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The present study aimed to examine an effective mathematics teacher’s qualifications from the perspectives of secondary school students. The study was a qualitative one carried out with the descriptive model.
1.
Universal Journal of Educational Research 7(2): 536-549, 2019 http://www.hrpub.org
DOI: 10.13189/ujer.2019.070226
Qualifications of an Effective Mathematics Teacher
from the Perspectives of 5th to 8th Grade
Secondary School Students
Elif Ertem Akbaş1,*, Murat Cancan1, Esra Kılıç2
1
Department of Mathematics, Faculty of Education, Van Yüzüncü Yıl University, Turkey
2
Mathematics Teacher, Ministry of Education, Van, Turkey
Copyright©2019 by authors, all rights reserved. Authors agree that this article remains permanently open access under
the terms of the Creative Commons Attribution License 4.0 International License
Abstract The present study aimed to examine an rapid changes and developments like globalization and
effective mathematics teacher’s qualifications from the restructuring have brought about renovations in the field of
perspectives of secondary school students. The study was a education [1]. As a result, various changes have occurred in
qualitative one carried out with the descriptive model. The the understanding of learning and teaching. With these
study was carried out with 40 students from all the four changes, it is now more important to apply our knowledge
class grades of a secondary school (10 students from each in our lives. In order to keep up with these changes,
class grade) in Turkey in the academic year of 2017-2018. individuals who are in their education process are expected
The participants were determined using the purposeful to have such effective qualifications as researching,
sampling method. As the data collection tool, questioning, problem solving, critical thinking, making use
semi-structured interview questions were used, and the of technology, expressing one’s thoughts and producing
interviews were audio-recorded to avoid any data loss. For information [2].
the analysis of the data, first, the interviews were It is the educational institutions’ duty and responsibility
transcribed and then analysed using the content analysis to meet the requirements of this era. In order for
method. The results revealed that according to the students’ educational institutions to carry out these duties, it is
views, the qualifications of an effective mathematics necessary to increase the quality within the education
teacher were grouped under four categories: “personal system [3]. Studies on increasing the quality of the
traits”, “communication skills”, “class management and education system make it compulsory to introduce
teaching methods” and “measurement-evaluation”. It was comprehensive reforms to teacher training programs [4].
also seen that regardless of the school type they would In this respect, the teacher and his or her qualifications,
choose for their high school education, all the students had which constitute the basis of the education system,
an idea about the qualifications of a mathematics teacher become prominent [3-7]. Therefore, the reforms to be
and that it was not much easy to become an effective introduced to the education system should not only cover
mathematics teacher. In addition, it was found that there the teacher training process but also be involved in the
were differences between the views of the 5th, 6th, 7th and self-development process of teachers. In this process, it is
8th grade students with respect to their cognitive levels and
important for teachers to update themselves in line with
needs. In line with the qualifications examined, various
the current developments and changes and to become an
suggestions were put forward to increase the effectiveness
effective teacher. When studies on the qualifications of an
of the mathematics teachers and of the process of
effective teacher are examined, it is seen that a teacher
mathematics teaching.
should have certain qualifications apart from efficacy in
Keywords Secondary School Students, Teacher teaching [8-21] and that these qualifications have
Qualifications, Effective Mathematics Teacher, generally been classified as personality traits, intellectual
Mathematics Teaching qualifications and approaches to teaching. This situation
shows that the qualifications mentioned in related studies
should be taken into account in education systems as well
as in teaching training institutions.
1. Introduction Our education system, which has constantly been
reformed in line with the changes and developments in
In the 21st century, an era which requires information use, recent years, has gone through related innovations in
2.
Universal Journal of Educational Research 7(2): 536-549, 2019 537
terms of the curricula applied in elementary, secondary not enough success has been achieved specifically in
and high schools [22]. In secondary school course mathematics [36]. These results show that we are not
curriculum of mathematics, the overall course objective is successful enough to have our students acquire the
said to help students acquire the attitudes, knowledge and intended skills. Therefore, whether this situation is based
skills necessary in their lives as well as in their education on the teaching-learning process or on the student-teacher
process [22]. The fact that mathematics is abstract and that has always constituted the research questions directed in
students fail to understand it well and that it is mostly related studies. In this respect, the present study focused on
regarded as a difficult field for students to learn [23] is students’ views about whether the problem in question is
one of the causes that lead to this innovation. Altun [24] related to mathematics teaching or to the qualifications of
and Van de Walle [25] point out that dealing with math the mathematics teacher.
does not just involve solving numerous mathematical Students’ views constitute an important reference to be
problems on behalf of the teacher but includes mental taken into account while determining efficacies of a teacher.
processes such as developing solutions together with A frequent method to define the characteristics of a
students and evaluating whether the application and its qualified teacher is to make use of students’ views for the
consequence are meaningful or not. To a great extent, it is evaluation of teachers [16]. Due to the fact that the student
the mathematics teacher who will develop students’ skills and the teacher are regarded as the main building blocks of
like reasoning, relating and problem solving within the education, in the present study, students’ views were taken
scope of mathematics teaching and who will help students into account while determining the teacher qualifications.
