European Journal of Education Studies
ISSN: 2501 - 1111
ISSN-L: 2501 - 1111
Available on-line at: www.oapub.org/edu
10.5281/zenodo.162458
Volume 2│Issue 8│2016
THE EFFECT OF THE SUCCESS IN TEACHING GEOMETRY OF
BASIC LEVEL EDUCATION MATHEMATICS
Ayşe Yavuzi, Bünyamin Aydınii, Musa Avcıiii
i
Department Of Mathematics Education, Elementary School Math. Teaching Program,
Necmettin Erbakan University, Turkey
ii
Department Of Mathematics Education, Secondary School Math. Teaching Program,
Necmettin Erbakan University, Turkey
iii
Undergraduate of Department Of Mathematics Education, Secondary School Math. Teaching Program,
Necmettin Erbakan University, Turkey
.
Abstract:
The purpose of this study was to investigate primary and secondary mathematics
teachers’ candidates’ effect of the success in geometry education. The sample of the
study consists of students first and last class preservice primary mathematics teachers
which are enrolled program education at department of mathematics and students first
and last class in preservice secondary mathematics teachers enrolled to Necmettin
Erbakan University Ahmet Keleşoğlu Faculty of Education. As data collection tool, the
2016 Transition to Higher Education Examination questions asked in geometry was
used. Data obtained were analysed using Mann Whitney U test. Based on the findings,
investigated that in first and last class of primary classroom teacher candidates and in
first and last class of secondary mathematics teacher candidates were revealed in that
whether there were statistically significant differences in terms of their success.
Keywords: Mathematics education, geometry education, secondary mathematics
teachers’ candidates.
Copyright © The Author(s). All Rights Reserved
Published by Open Access Publishing Group ©2015.
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Ayşe Yavuz, Bünyamin Aydın, Musa Avcı THE EFFECT OF THE SUCCESS IN TEACHING GEOMETRY OF BASIC
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1.
Introduction
Mathematics is a branch of science which investigates the characteristics of abstract
concepts like number, quantity, geometrical shapes, expressions, operation etc. and
relations among these with reasoning methods (Tuncer, 1995). Mathematics, to
understand humanity`s objective reality, deals with some concepts to shape it from
objective reality and the relations among these concepts. Formulas and symbols are one
apiece tool or just the language of mathematics. For this reason mathematics is an
abstract systematic of the method that we use in art, law, in short in life
(Tepedelenlioğlu, 1995).
Geometry is a branch of science which helps an individual gain vision, ease
thinking and reach a solution by realizing the shapes before the eyes (Hızarcı, 2004).
Geometry, whose content area is shapes and objects, has an essential place in human
life. In science, art, architecture, engineering, in short in every element that humans
created geometry makes itself evident and nested with the daily life (Van De Walle,
2001). Geometry gives students opportunity to stimulate their minds, make mind
exercises and problem solving, comparing, generalizing and summarizing skills’
development. In general, geometry is a significant tool for a student to give meaning to
his/her surroundings (NCTM, 2000; Napitupulu, 2001). Geometry has a wide place in
understanding the axiomatic structure of mathematics and in mathematics program
which containing learning of students. Throughout the geometry topics, students learn
geometrical shapes, its structures, how to analyse its characteristics, and their relation
with one another. Geometry provides a natural setting for the students in the
development of their deduction, proving skills. Students may solve problems thanks to
geometry and may create a bond between mathematics and life (Duatepe, 2000).
Mathematics, particularly geometry, is a subject that students approach with
bias. To eliminate this bias and to provide a positive attitude for geometry can only be
possible with the education to be given to them (Pusey, 2003: 66-74). Geometric thinking
structure is closely related to the geometry education given in primary school era.
