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Cite as: Yıldız, A., Baltacı, S. & Kartal, B. (2020). Examining the relationship between pre-service mathematics teachers’
mathematical thinking level and attitude towards mathematics courses. Acta Didactica Napocensia, 13(2), 256-270,
https://doi.org/10.24193/adn.13.2.17
Volume 13, Number 2, 2020 - DOI: 10.24193/adn.13.2.17
EXAMINING THE RELATIONSHIP BETWEEN PRE-SERVICE
MATHEMATICS TEACHERS’ MATHEMATICAL THINKING
LEVEL AND ATTITUDE TOWARDS MATHEMATICS COURSES
Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Abstract: This study is correlational research and aims to investigate the relationship between pre-
service mathematics teachers' mathematical thinking levels and attitudes for courses in
mathematics. We also examined whether gender, reasons for career choice, and academic
achievement lead to significant differences in pre-service teachers' attitudes and mathematical
thinking levels. Participants are 109 senior pre-service mathematics teachers from three different
state universities that have similar conditions. Participants are selected via convenience sampling.
Seventy-nine of the participants are female, and 30 are male. "Attitude scale for courses in
mathematics" and "Mathematical Thinking Scale" are used to collect data. Data were analyzed by
using SPSS package program. Pre-service teachers are found to have moderate attitudes while their
mathematical thinking levels are at a high-level in the sub-domains of higher-order thinking
tendency, reasoning, and problem-solving and at a moderate level in the subdomain of
mathematical thinking skill. Pre-service teachers' attitudes for courses in mathematics have a
significant moderate relationship with higher order thinking tendency, and reasoning and have a
significant and weak relationship with problem-solving.
Key words: Mathematical thinking, Attitudes, Attitudes for courses in mathematics, Pre-service
mathematics teachers, Correlation
1. Introduction
The permanency and utility of learning about content depend on individuals' attitudes towards that
content (Eshun, 2004; Kupari & Nissinen, 2013). Baki, Kösa, and, Berigel (2007) suggested that
permanent change in behaviors may occur if positive attitudes towards the content are developed.
From this viewpoint, it is possible to say that individuals' positive attitudes towards content promote
their content-related success. National Council of Teachers of Mathematics (NCTM) (2000) argued
that students' attitudes towards mathematics could affect their mathematical knowledge, interest,
performance, and willingness to learn mathematics and their thoughts about the mathematics course.
The importance of students' mathematic attitudes makes teachers' in-class behaviors more important
and makes it essential to determine pre-service teachers' attitudes that can affect their future students.
Attitude towards mathematics is an essential factor that is closely related to the students' behaviors and
motivation in this course. Attitudes towards mathematics are related to liking mathematics, being
disposed to engage with mathematical activities, and beliefs about mathematics abilities, and
mathematics value (Ma & Kishor, 1997). Students with positive attitudes enjoy mathematics and
engaging with mathematics, and they believe that he/she is good at mathematics and that mathematics
is useful (Kartal, 2020). On the other hand, students with negative attitudes do vice versa. Leder
(1992) identifies that the fundamental purpose of mathematics should be to make students develop
positive attitudes towards mathematics. Students' attitudes toward learning mathematics may play a
crucial role in mathematics education (Kislenko, Grevholm & Lepik, 2005). Students who have
negative attitudes towards mathematics are inclined to avoid doing mathematics and believe that they
are incapable of mathematics (Aljaberi, 2014; Kargar, Tarmizi & Bayat, 2010).
Students' prior experiences related to mathematics lead to positive or negative attitudes towards
learning mathematics (Beswick, 2006; Raymond, 1997). Most of the students in Turkey believe that
Examining the relationship between pre-service mathematics teachers’ mathematical thinking level and attitude 257
Volume 13 Number 2, 2020
mathematics is difficult to learn; they feel anxious because of the low level of self-efficacy in
mathematics, and develop negative attitudes towards mathematics (Baykul, 2000; Duru, Akgün &
Özdemir, 2005; Günhan & Başer, 2008; Küçük, Kahraman & İşleyen, 2013). It is known that pre-
service teachers also have negative attitudes toward mathematics (Lutovac & Kaasila, 2011). Teachers
with negative attitudes may prefer traditional teaching methods and reflect their feelings, such as
mathematics anxiety (Pietila, 2002), or overprotect their students from unfavorable learning
experiences (Gellert, 2000). Teachers' attitudes towards mathematics also significantly affect their
students' attitudes (Ford, 1994). Pre-Service teachers may lead to unfavorable experiences for their
students when they became teachers. Teacher educators should enhance teacher preparation programs
to prevent these undesired results. Identifying pre-service teachers' attitudes and articulating the
relationship between pre-service teachers' attitudes and mathematical thinking levels may be an
efficient way to overcome difficulties stemming from unfavorable teacher attitudes.