acquire the mathematical knowledge, skills and other In addition, considering the importance of mathematics
related positive attitudes. When viewed from this during secondary school education, a period of transition to
perspective, the qualifications of a mathematics teacher high school in which students develop their basic
and his or her roles and behaviours are of great mathematical knowledge, it is fairly necessary to evaluate
importance. Therefore, in renewed mathematics curricula, the qualifications of a mathematics teacher. In this respect,
the reforms especially regarding the qualifications of a examination of especially secondary school students’
teacher have been introduced in line with the points views about the qualifications of a good mathematics
mentioned above. It is reported that as one of the basic teacher is thought to provide field experts, teachers and the
qualifications of an effective teacher, he or she should education system with insights into what qualifications an
have good professional knowledge as well as good effective mathematics teacher is expected to have.
knowledge of mathematics [7,26], yet it is also pointed Therefore, the purpose of the present study was to examine
out that this type of knowledge is not sufficient alone. In the qualifications of an effective mathematics teacher from
their study, Foss and Kleinsasser [27] concluded that a the perspectives of secondary school 5th, 6th, 7th and 8th
good teacher should not only be patient, flexible and grade students. In line with this purpose, the main research
motivating but also create an entertaining class problem was the question of “what are qualifications of an
atmosphere that supports learning mathematics. When the effective mathematics teacher from the perspectives of
related literature is reviewed, it is seen that there are secondary school students (5th to 8th grade)”
several studies focusing on the qualifications that
especially mathematics teachers should have [1,28-30]. 1.1. Grades in Turkish Education System and School
All these studies revealed that mathematics teachers were Type Preference
able to use the developing technology in their courses and
to create student-centred class environments and that they The education system in Turkey is centrally organized,
had effective communication skills. Similarly, other and the Ministry of Education (known as MEB in Turkey)
studies reported that as part of their qualifications, is the main body for planning, programming, implementing,
teachers were expected to have field knowledge and to monitoring, and controlling education and for training
know how to teach mathematics [31,32]. Different from services including development of school curricula [37].
these qualifications, some other studies demonstrated that The curricula are prepared by commissions made up of
students develop anxiety regarding mathematics due to teachers, educational experts, academicians and
their negative experiences they had with their representatives from the relevant departments of MEB. In
mathematics teachers [33-35]. In general, anxiety will this way, the development of curricula is ensured by
lead to failure, which will inevitably cause students to teachers, parents, school administrators and experts from
have difficulty in learning mathematics. In this respect, it all over the country together with the MEB officials.
is seen that teachers’ attitudes towards their students are In Turkey, the education system is divided into grades.
of great importance with respect to shaping their students’ These grades include preschool education (kindergartens
viewpoints about mathematics so that they can approach or nursery schools), elementary school 1st step (primary
positively to mathematics. schools), elementary school 2nd step (secondary schools),
When the success level of our country in international high school education (high schools) and higher education
exams like PISA and TIMMS is examined, it is seen that (universities). Secondary school students include 5th, 6th,
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538 Qualifications of an Effective Mathematics Teacher from
the Perspectives of 5th to 8th Grade Secondary School Students
7th and 8th grade students aged between 10 and 13 years old mathematics, it is obvious that we will trigger students’
[22]. In addition, the High School Placement Test (known potential in mathematics. In other words, teaching
as LGS in Turkey) administrated to secondary school 8th efficacies of teachers are also influential on broadening
grade students at the end of the related academic year students’ horizons. Therefore, in the present study, it is
allows placing students in high schools in accordance with thought that it is important to evaluate qualifications of a
their levels of achievement in this test. Students who do not teacher influential on teachers’ efficacies from the
take LGS are placed in other high schools based on their perspectives of students.
average academic scores in their secondary school
education. According to MEB, high school types can be
classified based on the intensity of the course of 2. Materials and Methods
mathematics as follows: science high schools, Anatolian This part presents information about the research model,
high schools, vocational and technical Anatolian high the study group, data collection tools and about data
schools, social sciences high schools, religious high analysis.
schools, multi-program Anatolian high schools, fine arts
high schools and sports high schools. In this respect, the
school type with the most intensive mathematics is the 2.1. Research Model
science high school. Therefore, it was thought that the The present study aimed to provide a viewpoint
school type could be influential on determining the regarding what qualifications an effective mathematics
qualifications of a math teacher based on the views of teacher should have in line with students’ views. In line
secondary school students, who constituted the research with this purpose, the study was carried out as a qualitative
sample in the present study. one with the descriptive model. The qualitative research
design is a technique favoured since it allows revealing
1.2. A Mathematics Teacher’s Efficacies in Teaching individuals’ understandings, emotions and thoughts as a
Mathematics whole within their own natural and realistic context [42].
