics of the individuals that have the ability to apply estimation and checking criteria
of the algorithms of the arithmetic operations and the factors that contribute to this ability
significantly.
The methodology of the research is consisted in: a) giving a test and v) the realisation
of an interview. The sample of the research is composed of 304 5
th
grade students, 329 6
th
grade students, 252 10
th
grade students, 261 11
th
grade students that attended schools in
Heraklion as well as 244 students of the Department of Education of University of Crete. The
test was given to all the subjects of the research in two versions: one for the 5
th
and 6
th
grade
students and another one for the 10
th
and 11
th
grade students and the University students. The
interview was realised in students which had filled in the test. Specifically, according to their
success in the estimation calculations, 37 students were selected with excellent or very good
record, 34 students with mediocre record and 35 students with low record.
According to the analysis of the results that concern the test, the slow development of
the ability to apply estimation and checking criteria of the algorithms of the arithmetic
operations emerges. Up to the 10
th
grade no differentiationis observed while the 11
th
grade
students have significantly better record than the 10
th
grade students as well as the University
students than the 11
th
grade students. Also, the low record atthe estimation calculations is
obvious atall the age groups.
The results indicate that there is a high correlation between the ability to apply
estimation and checking criteriaof the algorithms of the arithmetic operationsand the ability
to do precise mental calculationsas well as the ability to solve problems of proportionality.
Besides, there is a correlationwith the ability to do arithmetic operations vertically and the
ability to solve problemsof additive structures. Regarding the relationbetween the ability to
apply estimation and checking criteriaof the algorithms of the arithmetic operations and the
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ability to apply other type estimation criteria, it appears that there is a correlation with the
ability to estimate the mean of numerical data, volume estimation and numerosity estimation.
According to the analysis of the results that concern the interview as well asthe test,
specific characteristics of the individuals that have the ability to apply estimation and
checking criteria of the algorithms of the arithmetic operations were determined and
specifically: a) good mathematic background and mainly good record at precise mental
calculations and atproblems of proportionality, v) preference tothe course ofMathematics, c)
positive self-concept about their ability to apply estimation and checking criteria of the
algorithms of the arithmetic operations, d) positive self-concept about their ability to do
precise mental calculations from the first classes of Public school, e) positive self-concept
about their memory ability and particularly about their numerical data memory ability, f) high
parents’ educative level and particularly father’sone, g) academic ambitions and h) sex (the
boys have better record at the estimation calculations). These characteristics, constitute
factors which can contribute to the ability of doing estimation calculations in a big
percentage, according to the analysis of multiple linear regression.
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