Mathematical thinking is the process of finding the unknown from the known that includes assuming,
gathering evidence, and generalization (Baki, 2008; Breen & O'Shea, 2010). Liu (1996) also defined
mathematical thinking as the union of the prediction, induction, deduction, representation,
generalization, formal and informal reasoning, and verification. It is seen that the definitions of
mathematical thinking highlight higher-order thinking, reasoning, and problem-solving.
Mathematical thinking helps individuals acquire and understand the needed knowledge and problem-
solving skills (Katagiri, 2006). Mathematical thinking may occur in routine and non-routine problem-
solving when individuals identify the solving strategies, interpret the given information in the
problem, justify the problem solution, and convince the others who think differently (Breen & O'Shea,
2010; Schoenfeld, 1992). On the other hand, the strength of attitudes affects the depth of mathematical
knowledge (Ernest, 1988). Attitudes towards mathematics promote thinking about mathematical
methods and content (Katagiri, 2006). Therefore, high-level mathematical thinking has the potential of
developing positive attitudes towards mathematics (Kargar et al., 2010). Individuals who have
positive attitudes tend to engage with mathematical activities, learn mathematics more permanently,
take advanced mathematics courses, and choose a career related to mathematics (Liu & Niess, 2006).
Negative attitudes restrict preservice teachers' learning experiences (Battista, 1986). It is possible to
say that students' knowledge would differentiate via mathematical thinking, which would change their
attitudes towards mathematics.
Trends in International Mathematics and Science Study (TIMSS) results of Turkey are below of
international average even though an increase occurs. For example, Turkey is ranked 31st with 429
points in 1999, 30th with 432 points in 2007, 24th with 452 points in 2011, and 24th with 458 points
(Bütüner & Güler, 2017). Programme for International Student Assessment (PISA) results also
indicate Turkey is under the average of the Organisation for Economic Co-operation and Development
OECD countries (Aydın, Sarıer & Uysal, 2012). Teachers' negative emotions and opinions related to
mathematics may be associated with these undesired results. On the other hand, pre-service teachers in
Turkey have a national exam to be employed as a teacher. Secondary school pre-service mathematics
teachers had a success average of 12,478 (Sd=5,219) in 50 questions in content knowledge test in 2018
(ÖSYM, 2018). The average of pre-service teachers is lower than expected. This study aims to
investigate pre-service teachers’ attitudes towards mathematics courses and mathematical thinking,
and the relationship between these constructs. Recommendations of this study may affect pre-service
teachers’ academic achievement in their mathematics courses.
Researches related to pre-service teachers’ attitudes towards mathematics in Turkey mostly
investigates the attitudes in terms of variables such as gender and grade level (Boran, Aslaner &
Çakan, 2013; Bulut, Yetkin & Kazak, 2002; Cakiroğlu & Isiksal, 2009; Celik & Bindak, 2005; Duru et
al., 2005; Kandemir, 2007; Küçük et al., 2013; Memnun & Akkaya, 2012). Unlike these studies,
Sarpkaya, Arık, and Kaplan (2011) examined pre-service mathematics teachers’ attitudes towards
mathematics and awareness of using metacognition strategies. On the other hand, there are up-to-date
researches that examined the relationship between attitudes towards mathematics and achievement,
motivation, and performance (Bakar et al., 2010), mathematical thinking and mathematics anxiety
(Kargar et al., 2010), and problem-solving skills (Marchiş, 2013).
258 Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Acta Didactica Napocensia, ISSN 2065-1430
Researches related to mathematical thinking in Turkey focused on the development of mathematical
thinking (Alkan & Bukova-Güzel, 2005; Bukova-Güzel, 2008; Kılıç, Tunç-Pekkan & Karatoprak,
2013) and mathematical thinking processes (Arslan & Yıldız, 2010; Keskin, Akbaba & Altun, 2013;
Yeşildere & Türnüklü, 2007; Yıldırım & Yavuzsoy-Köse, 2017). Arslan and İlkörücü (2018)
examined pre-service science and mathematics teachers' mathematical thinking. Yorulmaz, Altuntaş,
and Sidekli (2017) also investigated the relationship between pre-service elementary teachers'
mathematical thinking and mathematics teaching anxiety.