According to Özdemir [43], qualitative data analysis is the
In the process of learning mathematics, there are a whole of activities such as organizing the data collected
number of factors influential on students’ viewpoints with data collection tools like interviews, categorizing
regarding mathematics. Among these factors, the efficacies these data, revealing the related themes, and reporting the
of a mathematics teacher in teaching mathematics play an results obtained.
important role in the process. In this respect, MEB gathered
the efficacies of teachers who will apply a student-centred
2.2. Participants
curriculum under the headings of “knowing the student,
learning and teaching process, monitoring and evaluating While determining the study group, the purposeful
students’ learning and development, school-family and sampling method, which allows in-depth examination
society relations, program and content information” [22]. within the scope of convenient sampling based on the
When the related international literature is reviewed, it is purpose of study, was used [44]. In this respect, the study
seen that research conducted previously on a teacher’s was carried out with a total of 40 secondary school 5th, 6th,
professional efficacies [38,39] is prominently on the 7th and 8th grade students (10 from each class grade) in the
agenda today as well [40]. In this respect, An, Kulm and academic year of 2017-2018 (In Turkey, secondary school
Wu [41] and Shulman [32] claim that field knowledge is period covers the class grades ranging between the 5th and
not enough alone for an effective teaching process, and 8th class grades, and students aged between 10 and 13 years
they point out that dimensions such as knowing the nature old take this education). While determining the students’
of mathematics, recognizing students’ misunderstandings, views about the “qualifications of an effective mathematics
developing students’ mathematical ideas and increasing teacher”, the school type they would prefer in future were
students’ mathematical thinking are also important for the specifically identified (see 1.1). In addition, the students
process of teaching. When these dimensions are considered took part in the study on voluntary basis, and the Table 1
to be among mathematic teachers’ efficacies in teaching below presents information about the students.
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Universal Journal of Educational Research 7(2): 536-549, 2019 539
Table 1. Information about the Students Participating in the Study
School Type to Be Preferred
Number of
Class Grade Code Gender Science High Anatolian High Vocational and Technical Social Sciences Students (Total)
School School Anatolian High School High School
S1 Female X
S2 Female X
S3 Male X
S4 Male X
th
5 Grade S5 Male X
10
Students S6 Male X
S7 Female X
S8 Female X
S9 Male X
S10 Female X
S11 Female X
S12 Female X
S13 Female X
S14 Male X
th
6 Grade S15 Male X
10
Students S16 Male X
S17 Male X
S18 Female X
S19 Female X
S20 Male X
S21 Female X
S22 Female X
S23 Female X
S24 Male X
7th Grade S25 Male X
10
Students S26 Male X
S27 Female X
S28 Female X
S29 Male X
S30 Male X
S31 Female X
S32 Female X
S33 Female X
S34 Male X
8th Grade S35 Male X 10
Students S36 Male X
S37 Female X
S38 Female X
S39 Male X
S40 Male X
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540 Qualifications of an Effective Mathematics Teacher from
the Perspectives of 5th to 8th Grade Secondary School Students
When Table 1 is examined, it is seen that there was an have defined use to evaluate learning in his or her
equal distribution of the gender of the students course?
participating in the study with respect to each class grade
(Distribution of the students’ gender depending on their 2.4. Data Analysis
class grades: 5 male, 5 female; total distribution 20 male;
20 female). In addition, there were four school types that In the first phase of the analysis of the data collected in
the students preferred to attend in future (science high the study, first of all, the data collected via the
school, Anatolian high school, vocational and technical semi-structured interviews were transcribed. Following
Anatolian high school and social sciences high school). this, the qualitative data were examined using the content
According to Table 1, there were 15 students willing to analysis method and the code-definition table was formed.
attend science high school, 11 students to attend Anatolian Content analysis is a technique that gathers similar data
high school, eight students to attend vocational and within the framework of certain concepts and themes and
technical Anatolian high school and six students willing to arranges them in a way to allow the reader to understand
attend social sciences high school. These school types were the data easily [44]. For the analysis of the data, the
general those involving intensive mathematics (See. 1.1.). students participating in the study were coded based on
It is thought that this preferences of the students might have their class grades as S1, S1, … , S10 for the 5th grade; S11,
been influenced by the importance of the course of S12, ... , S20 for the 6th grade; S21, S22,..., S30 for the 7th
mathematics in their daily lives. grade and S31, S32,… , S40 for the 8th grade. In the second
phase, the qualitative data collected from the students were
2.3. Data Collection Tool examined by two faculty members experienced in the field
of qualitative research. Of the research data, 20% of them
Within the scope of the study, for the purpose of [46] were randomly given to the coders, and they were
revealing the participants’ emotions, thoughts, beliefs and asked to recode the data according to the code-definition
viewpoints regarding the research topic [42], the table prepared by the researchers. The reliability of the
semi-structured interview method was used it allows qualitative analysis was calculated based on the codings
changing the order of the questions and explaining the
done by the researchers and by the two coders with the
questions in a more detailed manner [45]. In order to find
formula suggested by Miles and Huberman [47]
answers to the main research problem, eight open-ended
[Reliability = Agreement / Agreement +
interview questions were determined and presented to three
Disagreement.100]. In the study, when the agreement
field experts’ views. The interview questions arranged in
percentages regarding the codings were examined, it was
line with the experts’ views were directed to the
participants at their own schools. For the purpose of seen that for all the codings, the overall agreement
avoiding any data loss, the interviews were audio-recorded. percentages were 0.84 for the researchers and the first
In the study, the questions directed to the students were as coder and 0.80 for the researchers and the second coder. As
follows: for the average agreement for the researchers and the two
(1) Do you like the course of mathematics? What is the coders, it was calculated as 0.82. In relation to the coding
influence of your teacher on this emotion of yours? reliability of the researchers, it is reported that the
(2) What is your communication with your mathematics agreement percentage should be over 70% [47].