Teacher is an important factor during this process (Terzi, 2010). Geometrical field
knowledge and students’ knowing on which level they are geometrically are two
fundamental points necessary for an efficient geometry teaching (Toluk, taken from
1994: Toluk, Olkun ve Durmuş, 2002). Although geometry has a more concrete structure
of mathematics compared to other branches, forming geometrical concepts and
algebraic expressions used during problem solving show its abstract structure. Even
though presence of concrete structure creates a cognitive positive effect on recognizing
geometrical concepts, this situation does not mean that it can be learned more easily
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Ayşe Yavuz, Bünyamin Aydın, Musa Avcı THE EFFECT OF THE SUCCESS IN TEACHING GEOMETRY OF BASIC
LEVEL EDUCATION MATHEMATICS
compared to other branches of mathematics. And for this reason, teacher’s, as well as
field knowledge, transferring his/her knowledge to students, namely the pedagogic
field knowledge should also be strong. Transfer of concept delusion or knowledge
deficiency which are present in the teacher to the students, without a doubt, will be
inevitable. (Altaylı, Konyalıoğlu, Hızarcı, Kaplan, 2014).
Holmes group (1990) that investigates the question `how the twenty-first century
teacher should be` explains it as “if you want to increase the performance of the students, you
have to train quality teacher” (From: Baki et al., 1996). In the conducted studies, the first
step to interfere to increase the quality of the education was emphasized the necessity of
understanding the value and beliefs of those who had a role in execution of these
processes (Carter ve Norwood, 1997).
Some studies emphasized that geometrical thinking levels of primary and
secondary education students were below the expected level (Halat, 2006; Alex and
Mammen, 2012). In some studies, it was stated that geometrical thinking levels of
teachers and teachers` candidate were below the expected level (Olkun, Toluk and
Durmuş, 2002; Knight, 2006; Halat, 2008). When the studies conducted with these two
different samples are taken into consideration, it can be said that the reason students’
geometrical thinking levels were low is related to that teachers’ geometrical thinking
levels were low. Upon finding out the geometrical thinking levels of teachers and
teachers’ candidates and determining any lowness’s existence, it is of importance to find
the possible reasons of this lowness. On taking necessary precautions related to the
causes that occurred, it can be provided to increase the geometrical thinking levels of
teachers’ candidates and teachers, and so students (Çakmak, Güler).
From the above mentioned information, in this study investigation of
geometrical information levels of primary and secondary education mathematics
teachers’ candidates in terms of group variances. In linear to this purpose, answers
were sought to the following problems:
1. Is there a significant difference in the geometrical information levels of first and
last class students of primary education mathematics teaching?
2. Is there a significant difference between the geometrical information levels of
secondary education mathematics teaching first and last class students?
3. Is there a significant difference between the geometrical information levels of
primary education mathematics teaching first class and secondary education
mathematics teaching first class students?
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2.
Methodology
2.1
Sample and Working Group
Sampling of the study consist of 36 first and 38 last grade students enrolled in
Necmettin Erbakan University Ahmet Kelesoglu Faculty of Education as preservice
primary mathematics teacher and 22 first and 19 last grade students of preservice
secondary mathematics teachers.
2.2
Data Collecting Tool and Analysis of Data
As a data collecting tool in this study, questions asked in geometry in 2016 Transition to
Higher Education Examination are used. Students were given 1 point for each correct
answer and no point for incorrect answers in the success test. In a success test, a student
may get utmost 7 points.
Before analysing the collected data, normal distribution of data was checked, and
according to the result it was decided which parametric or non-parametric statistical
technique to be used. Since the sampling number was less than 50, to test the
conformity of data to normal distribution Shapiro-Wilks test was used (Yazıcıoğlu,
2004).
As a result of this conducted test, final significance test points were calculated as
p<.05 and information related to this test results is given in the findings section.
Since the collected data did not show a normal distribution, data of the study was
analyzed using Mann Whitney U-test which is a non-parametric equivalent of unrelated
t-test used to investigate significant differences.
3.
Findings and Comments
Percentage and frequency distribution related to test results applied to preservice
primary mathematics teacher department first and last grade are given in Table 3.1.
Table 3.1: Distribution related to test results applied to preservice primary mathematics teacher
department first and last grade
Grade Level
Correct number
f
%
2
1
2.8
3
1
2.8
Preservice Primary Mathematics Teacher
4
1
2.8
First Grade Students
5
5
13.9
6
13
36.1
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Ayşe Yavuz, Bünyamin Aydın, Musa Avcı THE EFFECT OF THE SUCCESS IN TEACHING GEOMETRY OF BASIC
LEVEL EDUCATION MATHEMATICS
7
15
41.7
Total
36
100.0
2
0
0
Preservice Primary Mathematics Teacher
3
2
5.3
Last Grade Students
4
2
5.3
5
2
5.3
6
8
21.1
7
24
63.2
Total
38
100.0
As it can be seen from the given table above, majority of the preservice mathematics
teacher department first grade students participated in the study (41.7%) does not have
incorrect answer. Along with this, a significant portion of the teachers’ candidate
participated in the study (36.1%) have only 1 incorrect answer. Some of them (13.9%)
answer 5 questions out of applied test questions. Additionally, majority of the questions
were answer incorrectly by a few of the students. These distributions are shown in the
figure below.
