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The use of the history of mathematics in teaching-learning process: The
perspectives of faculty members and teachers
Article · August 2021
DOI: 10.52963/PERR_Biruni_V10.N2.17
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Psycho-Educational Research Reviews | Vol. 10, No. 2 (August 2021)
THE USE OF THE HISTORY OF MATHEMATICS IN TEACHINGLEARNING PROCESS: THE PERSPECTIVES OF FACULTY
MEMBERS AND TEACHERS
1
Abstract: The aim of this study was to investigate the faculty
members’ and the middle school mathematics teachers’
perspectives regarding the use of the history of mathematics in
the learning-teaching process of mathematics. As a
phenomenological study, the qualitative data were collected
through semi-structured interviews from 27 middle school
mathematics teachers and seven faculty members and then,
subjected to the content analysis. The findings revealed that both
teachers and faculty members believed that using the history of
mathematicsis a worthwhile effort, with the potential to not only
provide meaningful learning opportunities for students but also
enrich teachers’ professional development. However, it was also
found that lack of historical perspective in the curriculum,
teachers’ inadequate knowledge, time constraint, no room for
the history of mathematics in the textbooks and exams,
overloaded curriculum and students’ inadequate desire to learn
were some of the reasons for rarely-use of the history of
mathematics. Based on the overall findings of the study, it is
concluded that teacher education (both pre-service and inservice), the structure of mathematics curriculum, teachers’ and
students’ characteristics were the most important dynamics to
integrate the history of mathematics into teaching effectively.
Keywords: the history of mathematics, mathematicians,
mathematics teachers
Gençkaya Şeyda, MsC
Mathematics Teacher
Şehit Meriç Alemdar Middle School Turkey
Contact:
E-mail: <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>
ORCID: 0000-0003-4970-8336
Tan-Şişman Gülçin
2
, PhD
Assist. Prof. Dr.
Department of Educational Sciences
Hacettepe University
Turkey
Contact:
E-mail: <PRESIDIO_ANONYMIZED_EMAIL_ADDRESS>
ORCID: 0000-0002-3806-6086
1 The present study is partly based on the first author’s master thesis under the supervision of the second author.
2 Corresponding author
Psycho-Educational Research Reviews | Vol. 10, No. 2
London Academic Publishing, August 2021, pp 241–257
https://www.journals.lapub.co.uk/index.php/PERR
DOI: 10.52963/PERR_Biruni_V10.N2.17
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Psycho-Educational Research Reviews | Vol. 10, No. 2 (August 2021)
INTRODUCTION
Mathematics is a branch of science that manifests itself in every field from the smallest building blocks to
the most complex formations in the universe. Striking reflections of mathematics can be seen in countless
natural settings including the number of daisy flower petals, the intersecting spirals of pine seeds on cones,
the elliptical orbits of the planets around the sun, the fixed value of division of the circumference by the
diameter of all circles, or the helix curve shape of ivy around trees (Altun, 2008; Sertöz, 2011). Not only
Galileo’s description of nature as “a book written in the language of mathematics” (as cited in Topdemir,
2011, p.104) and also Sertöz's description mathematics as “creator’s hints left in the nature” (2011, p.3)
imply that mathematics has in fact existed in the universe since the genesis.
Since the first years of history, human beings started laying the foundations of mathematics in order to
solve the daily needs, encountered problems, and to understand the universe. The earliest mathematical
activity started approximately 5000 B.C. around Egypt, Mesopotamia, China, and India (Baki, 2014; Bell,
1992). The discipline gradually flourished as number systems were invented by the Babylonians, the
Egyptians, the Chinese, and the Greeks fulfilling their daily needs; mathematical and arithmetic studies
were carried out by mathematicians such as Pythagoras and Euclide; and Plato performed studies on
irrational numbers and smooth polyhedrons (Abdulhay, 2014; Baki, 2014; Cajori, 1919/2014). In the
following years, significant progress were made in the finest calculation of trigonometric values, in algebra,
cubic equations, and logarithm, derivatives, integral, and complex numbers, eventually resulting in an
exponential accumulation of mathematical knowledge (Baki, 2014; Cajori, 1919/2014; Zeki Bey, as cited
in Demir, 2004). After the 19th century, developments in mathematics have spread across the world; as a
result, significant numbers of mathematicians in different parts of the world have contributed to
mathematics in various ways.