teacher like? How do you think this communication Following this, the codings were examined with respect
should be? to their fit, and the data were categorized. The data
(3) What should your class environment and the teacher categorized were made meaningful to the reader with the
be like for the course of mathematics? help of the codings and frequencies. In addition, within the
(4) While teaching the mathematics-related subjects, scope of the reliability of the study, direct quotations
what type of materials would you you’re your teacher regarding the data were used to help reveal from what
to use? Please state your reasons. perspective the codings were done. For the presentation of
(5) What are your expectations from an effective the data, the criteria of being impressive (different views),
mathematics teacher? While answering this question, being explanatory (appropriateness to the code) and variety
do not consider the school type you would like to were taken into account while choosing the quotations
choose in future. [48].
(6) What type of a role model should your dream
mathematics teacher be for you? 2.5. Results
(7) What should a mathematics teacher who will meet
your expectations from a mathematics teacher do to As a result of the content analysis conducted on the data,
achieve meaningful learning in the course of four main categories and the sub-codings for these
mathematics? categories related to the qualifications of a mathematics
(8) What type of a measurement-evaluation (exam teacher were revealed. Figure 1 presents the categories
system) should the ideal mathematics teacher you obtained via the students’ views. When Figure 1 is
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Universal Journal of Educational Research 7(2): 536-549, 2019 541
examined, it is seen that the students’ views about the S22: My math teacher should behave equally and avoid
qualifications of an ideal teacher were gathered under four discrimination among his or her students. He should
main categories: “personal traits”, “communication skills”, always be good-humored, entertaining, tolerant and
“class management and teaching methods” and dependable (Personality Traits).
“measurement and evaluation”. Tables 2, 3, 4, 5 and 6 S3: We should be able to talk to our teacher not only in
demonstrate the sub-codings regarding the students’ views class but in out-of-class environment as well. We should
for these categories. consult him or her when necessary (Communication
When Table 2 is examined, it is seen that among the Skills).
qualifications of a mathematics teacher, most of the S11: He or she should teach mathematics without boring
students mentioned personality traits and communication us, and we should enjoy listening to him or her in class.
skills most regardless of the school type they would choose He or she can use the smart board or the computer while
at high school. In addition, the 5th and 6th grade students teaching because we then learn more easily and
reported that personality traits and communication were participate more in the lesson (Class Management and
the most important among the qualifications of a Teaching Methods).
mathematics teacher. It was also found that the 7th and 8th S5: My math teacher should consider my performance
grade students reported more views about the categories of during the lesson. I mean not all students are the same.
class management, teaching methods and Some are good at multiple-choice tests and some are
measurement-evaluation. Below are the related views of good at practice. Thus, he or she should evaluate us
some of the students. accordingly (Measurement and Evaluation).
Figure 1. Categorization of the Qualifications of a Mathematics Teacher in Line with the Students’ Expectations
Table 2. Categorization of the Qualifications of a Mathematics Teacher in Line with the Students’ Expectations
Categories f* Student Codes
S1, S2, S3, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S17, S18, S19, S20, S21, S22, S23,
Personal Traits 38
S24, S25, S26, S27, S28, S29, S30, S31, S32, S33, S34, S25, S36, S37, S38, S39, S40
S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19, S20, S21, S22,
Communication Skills 37
S23, S24, S25, S26, S28, S29, S30, S32, S33, S34, S35, S36, S37, S38, S39
Class Management and S1, S4, S7, S8, S11, S12, S14, S17, S19, S20, S21, S23, S24, S25, S26, S27, S28, S29, S30, S31,
27
Teaching Methods S32, S34, S35, S36, S37, S38, S40
S2, S5, S6, S13, S17, S18, S20, S21, S23, S24, S25, S26, S28, S29, S30, S31, S32, S34, S36, S37,
Measurement and Evaluation 22
S38, S39
*Some of the students participating in the study reported more than one view.