Figure 3.1
More than half of the Preservice Mathematics Teacher department last grade students
asked the study questions (63.2%) answered the questions fully correct. At the same
time, a significant portion (21.1%) answered only one question incorrect. These
distributions are stated on the figure below.
Table 3.2: Distribution related to test results applied to Preservice secondary mathematics
teacher department first and last class
Grade Level
Correct Number
f
%
2
4
18.2
Preservice Secondary Mathematics Teacher
3
4
18.2
First Grade Students
4
3
13.6
5
4
18.2
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LEVEL EDUCATION MATHEMATICS
6
7
6
27.3
1
4.5
22
100.0
2
0
0
Preservice Secondary Mathematics Teacher
3
0
0
Last Grade Students
4
2
10.5
5
2
10.5
6
9
47.4
7
6
31.6
19
100.0
Total
Total
Figure 3.2
Percentage and frequency distribution related to test results applied to Preservice
secondary mathematics teacher department first and last class are shown at Table 3.2.
Of the group which consisted of preservice secondary mathematics teacher department
first grade students, 27.3 percent answered 6 questions correct, 4.5 percent did 7 correct
and 13.6 percent did 4 correct. Remaining part, with the same percentage ratios,
answered the questions with 2, 3 and 5 correct answers. The figure that shows the
distribution of this group is below.
Figure 3.3
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According to the study results, of preservice mathematics teacher department last grade
students, 47.4% answered 6 of the directed geometry questions correctly. Likewise,
31.6% of the group answered all of the questions correctly. Remaining part, with the
same percentage ratio, answered 4 and 5 questions correctly. These expressions were
also shown in Table 3.4.
Figure 3.4
Results of Mann Whitney U test which is conducted to determine if there is significant
different between preservice mathematics teacher first grade and preservice
mathematics teacher last grade students in terms of geometrical knowledge are given in
Table 3.3.
Table 3.3: Results of Mann Whitney U-test conducted relating to the test points of groups
Groups
N
Mean Rank
Rank Sum
U
p
549.00
.109
Preservice Primary Mathematics Teacher First grade
36
33.75
1215.00
Preservice Primary Mathematics Teacher Last grade
38
41.05
1560.00
It can be referred from the Table 3.3 that the difference of the correct numbers` mean
rank in the geometry test is 7.3. To check the importance of this difference Mann
Whitney U test is conducted. As a result of the test no significant different between the
first and the last grade students’ correct answer numbers in the 7-item geometry test
(U=549.00, p>.05). Successes in geometry of 1st and 2nd group students have a similar
structure as it can be understood from the test results.
Mann Whitney U Test is conducted to see if there is a significant difference in
terms of geometric knowledge levels between preservice secondary mathematics
teacher first grade students and preservice secondary mathematics teacher last grade
students, or not. Obtained results are given at Table 3.4.
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Table 3.4: Mann Whitney U-test Results relating the Test Points of the Groups
Groups
N
Mean Rank
Rank Sum
Preservice Secondary Mathematics Teacher First grade
22
15.23
335.00
Preservice Secondary Mathematics Teacher Last grade
19
27.68
526.00
U
p
82.00 .001
From the Table 3.4, it can be seen that secondary education first grade group’s mean
rank is 15.23 and secondary education last grade group’s mean rank is 27.68. As a result
of Mann Whitney U-test, it is confirmed that the difference between group’s geometry
test points is statistically significant (U=82.00; p<.05). This finding show that compared
to preservice secondary mathematics teacher first grade students, preservice secondary
mathematics teacher last grade students have a significantly increased geometry success
point.
At Table 3.5, results of Mann Whitney U-test conducted to determine if there is a
significant difference between the geometrical knowledge levels of preservice primary
mathematics teacher first grade students and preservice secondary mathematics teacher
first grade students.