Mathematical thinking and attitudes towards mathematics affect academic achievement, and teachers'
attitudes play an essential role in students' attitudes. Given these results, we can say that it is essential
to examine the relationship between pre-service mathematics teachers’ mathematical thinking and
attitudes towards mathematics courses. Only one study (Aljaberi, 2014) has examined the relationship
between pre-service elementary school teachers’ mathematical thinking and attitudes towards
mathematics. This study has considered attitudes towards mathematics courses that pre-service
teachers take in their undergraduate education, and this special consideration distinguishes this study
from the mentioned study. The research questions are specified as follows:
1. Do senior pre-service mathematics teachers’ attitudes towards mathematics courses differ
significantly in terms of gender, their reasons for career choice, and their academic achievement?
2. Do senior pre-service mathematics teachers’ mathematical thinking differ significantly in terms of
gender, their reasons for career choice, and their academic achievement?
3. Is there a relationship between senior pre-service mathematics teachers’ attitudes towards
mathematics courses and mathematical thinking?
2. Methodology
2.1. Research design
This study that investigates the relationship between pre-service secondary school mathematics
teachers’ attitudes towards mathematics courses and mathematical thinking is correlational research.
Researchers aim to reveal the relationship between two or more variables without manipulating or
intervening in individuals' experiences and behaviors in correlational research (Fraenkel, Wallen &
Hyun, 2011; Plano-Clark & Creswell, 2015). Correlational research also seeks how a change in one of
the variables affects the other variable's change. This study examines what kind of a change in
attitudes towards mathematics courses may occur when a change in mathematical thinking occurs.
2.2. Participants
At least 30 subjects selected via convenience sampling is enough for correlational research (Fraenkel
et al., 2011). A sample size of more than 30 can provide less error variance and can support to have
propositions that would explain the relationships better (Creswell, 2012).
Senior pre-service mathematics teachers participated in the study because senior pre-service teachers
have taken all the mathematics courses in their undergraduate education. Their mathematical thinking
level may be regarded as enough to reveal the relationship with attitudes towards mathematics courses.
Participants are 109 senior pre-service secondary school mathematics teachers from three different
universities in Turkey in the 2018-2019 academic year. Pre-service mathematics teachers must receive
a bachelor’s degree to be employed as a mathematics teacher. Besides, teacher preparation programs
admit students based on the results of a national examination called Higher Education Institutions
Entrance Exam. The universities from which data was collected require similar national exam-based
results to enter a mathematics teacher preparation program, and have similar physical and technical
conditions. Additionally, mathematics teacher preparation programs follow a similar curriculum
proposed by the Higher Education Council. Seventy-nine of the participants are female, and 30 are
male.
Examining the relationship between pre-service mathematics teachers’ mathematical thinking level and attitude 259
Volume 13 Number 2, 2020
2.3. Data collection tools
Attitude Scale for Courses in Mathematics and Mathematical Thinking Scale were used to collect data.
Detailed information about these scales is given below.
2.3.1. Attitude Scale for Courses in Mathematics. The scale is developed by Turanlı, Karakaş, and
Keçeli (2008), and it aims to examine pre-service mathematics teachers’ attitudes towards
mathematics courses. This five-point Likert scale consists of 20 items; 11 are positively worded, and
nine are negatively worded. The Cronbach’s Alpha was reported as .93 in the original article. We
calculated the reliability coefficient for this study with the data obtained from 109 pre-service teachers
and found the coefficient as .934, indicating high reliability.
2.3.2. Mathematical Thinking Scale. The scale is developed by Ersoy and Başer (2013) to examine
senior pre-service mathematics teachers' mathematical thinking levels. This five-point Likert scale
consists of 25 items and four factors. Twenty items are positively worded, while 5 of them are
negatively worded. The factors are high order thinking tendency (6 items), reasoning (4 items),
mathematical thinking skill (8 items), and problem-solving (7 items). The maximum score is 125, and
the minimum is 25 for the scale. The total score obtained from items is used for data analysis. A
higher total score means a higher level of mathematical thinking (Ersoy & Başer, 2013). The
Cronbach's alpha is reported as .78 in the original form, and calculated as .759 in this study.
There are three types of evidence of validity researchers should consider; content-related evidence of
validity, criterion-related evidence of validity, and construct-related evidence of validity. Expert
review (asking knowledgeable people to assess items of the instrument in terms of content and format)
is a way to obtain content-related evidence of validity. Researchers reported that experts judged items
of both instruments used in this study to clarify they have the appropriate content and format to
measure mathematical thinking and attitudes towards mathematics courses (Ersoy & Başer, 2013;
Turanlı et al., 2008). The criterion-related evidence was obtained by comparing the participants' scores
of the mathematical thinking scale and the attitude scale for mathematics courses with their academic
achievement as an independent criterion (Fraenkel et al., 2011). Lastly, the think-aloud strategy was
used to ensure construct validity (Bowles, 2010). Three pre-service teachers from different participant
universities were asked to read, think, and answer the items in the instruments aloud to determine how
pre-service teachers understand the items.