In the 21st century, understanding of mathematics has of utmost importance since learning mathematics
provides individuals to develop scientific thinking skills, apply them to different situations, produce original
ideas, make research, gain self-regulation skills, and develop self-confidence (Hattatoğlu, 2010; Işık, Çiltaş
& Bekdemir, 2008; Karakurumer, 2003; National Council of Teachers of Mathematics, 2000; Rizki &
Priatna, 2019). Putting emphasis on the essence of mathematics literacy, Ojose (2011, p.91) stated that
“Mathematics is so entwined with today’s way of life that we cannot fully comprehend the information that
surrounds us without a basic understanding of mathematical ideas”. According to the framework of the
Programme for International Student Assessment (PISA) 2021, mathematical literacy is “an individual’s
capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems
in a variety of real world contexts. … It assists individuals to know the role that mathematics plays in the
world …” (OECD, 2018; p.7). Tekin and Tekin (2004) also argued that mathematically literate person has
knowledge and skills about the following areas: (a) content area literacy; (b) mathematical thinking process;
(c) up-to-date knowledge of mathematics, and (d) historical evolution of mathematics. In a similar vein,
Steen (2001) acknowledged “Cultural Appreciation” as one of the fundamental elements for the concept of
quantitative literacy, and defined as “Understanding the nature and history of mathematics, its role in
scientific inquiry and technological progress, and its importance for comprehending issues in the public
realm” (p.8). In this respect, being mathematically literate requires understanding of the historical side of
mathematics including not only evolution of mathematics as a discipline but also the leading
mathematicians and their contributions. Comparing the perspectives from past to present, Ding (2019) also
emphasized the essence of the history of mathematics as follow:
“In the past, it was generally believed that the study of mathematics history was an elegant, sunny and
white snow-like model. However, in today's era, mathematics teaching … pays more attention to the
cultivation of ideological methods and emotional attitudes and values. The history of mathematics has
thus got rid of the situation … and it has gradually been valued …” (p.783)
The history of mathematics is a field of study that put forwards past obstacles and difficulties which
mathematicians have overcome in the development of mathematics; reveals mathematics’ dynamic nature
(Liu, 2003) and “shows the evolutionary and progress of mathematical knowledge through civilizations”
(Baki, 2014, p.3). In other words, history of mathematics is a comprehensive area that deals with the growth
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processes of mathematics, the lives, works, achievements or failures of leading figures who have
contributed to mathematics, the social and cultural dimension of mathematics, and development and
progression of mathematical knowledge (Bidwell, 1993; Burton, 2003; Eves, 1990; Katz, 1993; Otte, 2007;
Pepe, & Guerraggio, 2017; Yee and Chapman, 2011). Studies on the use of history of mathematics in
mathematics education first appeared in the 1970s. The research in this area is now being supported by
various world-wide institutions and organizations concerned with mathematics education (e.g. the
International Commission on Mathematical Instruction [ICMI]) (Clark, Kjeldsen, Schorcht, Tzanakis and
Wang, 2016; Fauvel and Maanen, 2002; Fried, 2001).