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542 Qualifications of an Effective Mathematics Teacher from
the Perspectives of 5th to 8th Grade Secondary School Students
Table 3. Personal Traits
Personal Traits 𝐟∗ Student Codes
Frank/sincere 13 S2, S5, S10, S11, S19, S20, S24, S28, S30, S31, S35, S37, S39
Making the lesson pleasant 11 S1, S5, S6, S8, S13, S17, S18, S25, S33, S32, S38
Easy-going/Good-humored 14 S3, S6, S10, S11, S12, S14, S22, S23, S26, S27, S30, S31, S39, S40
Entertaining/Humorous 9 S21, S22, S25, S28, S31, S33, S34, S36, S38
Egalitarian and Fair 17 S13, S14, S15, S17, S18, S19, S20, S21, S22, S23, S24, S25, S27, S30, S31, S33, S35
Respectful 11 S6, S8, S18, S21, S23, S25, S26, S28, S34, S35, S38
Tolerant/Merciful 16 S1, S2, S7, S9, S12, S14, S18, S19, S20, S22, S28, S30, S31, S34, S35, S40
Hardworking and effective 10 S15, S20, S21, S24, S28, S29, S30, S36, S39, S40
Good-looking 9 S3, S4, S5, S8, S9, S26, S29, S30, S32
Speaking fluently and well 9 S11, S12, S13, S15, S27, S29, S30, S34, S39
Giving confidence 9 S3, S7, S9, S10, S20, S22, S23,S37, S38
Benevolent 9 S12, S16, S17, S24, S25, S33, S34, S37, S38
*Some of the students participating in the study reported more than one view.
Table 3 presents the sub-codings, student codes and S19: To me, my math teacher should be tolerant, behave
frequencies for the category of “personal traits” obtained everyone fairly and equally. Also, I also take the honest
via the students’ views about the qualifications of a side of my teacher as a role model (Tolerant/merciful,
mathematics teacher egalitarian and fair, frank/honest).
When the qualifications mentioned by the students S37: The teacher should be helpful and sensitive to
regarding the personality traits of an effective students, and they should be able to talk about their
mathematics teacher were examined, it was seen that problems. Also, the teacher should earn students’ trust
being egalitarian/fair and being tolerant/merciful were (Giving confidence, benevolent).
among the most frequent personal traits that an effective S26: I think my math teacher should be someone who is
mathematics teacher should have. Other important respectful to his or her students and who should dress
personal traits included being easy-going/good-humoured, well and have a smiling face (Good-looking, respectful,
frank/sincere, respectful, making the lesson pleasant, easy-going/good-humored).
hardworking/effective, benevolent, entertaining/humorous, S36: To me, the teacher should be entertaining,
speaking fluently/well, giving confidence and humorous and hardworking. I mean he or she should not
good-looking. In addition, there were students who be too serious (Entertaining/humorous, hardworking
reported that a mathematics teacher should give and effective).
importance to discipline and planning. When the students’ S33: I think mathematics is a difficult course, and the
responses were examined, it was seen that the 5th and 6th teacher is the person who will make the lessons
grade students mostly mentioned such personal traits of an entertaining. Thus, the teacher should draw students’
effective mathematics teacher as being frank/intimate, interest and help them love the course. Also, the teacher
tolerant/merciful, making the lesson pleasant and that the
th th should be benevolent (Making the lesson pleasant,
7 and 8 grade students mostly mentioned personal traits
benevolent).
such as being egalitarian/fair and hardworking/effective.
S40: The teacher should be intelligent, hardworking,
This difference is thought to be due to the fact that
and tolerant and have a smiling face and do
students from different age groups have different needs.
mathematical calculations quickly in mind
Some of the students’ views about the personal traits of a
(Hardworking and effective, easy-going/good-humored,
mathematics teacher were as follows:
tolerant/merciful).
S15: An ideal mathematics teacher should be honest,
hardworking and equal, give equal talking time to Table 4 presents the sub-codings, student codes and
everyone in class and speak fluently and well in class frequencies for the category of “communication skills”
(Egalitarian and fair, speaking fluently and well, obtained via the students’ views about the qualifications of
hardworking and effective). a mathematics teacher.
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Universal Journal of Educational Research 7(2): 536-549, 2019 543
Table 4. Communication Skills
Communication Skills f* Student Codes
Out-of-class
16 S1, S3, S7, S8, S11, S14, S18, S20, S21, S23, S25, S30, S32, S34, S38, S40
communication
S1, S2, S6, S9, S10, S12, S14, S16, S17, S18, S19, S20, S21, S22, S24, S25, S26, S29, S30, S33,
Attitude towards students 26
S35, S36, S37, S38, S39, S40
Caring 11 S21, S22, S23, S24, S25, S29, S32, S33, S34, S36, S38
Good use of tone of voice 11 S1, S8, S13, S15, S16, S19, S30, S35, S37, S38, S40
Effective use of Turkish 8 S4, S11, S12, S15, S23, S26, S28, S34
Calling students by their
6 S5, S8, S9, S17, S22, S39
names
* Some of the students participating in the study reported more than one view.