Plano-Clark and Creswell (2015) suggested that mentioning the other research that used the same
instruments, asking experts to review the instrument’s content, and revealing relationships between the
scores from the instruments and other variables are good validity indicators. The results of the study
may be considered valid because of having all these indicators.
2.4. Data collection process
Threats to internal and external validity were attempted to minimize in the data collection process.
Data were collected in one session via different data collectors. Administering the data instruments in
one session may support to preclude the threat of instrument decay. On the other hand, different data
collectors may also overcome the bias derived from only one data collector’s characteristic (Fraenkel
et al., 2011). Data were collected in three different universities. The conditions of universities were
similar, and this has affected our choice of universities. This choice is important because similar
characteristics of different locations may minimize the threats to internal validity (Creswell, 2012).
Lastly, collecting data face to face from participants has been expected to minimize data loss
(mortality) (Fraenkel et al., 2011). Assigning individuals randomly to collect data and encouraging as
many participants as possible to respond may also increase the opportunity to generalize our results to
the population of senior pre-service mathematics teachers.
2.5. Data analysis
Data collected from pre-service teachers were analyzed by using the SPSS packet program. We first
entered the data into the SPSS environment and then controlled whether missing data exists or not.
SPSS used the mean as an estimate for missing data. Both data collection tools consist of negatively
260 Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Acta Didactica Napocensia, ISSN 2065-1430
worded items. These items were reverse-coded ranging from 1 (completely agree) and 5 (completely
disagree). After these adjustments, the normality of the data was investigated.
Non-parametric tests were utilized in data analysis because data is significantly different from the
normal distribution. Mann-Whitney U test was used to determine whether there is a significant
difference in pre-service teachers' attitudes towards mathematics courses and their mathematical
thinking in terms of gender. Besides, the Kruskal-Wallis test was also employed to identify a
significant difference in pre-service teachers’ attitudes towards mathematics courses and their
mathematical thinking in terms of reasons for career choice and academic achievement. In case of
revealing a significant difference from the Kruskal-Wallis test, the Mann-Whitney U test was
performed again by selecting groups in twos to determine the source of the significant difference
(Field, 2009).
Correlation analysis was conducted to reveal the relationship between pre-service teachers’ attitudes
towards mathematics and mathematical thinking. Correlation analysis is a statistical test used to
identify the trend or the pattern between two variables or two data sets (Creswell, 2012). Spearman’s
Rho (ρ) was used to interpret results as data does not have a normal distribution. The Correlation
coefficient (ρ) gives the degree of the relationship between variables, while the square of correlation
coefficient (ρ2) gives the strength of the relationship. In other words, it is the extent to which the
variance in a variable is explained by another variable. If the correlation coefficient is less than 0.30,
the relationship is considered as weak; if the coefficient is in the range of .30-.70, the relationship is
considered as moderate; and if the correlation is more than .70, the relationship is considered as strong
(Büyüköztürk, 2011).
Table 1 was used to interpret the levels of pre-service teachers' mathematical thinking and its sub-
domains and attitudes towards mathematics courses. Maximum and minimum scores that can be
obtained from scales and sub-scales were identified, and the minimum score has been subtracted from
the maximum score. The result was divided into three because we considered three levels as low,
moderate, and high.
Table 1. Ranges used to interpret mathematical thinking and attitude levels
Low
Moderate
High
The Sub-Domains of
Mathematical Thinking
Scale
Higher-order thinking
tendency
6-13.,33
13.34-21.67
21.68-30
Reasoning
4-8.66
8.6-14.33
14.34-20
Mathematical thinking skill
8-18
19-29
30-40
Problem-solving
7-15.66
15.67-25.33
25.34-35
Mathematical Thinking
Scale
Total score
5-44.33
44.34-84.67
84.68-125
Attitude Scale for
Courses in
Mathematics
Total score
20-46
47-73
73-100
3. Findings
Kolmogorov-Smirnov test was employed to examine whether the data obtained from the mathematical
thinking scale and attitude scale for mathematics courses had a normal distribution or not. Table 2
indicates the Kolmogorov-Smirnov test results and the levels of pre-service teachers’ levels of
mathematical thinking and attitudes.