The findings of various research studies pointed out that the use of history of mathematics in learning and
teaching process bears potential contributions to both students and teachers. Specifically, it is stated that
the history of mathematics helps students to comprehend the formation of mathematical thinking, improve
problem-solving skills, assess mathematical topics in a comparative way between the past and present,
establish relationships between mathematical topics and other disciplines, and appreciate that mathematics
is a constantly evolving discipline (Alpaslan, 2011; Ho, 2008; Jankvist, 2009; Lim & Chapman, 2015; Liu,
2003; Sullivan, 1985; Wilson and Chauvot, 2000). Besides, the history of mathematics has a supporting
role for teachers to gain different perspectives, to comprehend mathematical facts unnoticed before, and to
move from product-oriented instruction to process-oriented (Radford, 2014). Teachers, while blending their
qualified knowledge about the history of mathematics with in-class activities, can develop their creativity
and also acknowledge the reason for teaching each specific topic. As a result, their teaching skills might
improve (Furinghetti, 1997; Guillemette, 2017; Haile, 2008; Kjeldsen, 2011; Liu, 2003; Nataraj & Thomas,
2009; Pengelley; 2002). Bidwell (1993, p.461) notes that students think mathematics “as a closed, dead,
and emotionless island; where teachers can rescue them for replacing them on an alive, open, full of
emotion, and always interesting mainland” when they integrate history of mathematics in the learning and
teaching of mathematics. In the literature, there have been numerous studies emphasizing that the
integration of mathematics history into the learning and teaching process might provide more meaningful
and real-life connected learning environment, yet there have been some factors affecting the development
of such environment. According to the literature, such issues as no room for the history of mathematics in
the curriculum, lack of instructional resources and/or materials, teachers’ limited or lack of knowledge
about the history of mathematics, etc. (Baki & Yıldız, 2010; 2016; Başıbüyük, & Şahin, 2019; Sözen, 2013;
Fried, 2001; Siu, 2007; Niitsuma & Nagaoka, 2014; Tan-Şişman & Kirez, 2018).
Although there have been various research studies conducted with mathematics teachers on why’s and
how’s of the mathematics history, to our knowledge, there is no research study on the views of
mathematicians regarding the use of the history of mathematics. Ding (2019) argued that neither theory
(the pure knowledge of mathematics history) nor practice (the pure knowledge of how to teach
mathematics) has produced better ways to integrate the history of mathematics. In this respect, the purpose
of the present study was to investigate the views of faculty members’ and mathematics teachers’ regarding
the use the history of mathematics in the learning-teaching process of mathematics. More specifically the
study seeks to answer the following research questions:
1. What are the faculty members’ opinions about the use of the history of mathematics in learning and
teaching process?
2. What are the the mathematics teachers’ opinions about the use of the history of mathematics in
learning and teaching process?
It is believed that portraying comparatively the views of faculty members, who have deep theoretical
knowledge of the mathematics discipline, and the mathematics teachers, who are practitioners of the
learning-teaching process, about why and how to use the history of mathematics is essential to promote
theory-enhanced practice for the integration of the history of mathematics. It is also expected that the results
of this study will be valuable for many stakeholders. Firstly, the findings will contribute to mathematics
teachers who are one of key actors in interpreting and transforming written curriculum into the learning and
teaching process. In addition to the mathematics teachers, the findings of this study may also be worthwhile
for curriculum developers to provide comprehensive bases of why and how the history of mathematics
should be used in mathematics education in terms of the different points of view. Besides, this study might
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provide helpful insights and implications, emerged from not only the experiences of the mathematics
teachers but also from the suggestions of the faculty members with their in-depth content knowledge, both
for curriculum development and implementation process.
METHOD
RESEARCH DESIGN
In this qualitative study, the phenomenological approach that focuses on “to seek reality from individuals’
narratives of their experiences and feelings, and to produce in-depth descriptions of the phenomenon”
(Yüksel & Yıldırım, 2015, p.1) was used. Since the focus of this study was on the insights of faculty
members and mathematics teachers about why and how the history of mathematics should be used in
teaching and learning process; the phenomenological research design was employed to understand how a
phenomenon, which in this case was the use of mathematics history in learning and teaching processes,
comprehended among different stakeholders.
PARTICIPANTS
The study was conducted with seven faculty members working at different Turkish public universities and
27 mathematics teachers working at the public middle schools located in six central districts of Ankara.