When Table 4 is examined, it is seen that according to family-related problem, and he cares all students and
the students’ views, the most important communication tries to solve their problems, if any, whether they are
skill of a mathematics teacher was the math teacher’s hardworking or lazy. He is sincere, and when necessary,
attitude towards students. The students who reported that a serious. I think an ideal math teacher should be like him
mathematics teacher should demonstrate good and sincere (Attitude towards students, caring).
attitudes towards students believed that the teacher should S14: We have a good and sincere communication. He
not behave students offensively. The students also pointed never shouts at us or gets angry with us. He really
out that in a difficult course like mathematics, the teacher’s understands us. A good teacher should be like him. If not,
attitudes towards students were fairly influential on I will never be interested in math, and if so, I will not be
students’ interests and achievements in the course. able to learn anything in lessons. Also, a student should
According to a great majority of the students, other have the chance to communicate with the teacher out of
important communication skills of an effective class (Out-of-class communication, attitude towards
mathematics teacher included out-of-class communication, students).
caring students and using tone of voice well in class. In S37: The teacher should not talk to students too loudly in
addition, there were some other students who believed that class. I mean he should not shout or yield at them. He
an effective teacher should use Turkish effectively and call should pay attention to this while trying to establish
his or her students by their names. Some of the students’ communication with us (Attitude towards students, good
use of tone of voice).
views about the communication skills that a mathematics
S15: To me, a teacher should not shout while
teacher should have were as follows:
communicating. He should speak well and fluently
S25: We have a teacher-student relationship with our
(Good use of tone of voice, effective use of Turkish).
math teacher in class and a teacher-friend relationship
S5: Our teacher should call us by our names while
during break times. Our teacher behaves us sincerely
talking to us. He should communicate with us in this way
out of class, and we have a very good communication.
(Calling students by their names).
To me, this relationship must be based on respect. Also,
an ideal teacher should not be offensive towards us Another qualification of a mathematics teacher
(Out-of-class communication, attitude towards students, identified via the students’ views was ‘class management
caring). and teaching methods”. Table 5 presents the sub-codings,
S29: I have a really good communication with my student codes and frequencies belonging to the category of
teacher. The teacher is interested when I have a ‘Class management and teacher methods’.
9.
544 Qualifications of an Effective Mathematics Teacher from
the Perspectives of 5th to 8th Grade Secondary School Students
Table 5. Class Management and Teaching Methods
Class Management and Teaching Methods f* Student Codes
Class Management 7 S21, S23, S27, S28, S30, S35, S38
Way of teaching the lesson (interesting, appropriate S1, S4, S7, S11, S14, S17, S19, S21, S23, S25, S27, S28, S29, S30, S32, S34,
20
to the level) S35, S36, S37, S38
S1, S7, S8, S12, S14, S17, S20, S21, S23, S26, S28, S30, S31, S32, S34,
Use of concrete materials 18
S35, S36, S40
Achieving active participation 13 S1, S11, S12, S14, S20, S21, S23, S27, S28, S31, S37, S38, S40
Giving efficient examples to achieve the target goals 12 S4, S19, S24, S25, S26, S27, S29, S32, S31, S35, S36, S38
Paying attention to individual differences 9 S21, S25, S26, S28, S30, S31, S34, S35, S40
Variety in methods and techniques 9 S20, S21, S24, S27, S28, S31, S32, S34, S38
Use of technology in class 14 S1, S4, S7, S11, S12, S17, S19, S20, S24, S25, S31, S34, S38, S40
Providing up-to-date information about the lesson
7 S21, S25, S28, S32, S37, S38, S40
subject
* Some of the students participating in the study reported more than one view.
When Table 5 is examined, it is seen that according to concrete materials, achieving active participation).
the students’ views, the most important qualifications of a S27: First of all, the student should enthusiastically say
mathematics teacher regarding class management and “I will solve this math problem on the blackboard”, and
teaching methods included way of teaching the lesson and the teacher should encourage students to solve as many
use of concrete materials. This situation was true for most math problems as possible until they understand the
of the students regardless of the school type they would subject because this is absolutely necessary for students
like to choose at high school. The students reported that a to get the right to attend a good high school. Also, the
mathematics teacher should teach the lesson subjects as teacher should not always use the same method of
appropriate to the students’ level and interest. Among the teaching in class. I mean he or she should use games and
participants, especially the 7th and 8th grade students activities to increase our participation in class. There
thought that a mathematics teacher should use technology shouldn’t be anything in class like noise, which will
actively in class and encourage students to participate distract our attention (Class management, way of
actively in lessons. In addition, the students pointed out teaching the lesson, achieving active participation,
that mathematics was important to get the opportunity to giving efficient examples to achieve the target goals,
good-quality schools and that dealing with more variety in methods and techniques).
mathematical problems would be influential on the S40: Our teacher should bring related materials into
development of problem solving skills. Also, it was class while teaching. I am an 8th grade student, and
reported that the teacher should solve a sufficient number many math subjects require visuality. I understand math
of mathematical problems via related games and activities subjects better via such materials. I mean the teacher
in class to achieve the target outcomes of the course. Some should teach the lesson in the way students learn easily.
of the students stated that a mathematics teacher should use In this way, we will participate more in class. Also, math
a wide variety of methods and techniques in class, provide is very important to have the opportunity to attend a
up-to-date information about the lesson subjects, have a good high school. For this reason, students have to solve
good class management and take students’ individual numerous math problems. We always see that everything
differences into consideration. Some of the students’ views is changing rapidly, and our teacher should share these
about class management and teaching methods to be changes with us (Use of concrete materials, achieving
adopted by a mathematics teacher were as follows:
active participation, paying attention to individual
S17: The teacher should teach the lesson subject well.