Examining the relationship between pre-service mathematics teachers’ mathematical thinking level and attitude 261
Volume 13 Number 2, 2020
Table 2. One sample Kolmogorov-Smirnov test results for the subdomains of mathematical thinking scale and
attitude scale for courses in mathematics
Level
Higher-order thinking tendency
109
25.100
2.759
High
0.005*
Reasoning
109
17.588
2.083
High
0.000*
Mathematical thinking skill
109
29.752
3.113
Moderate
0.004*
Problem-solving
109
26.624
2.808
High
0.007*
Mathematical Thinking Scale Total
Score
109
99.064
8.040
High
0.200
Attitude for Courses in Mathematics
109
71.266
14.108
Moderate
0.010*
Table 2 indicates that pre-service secondary school mathematics teachers have a high level of higher-
order thinking tendency, reasoning, problem-solving, and a moderate level of mathematical thinking
skill. Considering the overall scale of mathematical thinking results, we can say that participants have
a high level of mathematical thinking. However, pre-service teachers’ attitude level for mathematics
courses is found to be at a moderate level.
Normality test results reveal that data obtained from the attitude scale and the subdomains of
mathematical thinking tendency, reasoning, mathematical thinking skill, and problem-solving have
significantly differed from a normal distribution (p<.05). In other words, data does not have a normal
distribution, and for this reason, non-parametric tests were utilized in data analysis.
3.1. Findings related to the first research question
Mann-Whitney U test was employed to examine whether pre-service teachers’ attitudes for
mathematics courses differ in terms of gender, and Table 3 shows the results.
Table 3. Pre-service teachers’ attitudes for courses in mathematics in terms of gender
Groups
Mean Rank
Sum of ranks
M-Whitney U
Male
30
59,12
1773.50
1061.50
-0.838
0.402
Female
79
53,44
4221.50
*p < .05
Table 3 presents that male pre-service teachers have more positive attitudes for courses in mathematics
than female pre-service teachers. However, this difference between the means of males and females is
not statistically significant (p=0.402>.05).
Pre-service teachers' attitudes for courses in mathematics were examined in order to reveal whether
there is a significant difference in terms of their reasons for career choice. For this purpose, the
Kruskal-Wallis test was utilized, and the results are given in Table 4.
Table 4. Pre-service teachers' attitudes for courses in mathematics in terms of the reason for career choice
Reasons for career choice
N
Mean Rank
p
Intrinsic reasons
78
60.28
8.200
0.017*
Family guidance
18
45.31
Other
13
36.77
*p <.05
Pre-service teachers’ attitudes differ significantly in terms of the reasons for career choice. Mann-
Whitney U test was performed by selecting groups in twos to determine the source of the significant
difference. Mann-Whitney U test results indicate that pre-service teachers who chose to teach as a
262 Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Acta Didactica Napocensia, ISSN 2065-1430
career with intrinsic reasons have significantly more positive attitudes than those who chose this career
for other reasons such as a teacher or peer guidance (U=283,000; p=.011 < .05).
Whether there was a significant difference in pre-service teachers’ attitudes for courses in mathematics
in terms of academic achievement was investigated by utilizing the Kruskal-Wallis test (Table 5).
Table 5. Pre-service teachers’ attitudes for courses in mathematics in terms of academic achievement
Academic Achievement
N
Mean Rank
p
1.51-2.00
6
19.92
17.695
0.001*
2.01-2.50
25
40.94
2.51-3.00
53
60.17
3.01-3.50
20
64.08
3.51-4.00
5
76.30
*p <.05
Table 5 indicates that pre-service teachers’ attitudes have differed significantly in terms of academic
achievement (χ2=17,695; p < .05). The groups that were arranged based on academic achievement
were selected in twos, and the Mann-Whitney U test was utilized to examine the source of the
significant difference. Pre-service teachers who are at an academic level between 1,51-2,00 have been
found to have less positive attitudes than those who are at an academic level between 2,01-2,50
(U=32,500; p=.033 < .05), between 2,51-3,00 (U=49,500; p=.006 < .05), and between 3,51-4,00
(U=1,000; p=.011 < .05). Pre-service teachers whose achievement level is between 2,51-3,00 have
been seen to have more positive attitudes than those whose achievement level is between 2,01-2,50
(U=425,000; p=.011 < .05) and pre-service teachers whose achievement level is between 3,51-4,00
have been seen to have more positive attitudes than those whose achievement level is between 3,01-
3,50 (U=14,500; p=.007 < .05).
3.2. Findings related to the second research question
Research question 2 is related to the existing significant differences in pre-service teachers’ levels in
the subdomains of mathematical thinking scale in terms of gender, the reasons for career choice, and
academic achievement.