The faculty members were selected by convenient sampling. Through searching on the official web pages
of the Turkish state universities, the researchers listed the faculty members who were working as a fulltime faculty at the departments of mathematics or mathematics education and were interested in the history
of mathematics. Then, the faculty members were selected on the basis of their accessibility and convenience
to the researchers and they were invited to the study via e-mail. As given in Table 1, totally seven faculty
members from five different state universities volunteered to take part in this study. Among seven faculty
members, four of them were working as a full-time faculty at the department of mathematics education and
three were at the department of mathematics. With regard to the K-12 level teaching experience, three of
them have experience of 1-5 years, three have no experience and one has experience of 5-10 years. In
addition, while the majority of the faculty members (n=6) did not take any course about the history of
mathematics during their undergraduate or graduate education, four of them lectured the history of
mathematics course at undergraduate and/or graduate level.
Table 1. The Faculty Members’ Profiles
Faculty
Members’
Profiles
F1 F2 F3 F4 F5 F6 F7
Gender Male Male Male Male Male Male Male
Age 40-45 61-65 50-55 50-55 50-55 55-60 61-65
Title Asst. Prof. Dr. Assoc. Prof. Dr. Prof. Dr. Prof. Dr. Prof. Dr. Prof. Dr. Prof. Dr.
University A B C D B E C
Department Math Math Ed. Math Ed. Math Math Ed. Math Ed. Math
K-12 teaching
experience - 5-10 1-5 - 1-5 1-5 -
Taking HoM*
course
No No No No No Yes No
Lecturing
HoM course No Yes No No Yes Yes Yes
*HoM: The history of mathematics
Further, the mathematics teachers were selected through maximum variation sampling method that allows
researchers to collect in-depth information and mirror divergent perspectives rather than making a
generalization (LeCompte, Preissle, & Tesch, 1993; Patton, 2015). In this scope, 27 math teachers from 12
different middle schools located in Çankaya, Yenimahalle, Etimesgut, Keçiören, Pursaklar, and Altındağ
districts of Ankara took part on a voluntary basis. Besides, the central district where the school located, the
population of the schools, the types of schools (double-shift [DS]/single-shift [SS]), years of experience in
teaching, and educational background was taken into account while determining the participants. As seen
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in Table 2, 23 female and four male mathematics teachers were participated to the study. With regard to
teachers’ years of experience in teaching, it ranges from one to 35 years, while the majority (n=9) has
experience of 1-5 years. In addition, 22 of the participants graduated from faculty of education and five
from faculty of science.
Table 2. The Mathematics Teachers’ Profiles
Teachers Gender Graduation District Teaching experience School population Type of schooling
T1 Male F.ED* Keçiören 26 and above 1000-1499 DS
T2 Female F.ED Keçiören 11-15 1000-1499 DS
T3 Female F.ED Etimesgut 11-15 1500-1999 DS
T4 Female F.ED Altındağ 1-5 1000-1499 DS
T5 Female F.ED Yenimahalle 11-15 1000-1499 DS
T6 Female F.ED Pursaklar 1-5 1000-1499 DS
T7 Female F.ED Etimesgut 6-10 500-999 SS
T8 Female F.ED Etimesgut 16-20 500-999 SS
T9 Female F.ED Yenimahalle 11-15 1500-1999 DS
T10 Female F.ED Altındağ 1-5 500-999 DS
T11 Male F.SC** Yenimahalle 16-20 1000-1499 DS
T12 Female F.ED Keçiören 1-5 1000-1499 DS
T13 Female F.SC Keçiören 26 and above 1000-1499 DS
T14 Female F.ED Altındağ 1-5 500-999 DS
T15 Female F.ED Pursaklar 1-5 1500-1999 DS
T16 Female F.SC Altındağ 1-5 1000-1499 DS
T17 Female F.ED Çankaya 6-10 500-999 DS
T18 Female F.ED Pursaklar 1-5 1500-1999 DS
T19 Female F.ED Çankaya 11-15 500-999 SS
T20 Female F.ED Yenimahalle 11-15 1000-1499 DS
T21 Female F.SC Yenimahalle 21-25 1500-1999 DS
T22 Female F.ED Pursaklar 11-15 1500-1999 DS
T23 Male F.ED Çankaya 21-25 500-999 SS
T24 Female F.ED Çankaya 16-20 500-999 SS
T25 Female F.SC Çankaya 16-20 500-999 SS
T26 Female F.ED Yenimahalle 6-10 1500-1999 DS
T27 Female F.ED Pursaklar 1-5 1000-1499 DS
F.ED*
: Faculty of Education F.SC**: Faculty of Science
DATA COLLECTION INSTRUMENTS
In this study, Faculty Members Interview Form (FMIF) and Teachers Interview Form (TIF) were developed
by the researchers and used as the main data collection instruments. While developing the interview
schedules, first of all the literature was reviewed in detail to outline the important issues regarding the use
of the history of mathematics in teaching and learning process. Through synthesizing the information
gathered from the literature, the draft interview schedules were written in line with the research questions.