Table 3.5: Results of Mann Whitney U-test related to Test Points of Groups
Groups
N
Mean Rank
Rank Sum
U
p
Preservice primary mathematics teacher first grade
22
18.45
406.00
153.000
.000
Preservice secondary mathematics teacher first grade
36
36.25
1305.00
When the Table 3.5 was inspected, it was found that means rank of preservice primary
mathematics teacher first grade group was 18.45 and means rank of preservice
secondary mathematics teacher first grade group was 36.25. It was also confirmed that
the difference of test results of preservice primary mathematics teacher first grade
students and preservice secondary mathematics teacher first grade students was
statistically significant (U=153.00; p<.05). According to this finding, it can be said that
the groups are not equal in terms of success.
4.
Results and Suggestions
In this study in which the success in geometry of preservice primary mathematics
teacher students and preservice secondary mathematics teacher students are compared,
the following results are found.
In terms of mean of correct answers in geometry test, it has been detected that
there is no significant difference in geometric knowledge levels of preservice primary
mathematics teacher first grade students and preservice primary mathematics teacher
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last grade students. When correct number of answers of the test between preservice
mathematics teacher last grade students and preservice mathematics teacher first grade
students is compared, significant differences in favor of preservice secondary
mathematics teacher last grade students are found. A significant different is confirmed
between the test results of preservice primary mathematics teacher first grade student
and preservice secondary mathematics teacher first grade students. Therefore, there
was no different between the higher education entry examination scores of both of these
two groups, we can attribute this success to the geometry course given in the first
grade. As a result, we can say that, based on the observation of the study, there is a
direct proportion between having geometry course and success.
In education, the topic of teacher`s training and increasing their quality is one of
the most accentuated and discussed one. To train a teacher who can respond to the
needs of the information era it is essential to choose individuals who have the expected
knowledge and skills from a teacher (Oğuzkan, 1985). Along with this, it is expected to
provide these individuals with the education that can support the knowledge and skills
so that quality teachers can be trained. Ausubel ve Robinson (1969) have defined the
qualifications of a good teacher as; “high mental capacity, strong field knowledge,
academically prepared, sufficient development and teaching knowledge, having desired
characteristics” (Güçlü, 1996).
Proficiency fields of teachers are accumulated under three titles which are in
general field knowledge, professional teaching knowledge and general culture. There
are foreseen to be provided to the teachers’ candidate during the preservice teacher
training phase. As students have an education on a certain topic, their thinking level on
that topic is expected to increase. An education which does not increase the thinking
level of a student remained limited or even makes no headway (Clements & Battista,
1992). In this context, importance of the content of the undergraduate education comes
to existence. Courses in the programs of teacher training institutes and content of these
courses are regulated according to the foreseen proficiency to be provided to the
teachers.
Durmus, Toluk and Olkun, during their studies, stated that students of
mathematics teacher did not show the expected progress, both in geometry test and van
Hiele Geometric Thinking Test, in areas of geometry that requires high level thinking
like generalizing, classification (Durmuş, Toluk, Olkun).
Dindyal (2005), during his study, confirmed positive and significant relations
between students’ algebraic thinking levels and geometric thinking levels, and while
one increases, the other one also increases, and while one decreases the other one also
decreases. He also shows that geometric thinking level is not only connected to the
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geometry courses. Geometric thinking is not only related to algebra. Spatial thinking
contains skills related to the use of space and geometric forms (Olkun, 2003).
When the studies conducted in this field are investigated, it is generally observed
that in institutions where mathematics teachers are trained lack of geometry courses, in
general, is confirmed and therefore mathematics teachers’ candidates are also
insufficient in terms of geometric knowledge level. In accordance with the finding and
results obtained in this study, the followings can be suggested:
∑
The courses which are in the programs of the institutes that train mathematics
teachers and content of these courses should be regulated according to the
∑
proficiencies foreseen to bring to the teachers.
∑
teaching department should be increased.
∑
last grades.
Class hour and content of the course which is present to primary mathematics
Geometry courses should be added to the elective courses in the curriculum of
Teachers’ candidate should be given change to test their knowledge and to
develop skills and insufficient knowledge and skills efforts should be given.
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