Table 6 indicates the results of the Mann Whitney U test that was employed to investigate whether
there were significant differences in participants’ levels of higher-order thinking tendency, reasoning,
mathematical thinking skill, and problem-solving in terms of gender.
Table 6. Pre-service teachers’ levels in the subdomains of mathematical thinking scale in terms of gender
Groups
Mean Rank
Sum of
Ranks
M-
Whitney
U
Higher-order
thinking
tendency
Male
30
25.500
59.42
1782.50
1052.500
-.905
.365
Female
79
24.950
53.32
4212.50
Reasoning
Male
30
17.667
55.90
1677.00
1158.000
-.186
.852
Female
79
17.557
54.66
4318.00
Mathematical
thinking skill
Male
30
30.033
57.95
1738.50
1096.500
-.604
.546
Female
79
29.646
53.88
4256.50
Problem-
solving
Male
30
27.233
63.28
1898.50
936.500
-1.696
.090
Female
79
26.392
51.85
4096.50
Examining the relationship between pre-service mathematics teachers’ mathematical thinking level and attitude 263
Volume 13 Number 2, 2020
It is seen from Table 6 that male pre-service teachers have higher levels in all the subdomains than
female teachers. The differences between total scores of males and females are not found to be
statistically significant (U=1052,500; p=.365>.05; U=1158,000; p=.852 > .05; U=1096,500; p=.546
> .05; U=936,500; p=.090 > .05).
Table 7 gives the results of the Kruskal-Wallis test that was utilized to reveal whether the reasons for
career choice lead to significant differences in pre-service teachers’ higher-order tendency, reasoning,
mathematical thinking skills, and problem-solving.
Table 7. Pre-service teachers’ levels in the subdomains of mathematical thinking scale in terms of the reasons
for career choice
N
Mean Rank
p
Higher-order
thinking
tendency
Intrinsic reasons
78
24.910
53.06
3.483
0.175
Family guidance
18
24.889
52.39
Others
13
26.539
70.23
Reasoning
Intrinsic reasons
78
17.577
55.16
1.025
0.599
Family guidance
18
17.944
59.39
Others
13
17.153
47.96
Mathematical
thinking skill
Intrinsic reasons
78
29.488
52.57
5.732
0.057
Family guidance
18
31.222
70.81
Others
13
29.308
47.69
Problem-
solving
Intrinsic reasons
78
26.577
54.54
0.790
0.674
Family guidance
18
27.222
60.25
Others
13
26.077
50.46
*p < .05
Table 7 presents no significant differences in the mathematical thinking scale subdomains in terms of
the reasons for career choice.
The last analysis for research question 2 examined whether academic achievement results in a
significant difference in the mathematical thinking scale's subdomains. For this purpose, the Kruskal-
Wallis test was conducted, and the results were given in Table 8.
Table 8. Pre-service teachers’ levels in the subdomains of mathematical thinking scale in terms of academic
achievement
Academic
Achievement
N
Mean Ranks
p
Higher-order
thinking
tendency
1.51-2.00
6
25.333
56.50
4.640
0.326
2.01-2.50
25
24.040
43.52
2.51-3.00
53
25.359
57.57
3.01-3.50
20
25.500
59.65
3.51-4.00
5
25.800
64.80
Reasoning
1.51-2.00
6
17.500
49.50
3.015
0.555
2.01-2.50
25
17.000
46.52
2.51-3.00
53
17.774
58.39
3.01-3.50
20
17.700
56.35
3.51-4.00
5
18.200
62.70
Mathematical
thinking skill
1.51-2.00
6
28.167
37.00
3.384
0.496
2.01-2.50
25
29.280
52.80
2.51-3.00
53
30.076
57.04
3.01-3.50
20
30.200
60.25
3.51-4.00
5
28.800
45.00
Problem-
solving
1.51-2.00
6
26.167
49.50
4.301
0.367
2.01-2.50
25
25.920
47.68
2.51-3.00
53
26.793
56.40
3.01-3.50
20
27.050
60.20
264 Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Acta Didactica Napocensia, ISSN 2065-1430
3.51-4.00
5
27.200
62.60
*p<.05
As seen from Table 8, there were no significant differences in pre-service teachers’ levels of higher
order thinking tendency (χ2=4,640; p=0,326>.05), reasoning (χ2=3,015; p=0,555>.05), mathematical
thinking skill (χ2=3,384; p=0,496>.05), and problem-solving (χ2=4,301; p=0,367>.05) in terms of
academic achievement.