Afterwards, the drafts went through revision with the help of expert opinions gathered from two faculty
members from the department of Educational Sciences and two mathematics teachers. Based on feedbacks
received from the experts, the wording of some questions was changed and some follow-up questions and
prompts were either added or removed in order to make questions more clear and understandable. Then,
the draft TIF was piloted with three mathematics teachers and FMIF was piloted with two faculty members
to determine whether the questions make sense to the interviewees and as a result, no changes were applied
to the drafts. In this respect, the final interview schedules were composed of the questions about
demographic information (e.g. age, educational background, etc.) and the use of history of mathematics in
learning and teaching process (e.g. “What is your opinion about the integration of the history of
mathematics in teaching and learning of mathematics?”, “What do you think about the current situation of
the use of the history of mathematics in classrooms?”, “What should be done to use the history of
mathematics effectively?”).
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DATA COLLECTION AND ANALYSIS
Before the collection of the data, the necessary permissions from the Ethics Commission of Hacettepe
University and the Ministry of National Education were obtained. In order to conduct interviews with
mathematics teachers, the researchers contacted with the principals of the selected schools for scheduling
the short meetings to introduce the study. Then, the interviews were conducted with 27 mathematics
teachers who had volunteered to participate in the study. The faculty members were invited to the study via
e-mail and totally seven faculty members from five different state universities volunteered to take part in
the study. All interviews were audio recorded and lasted approximately between 30 to 45 minutes.
The collected data were subjected to content analysis. The steps followed during the content analysis
process were: (1) transcribing the raw data, (2) organizing and preparing data for analysis, (3) reading
through all data, (4) coding the data, (5) generating themes or description, (6) interrelating
themes/description and (7) interpreting the meaning of themes/descriptions (Creswell, 2013; Yıldırım &
Şimşek, 2013). In this respect, first of all, the interviews were transcribed word by word on a word
document. Then transcribed data were read thoroughly for a few times considering the research problems
to identify the conceptual framework. The coding was done by considering approximately every expression
used by participants not missing any important details. Finally, the codes focusing/implying the similar
ideas were combined under categories and themes. The teachers were coded as T1 through T27; while the
faculty members were represented with F1 to F7. The opinions of the participants were reported with direct
quotations.
TRUSTWORTHINESS
Trustworthiness of a research is characterized as provisions or actions that establish reliability and persuade
readers about accuracy of the findings (Lincoln & Guba, 1985). To enhance trustworthiness of the present
study, several strategies were used such as credibility, transferability, dependability, and confirmability. To
establish credibility, triangulation via data sources (Shenton, 2004) was carried out among the teachers’
and field experts’ perspectives. The codes in data analysis were submitted to one faculty member from the
department of Educational Sciences, who have knowledge of the research problem and qualitative research
methods, as required by peer debriefing for credibility. In addition, interviews were recorded with a
recording device with participants’ consent and the recordings were verified by participants at the end of
the interviews for member checks. Further in order to help transferability of the study, the scope and
limitations of this research were set out clearly and the methodology of the study was explained thoroughly.