differences, use of technology in class, providing
He or she can also bring related materials in class, use
up-to-date information about the lesson subject).
the smart board and videos as well. I learn better in this
way (Way of teaching the lesson, use of concrete Another factor related to the qualifications of a
materials, use of technology in class). mathematics teacher was reported by the students to be
S23: First of all, the math teacher should teach the “measurement and evaluation”. It was seen that
lesson subject very well. Also, he or she should use measurement and evaluation constituted an important
related materials while teaching. In this way, I factor for a teacher to be effective. Table 6 presents the
participate more in class. Also, he or she should control sub-codings, student codes and frequencies regarding the
the whole class during the lesson. This is quite important students’ views about the category of “measurement and
(Class management, way of teaching the lesson, use of evaluation”.
10.
Universal Journal of Educational Research 7(2): 536-549, 2019 545
Table 6. Measurement and Evaluation
Measurement and Evaluation f* Student Codes
S2, S5, S6, S13, S18, S20, S23, S24, S25, S26, S28, S29,
Considering in-class performance (personal success, feedback) 18
S31, S32, S34, S36, S37, S38
S6, S17, S18, S20, S21, S23, S24, S25, S29, S30, S31,
Considering cognitive level 14
S32, S38, S39
S2, S5, S13, S17, S20, S21, S25, S26, S31, S32, S36,
Considering individual differences 13
S37, S39
Variety in measurement and evaluation (traditional, multiple-choice
9 S20, S21, S23, S24, S29, S30, S32, S34, S37
test, theoretical, practice, high mark)
* Some of the students participating in the study reported more than one view.
When Table 6 is examined, it is seen that according to exam as appropriate to our level. The exam could be
the students’ views, a mathematics teacher should mostly practical even including games. It could also be
consider students’ in-class performance by giving feedback. traditional. I mean the exam should be varied. Our math
This situation was true for most of the students regardless exams should include questions like those directed in the
of the school type they would choose for their high school university placement exam. Also, our marks should not
education. Within the scope of in-class performance, it was be low; that’s, the teacher should not give low marks
pointed out that students’ personal success, participation in because our average mark in math is very important for
class, fulling the given the tasks, problem-solving skills us to attend a good high school in future (Considering
and their responses to the feedback given and to the cognitive level, variety in measurement-evaluation).
questions directed. Also, most of the students believed that
a teacher should consider students’ cognitive levels and
individual differences in the process of measurement and 3. Discussion, Conclusions and
evaluation. In addition, the 8th grade students pointed out Recommendations
that a high mark to be given in the course of mathematics
was necessary to have the chance to attend a good high Mathematics is a basic universal communication tool
school in future, and they also believed that math exams which constitutes the basis of analytical thinking and which
should be conducted in line with the university placement allows understanding the world. Besides the importance of
exam and that the teacher should not assign low scores for mathematics in students’ education lives and the
the exams. In addition, a mathematics teacher should use importance of the teacher to teach this course, it also plays
various exam techniques in the process of measurement an important role for students while determining their
and evaluation (traditional, multiple-choice and so on), future professions. Therefore, determining the
conduct practical exams and direct questions in the way qualifications of teachers of this course from students’
everyone can understand easily. Some of the students’ perspectives will not only allow mathematics teachers to
views about the measurement-evaluation process for a become more effective teachers but also contribute to the
mathematics teacher were as follows: development of students’ understanding mathematics. This
S23: First, the teacher should consider whether I development will have positive influence on the
participate in lessons or not and should prepare exams development of students’ carriers in their future lives as
appropriate to my level. I mean the exams should not be well. No one has claimed or can claim that it is easy to
too difficult but include all types of questions like become an effective and good teacher of especially
multiple-choice questions or traditional questions. Also, mathematics. In addition, all the interviews revealed that
if the teacher provides feedback, I will be able to see there were more than one way of becoming an effective
good and bad sides of my performance (Considering mathematics teacher. In this respect, the present study tried
in-class performance, considering cognitive level, to determine the qualifications of an effective mathematics
variety in measurement-evaluation). teacher from the perspectives of secondary school 5th, 6th,
S25: To me, my math teacher should not just consider my 7th and 8th grade students, who had the chance to observe
written exam score because not all students are the same. their teachers directly.
The teacher should consider how that child was in the When the findings obtained in the study were examined,
5th grade or 6th grade class, and he or she should think it was seen that the qualifications of a mathematics teacher
about how that student is now. Thus, the teacher should were gathered under four main categories: personal traits,
ask questions in exams according to my level and communication skills, class management and teaching
provide feedback. Also, he or she should consider my methods, and measurement and evaluation. When the
participation in lessons while evaluating me qualifications of a mathematics teacher were examined in
(Considering in-class performance, considering line with the students’ views, it was seen that in the
cognitive level, considering individual differences). categories of personal traits and communication skills, all
S32: While evaluating us, the teacher should give an the students mentioned the qualifications a teacher is
11.