3.3. Findings related to the third research question
Correlation analysis was performed to reveal the relationship between pre-service teachers’ attitudes
for courses in mathematics and the subdomains of the mathematical thinking scale. Table 9 indicates
the results of the correlation analysis.
Table 9. The Spearman’s Rho Correlation between attitudes for courses in mathematics and subdomains of the
mathematical thinking scale
Attitudes for courses in mathematics
Higher-order thinking tendency
.363*
Reasoning
.320*
Mathematical thinking scale
.164
Problem-solving
.273*
* Correlation is significant at the .001 level
The Spearman’s Rho correlation is .363 with the significance level of .001, which means that there is a
significant positive moderate correlation between higher-order thinking tendency and attitudes. The
Spearman's Rho correlation is .320 with the significance level .001, which means that there is a
significant positive moderate correlation between reasoning and attitudes. Finally, the Spearman's
Rho correlation is .273 with the significance level .001, which means that there is a significant positive
moderate correlation between problem-solving and attitudes. The correlation between the subdomain
titled mathematical thinking skill and attitudes was also weak and not statistically significant.
Considering the significant and positive correlations between attitudes for courses in mathematics and
higher-order thinking tendency, reasoning, and problem-solving, it was found that 13.17%
(ρ2=[0.363]2) of variance in attitudes can be explained by higher-order thinking tendency, 10.24%
(ρ2=[0.,320]2) by reasoning, and 7.45% (ρ2=[0.273]2) by problem-solving.
4. Conclusion and Discussion
This research aims to investigate (i) whether pre-service secondary school mathematics teachers’
attitudes for courses in mathematics differ in terms of gender, reasons for career choice, and academic
achievement, (ii) whether pre-service secondary school mathematics teachers’ mathematical thinking
levels differ in terms of gender, reasons for career choice, and academic achievement, and (iii) the
relationship between pre-service teachers’ attitudes and mathematical thinking levels.
Participants have been found to have a moderate level of attitudes for courses in mathematics. Some
researches report pre-service teachers’ moderate level of mathematics attitudes (Kargar et al., 2010;
Rech, Hartzell, & Stephens, 1993) and a high level of attitudes (Boran et al., 2013; Bulut et al., 2002;
Cakiroglu & Isiksal, 2009; Duru et al., 2005; Kandemir, 2007). Ma and Kishor (1997) suggested that
individuals’ levels of mathematics attitudes may decrease via an increasing number of mathematical
experiences even if they started school with positive attitudes. Similarly, Philippou and Christou
(1998) reported that students' mathematics attitudes might have a trend to diminish because of the
increasing level of the difficulties in mathematical activities and the increasing level of the pressure
that these activities put on the students as their grade levels increase. In a way that supports these
findings, Kaasila, Hannula, Laine, and Pehkonen (2008) reported negative mathematics attitudes of
pre-service teachers, while Malik (2018) found negative attitudes in college students.
Male pre-service mathematics teachers had more positive attitudes for courses in mathematics than
female pre-service teachers. However, the difference between the means of males and females is not
Examining the relationship between pre-service mathematics teachers’ mathematical thinking level and attitude 265
Volume 13 Number 2, 2020
statistically significant. Researchers (Awofala, 2016; Cakiroglu & Isiksal, 2009; Duru et al., 2005;
Sarpkaya et al., 2011) mostly found no significant differences in mathematics attitudes in terms of
gender. However, a few researchers (Bulut et al., 2002; Boran et al., 2013; Küçük et al., 2013) found
significant differences in favor of females. On the other hand, Fennema and Sherman (1976; 1978)
findings are consistent with this study.
Pre-service mathematics teachers' attitudes who chose to teach for intrinsic reasons differed
significantly from those who chose to teach with family guidance or teacher and peer guidance.
Research shows that teachers who chose to teach for intrinsic reasons are more open-minded about
learning and have higher intrinsic motivation (Aktürk, 2012), and have more positive attitudes towards
teaching as a career (Özder, Konedralı & Zeki, 2010). Pre-service teachers' attitudes are also related to
their efficacy beliefs (Kartal, 2020). Pre-service teachers with more positive attitudes may feel more
efficacious in mathematics. We think that pre-service teachers who chose to teach for intrinsic reasons
feel qualified and willing to solve mathematics course problems. For this reason, they may study
harder, and therefore their attitudes improved significantly from others. This assumption can be
explained by research in the literature. Liking mathematics is a common factor that occurs in pre-
service teachers' reasons in career choice (Boz & Boz, 2008; İncikabı, Mercimek, Biber & Serin,
2016; Kartal & Kıymaz, 2020; Papanastasiou & Papanastasiou,1997; Sinclair, 2008; Tataroğlu, Özgen
& Alkan, 2011) and this factor may explain the significant difference in attitudes.