Besides, the data were enriched by maintaining quotes from participants as well as displayed in details in
order to provide thick description for the sake of trustworthiness of the study. During the study
confirmability, namely “the qualitative investigator’s comparable concern to objectivity” (Shenton, 2004;
p.72), were provided by making use of audit trail and triangulation. The detailed methodological
descriptions were made to allow integrity of research results to be investigated. In addition, the data were
reported by reducing the effect of researcher bias. Lastly, Miles and Huberman’s (1994) formula
(Reliability = Number of agreements / (Agreements + Disagreements) x 100) was used for reliability
analysis. In this respect, two randomly selected transcriptions of the participants (two from teachers, two
from faculty members) were coded by one researcher and one expert separately and independently. The
agreement between coders was found as .87 for TIF and .84 for FMIF. To solve the disagreements, both
sets of data were compared, and through discussion, the disparities were reconciled to reach a consensus.
RESULTS
THE VIEWS OF THE FACULTY MEMBERS REGARDING THE USE OF HISTORY OF MATHEMATICS
The findings revealed that all of the faculty members expressed that the history of mathematics should be
used in learning and teaching process. They believed that students could benefit from using the history of
mathematics in the classroom as it provides opportunity to (a) internalize the idea that mathematics is a
human creation, (b) enhance their learning, (c) understand the process of mathematical knowledge
formation, (d) gain a rich perspective on mathematics and (e) appreciation of mathematics. In addition, the
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faculty members stated that making use of the history of mathematics might help for mathematics teachers
to enhance their content knowledge and support to implement student-centered instruction. In the Table 3,
the results were summarized with quotations from the faculty members’ views.
Table 3. The Benefits of Use the History of Mathematics
Benefits for Students f Faculty Members’ Views
Internalizing the idea
that mathematics is a
human creation
3 “…Most of the students leave the lessons with a wrong impression like this: ‘What I've
learned right now … is came out of the minds of a mathematician or a few mathematicians ...
as a whole like the way the teacher taught me’. In fact, what one needs to know what stages
have been through for bearing that theorem, its simple forms, the issues inspired that
theorem.” F7
Enhance students’
learning
2 “…According to the Fuzzy logic, there are gray areas between zero and one. You need to rate
them, too. So it's been a lot of application to technology. For example, dishwashers, you set
the program as very dirty, less dirty or even lesser dirty… That’s Fuzzy logic! Now, if this
kind of information is given during the lesson or on textbook or a teacher draws students’
attention by mentioning them in two or three minutes; s/he can transform abstract structure
of mathematics into concrete one.” F5
Understanding the
process of
mathematical
knowledge formation
1 “You know, students always ask about mathematics ‘What does that do? Where does it come
from?’ It is taught in a very abstract way. When it is taught with the historical perspective,
students can be able to see that in reality, every concept was born by a need, or this need
may be both the need of physics and math or came as a need in mathematics itself, but
nothing contains an abstract nature in the sense that students think. Abstract but that
abstraction surely solves a problem responding to something. That is the biggest advantage
of the historical perspective.” F4
Gaining a rich
perspective of
mathematics
1 “One day I asked; “Who is this Binomial, what is the nationality?” etc. Some of the students
said German, some said British. They think Binomial is a mathematician! There is no
mathematician called Binomial!... Then I felt that we should look at the history of
mathematics. For instance, the Pythagoras Theorem, who is Pythagoras? Is Pythagoras a
human? etc. Instead of focusing only the memorization of the theories, we need to provide
students with a deep and broad view of mathematics.” F2
Appreciation of
mathematics
1 “No matter which country you go to around the world, you see that mathematics and
mathematicians are always perceived differently. Mathematics is always regarded as
difficult, like in our country, but doing math is considered as the indicator of a much higher
standard. It is written in many articles, mathematics has a door opener position for
professional career, it is true for not only in our country, but for the whole world. This means
that through the history of mathematics, students can realize that how mathematics is
valuable and important.” F5
Benefits for Teacher f Faculty Members’ Views
Enhancing the content
knowledge
1 “The strength of the use of history of mathematics in terms of a teacher, s/he can teach better.