546 Qualifications of an Effective Mathematics Teacher from
the Perspectives of 5th to 8th Grade Secondary School Students
expected to have in general, and it was seen that in the According to the students’ views, the teacher’s offensive
categories of class management-teaching methods and attitudes, prejudiced behaviours and fixed ideas about
measurement-evaluation, all the students mentioned the students cause the teacher to behave differently to students
qualifications they expected a mathematics teacher to have. depending on their levels of achievement in the course.
This situation was true for most of the students regardless This situation saddens less successful students [19,57,58],
of the school type they would prefer at high school. In decreases their interest especially in the course of
addition, it was found that the 5th and 6th grade students mathematics, causes them to fear from mathematics and
mostly mentioned such qualifications of a mathematics leads to negative influence on their achievement in
teacher as personal traits and communication; that the 7th mathematics [59-64]. According to the students’ views,
and 8th grade students mostly reported views regarding the other important communication skills included out-of-class
categories of class management, teaching methods and communication, caring students, good use of tone of voice
measurement-evaluation. This situation shows that there is in class, effective use of Turkish and calling students by
not a single way of describing a mathematics teacher. As their names. This result is similar to those reported by Iossi
reported in other studies, there are various descriptions of [31], Shulman [32] and Vinson [65], who, in their studies,
an effective mathematics teacher at various other education pointed to the importance of the teacher’s field knowledge
levels (for example, elementary school, high school and so and his or her transfer of this knowledge to students. In this
on) [49-51]. Parallel to this finding, in the present study, respect, considering the fact that mathematics teachers’
when the students’ views regarding the categories of communication with students has a relationship with
personal traits, class management-teaching methods, and students’ interests and achievements in the course of
measurement-evaluation were examined, it was seen that mathematics, mathematics teachers’ patient and
there were differences between the views of the 5th, 6th, 7th self-sacrificing attitudes towards students could help
and 8th grade students with respect to their cognitive levels overcome students’ negative perceptions regarding
and needs. mathematics. In addition, it is thought that positive
In In relation to personal traits, the 5th and 6th grade perceptions regarding mathematics could allow increasing
students mostly focused on entertainment and appearance, the average success rate especially in the course of
while the 7th and 8th grade students mostly mentioned such mathematics to the desired level in Turkey as well as in
qualifications as being egalitarian/fair and international exams (like PISA, TIMMS and so on).
hardworking/effective. In addition, according to the 5th and In relation to another category, it was found that the
6th grade students, if a mathematics teacher has qualifications of a mathematics teacher regarding class
good-looking appearance and courtesy (dressing well, management and teaching methods had a relationship with
speaking well) and if he or she is easy-going, sincere/frank, being an effective mathematics teacher. In the study, it was
entertaining, enthusiastic and friendly, then students’ found that the 5th and 6th grade students focused more on
interest and achievement in the course of mathematics will the teacher’s way of teaching, while the 7th and 8th grade
increase. Similarly, other studies demonstrated that a students mostly mentioned use of technology, active
student’s achievement in a course has a relationship with participation, variety in methods and solving more
the teacher’s being entertaining, friendly and enthusiastic mathematical problems to be able to attend a better high
[18,52-55]. On the other hand, Gillett and Gall [56] school (In Turkey, students are allowed to attend
reported that a friendly and enthusiastic teacher does not better-quality high schools in accordance with their results
guarantee students’ achievement in a course though such a in the High School Placement Exam, which is conducted at
teacher will increase students’ interest and enthusiasm. In the end of the secondary school 8th grade class. Students
the present study, the views of the 7th and 8th grade students, who do not take this exam are placed in other high schools
who were preparing for the high school placement exam, in line with their average grades at secondary school. See
revealed that a mathematics teacher who was 1.1). Based on this situation, it could be stated that students
egalitarian/fair and hardworking/effective had positive at different levels have different needs. This result is
influence on the students’ achievement in the course of consistent with the results of other studies which reported
mathematics. Similarly, some other studies showed that the that an effective teacher is described differently at different
personal traits of an effective teacher with fair, objective education levels (for example, elementary school,
and democratic behaviours had influence on students’ love secondary school and high school) [49-51]. In addition, the
for the teacher and on their achievement in the course students generally believed that a mathematics teacher
[7,52,57]. should have such qualifications as ‘good class management,
According to the views of the students participating in considering individual differences, teaching lessons as
the present study, the most frequent and important appropriate to students’ levels and interests, use of
communication skills of an effective mathematics teacher technology, providing up-to-date information about the
included attitudes towards students. A teacher with good lesson subject, being clear’. It is in related literature that
and sincere attitudes towards students had influence on other researchers [53,66-71] reported similar results in
their interest and achievement in the course of mathematics. their studies. When the views of the students participating
12.
Universal Journal of Educational Research 7(2): 536-549, 2019 547
in the present study were examined, it was seen that due to related suggestions and make the mathematics teaching
the abstract nature of mathematics, a mathematics teacher process more effective.
can achieve effective and permanent learning in students
by working in a disciplined manner, using concrete
materials appropriate to the lesson subject, addressing
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