Pre-service teachers whose academic achievement is between 1,51-2,00 and 2,01-2,50 have lower
attitudes for courses in mathematics than pre-service teachers with higher academic achievement.
This finding is consistent with the researches that specify that attitude is a predictor of academic
performance (Aljaberi, 2014; Bakar et al., 2010; Papanastasiou, 2000). Pre-service teachers’ academic
achievement level should be at least 2,00 in order to graduate. It may not be wrong to consider pre-
service teachers whose academic achievement is 2,50 and above as successful. Since pre-service
teachers who had an achievement level above 2,50 may be accepted as successful, there may not be
significant differences in their attitudes in terms of academic achievement.
Participants have a high level of mathematical thinking, considering the full scale. They also had high
levels in the subdomains of higher-order thinking tendency, reasoning, and problem-solving and a
moderate level in mathematical thinking skills. Yorulmaz, Çokçalışkan, and Çelik (2018) and Arslan
and İlkörücü (2018) found that the pre-service teachers' mathematical thinking levels are high while
Kargar and colleagues (2010), and Aljaberi (2014) reported moderate levels of mathematical thinking.
Aljaberi (2014) also concluded that pre-service teachers’ mathematical thinking improved as their
grade levels increased. From this finding, it is possible to say that participants’ mathematical thinking
levels are high because they are seniors.
Many researchers investigated the affect (such as attitude, anxiety, and belief) in mathematical
thinking (Aljaberi, 2014; Hannula, 2004; Kargar et al., 2010; Zan, Brown, Evans & Hannula, 2006).
Individuals with negative attitudes towards mathematics may avoid doing mathematics and may not
gain thinking skills such as reasoning and problem-solving (Aljaberi, 2014; Kargar et al., 2010). On
the other hand, individuals who cannot think mathematically and fail in mathematical activities are
likely to develop negative attitudes towards mathematics. This study investigated the relationship
between pre-service teachers’ attitudes and mathematical thinking levels. The correlation analysis
indicated a moderate positive relationship between attitudes and the higher-order thinking tendency
and the reasoning, and a weak positive relationship between attitudes and problem-solving. The
relationships between attitudes and higher-order thinking tendency and reasoning may be stronger
because undergraduate mathematics courses may employ higher-order thinking tendency and
reasoning more frequently than problem-solving.
The findings of this study revealed the relationships between attitudes and mathematical thinking. The
importance of developing positive mathematics attitudes in pre-service teachers is seen again
(Marchiş, 2013) considering the effect of teachers’ positive attitudes on their students’ attitudes
(Küçük et al., 2013). Therefore, pre-service teachers’ mathematics attitudes should be measured
periodically during their teacher preparation programs to make arrangements conducive to developing
positive attitudes. One of the findings in this study is that pre-service teachers who chose to teach for
266 Avni YILDIZ, Serdal BALTACI, Büşra KARTAL
Acta Didactica Napocensia, ISSN 2065-1430
intrinsic reasons have more positive attitudes than others. It is known that these pre-service teachers
have higher levels of intrinsic motivation. It may be suggested to organize activities that improve pre-
service teachers' intrinsic motivation who did not choose to teach with intrinsic reasons. Making pre-
service teachers engaging in activities that require higher-order thinking and reasoning and making
them believe that they would be successful may help pre-service teachers develop positive attitudes. It
is essential to state that the subdomain of higher-order thinking tendency and reasoning explains 23%
of the variance in the attitudes for courses in mathematics.
This study has investigated the relationship between senior pre-service teachers’ attitudes for courses
in mathematics and mathematical thinking levels. Further research may investigate these variables and
the relationship between these two variables in all grade levels and examine whether grade level leads
to significant differences or not. The relationships between mathematical thinking and affective factors
such as motivation, beliefs, and values may also be explored.
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Authors
Avni YILDIZ, Associate Prof. Dr., Zonguldak Bülent Ecevit University, Eregli Faculty of Education,
the Department of Mathematics Education, Zonguldak (Turkey). E-mail: yildiz.avni@gmail.com
Serdal BALTACI, Associate Prof. Dr., Kırşehir Ahi Evran University, Faculty of Education, the
Department of Mathematics Education, Kırşehir (Turkey). E-mail: serdalbaltaci@gmail.com
Büşra KARTAL, Dr., Kırşehir Ahi Evran University, Faculty of Education, the Department of
Mathematics Education, Kırşehir (Turkey). E-mail: busra.kartal@ahievran.edu.tr.