Because s/he gains knowledge about where the concepts come from, how the problems are
related to. “F4
Supporting studentcentered instruction
1 “The history of mathematics is one of the best medium of instruction for the teachers who
would like to design student-centered learning environment; by making use of the examples
chosen from the history of mathematics, s/he might group students to work together and
implement problem solving method.” F6
Some of the faculty members also mentioned such restricting-issues related to the use of history of
mathematics as “loss of prestige and trust” and “extra workload” due to teachers’ poor/lack of knowledge.
In Table 4, the results were summarized with quotations from the faculty members’ views.
Table 4. The Restricting-issues about Use of the History of Mathematics
Teacher-related issues f Faculty Members’ Views
Loss of prestige and trust 2
“While teaching Binominal Theorem, one of the students asks, ‘When did Binomial live, my
teacher?’ if the teacher doesn’t know, s/he is ruined there! Ruined!” F2
Extra workload 1
“The history of mathematics is a completely different area. A math teacher is not normally
expected to know too much about the history of mathematics... It is an additional burden
for her/him to deal with the history of mathematics… Spending extra efforts on it spending
more time on...” F4
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Further, the results indicated that all faculty members thought that the history of mathematics is almost
never integrated in current mathematics lessons due to several reasons as summarized in Table 5.
Table 5. The Reasons for the Rarely-use of the History of Mathematics
Reasons f Faculty Members’ Views
Teachers’
inadequate
knowledge about
the history of
math
4
“Since the teacher did not get such training, s/he has not any experience or accumulated
knowledge of it (the history of math), the teacher is the biggest obstacle already. S/he is not trained
on that ... the most crucial thing is that the teacher is at that depth; aware of that work. First s/he
is introduced to the use of it (the history of math) become familiar with the activities then, s/he is
able to use of it when becomes a teacher in the future.” F6
“Of course, s/he (a teacher) needs to have adequate knowledge of the developmental journey of
mathematics. In fact, if s/he has enough knowledge, s/he automatically starts to talk about it at
least for two minutes. So s/he says it anyway. However, if a teacher cannot have enough knowledge,
s/he cannot reflect it. The teacher is particularly important here.” F5
Exam-oriented
education 3
“Above all, there are exams. As long as these exams are here, it (the history of math) will be like
an additional burden for students because the goal is to get ready for the exams not to learn
mathematics at all. It is very difficult to use the history of mathematics in such a system, we have
to accept it.” F4
MoNE’s
uninterested
approach
2
“MoNE should understand the importance of it (the use of the history of math). In order to do this,
a lot of work has to be done. We need to explain the importance of the history of mathematics to
them (MoNE). There is also an obstacle as well. For instance one is that the decision makers are
not aware of the importance of the issue enough and also they underestimate how to integrate this
issue into education and class. They think that it will be done as one says ‘Now do this!’ but it is
not the case in the class indeed.” F3
Overloaded
curriculum 1
“Teachers are required to follow and complete the curriculum but one can use the history of
mathematics if s/he wants. It looks like the main obstacle.” F5
Lack of historical
perspective in the
curriculum
1
“Well, there's no obstacle. Indeed, there is no room for it (the history of math) in the curriculum,
so it is not reflected. But if the curriculum includes it, I guess that our students will do it with
pleasure. Just put it in, I don't know why it is not taken into consideration, it must be included in
the curriculum. Because it is really needed. Look, we recall Pythagoras, but the student should be
able to say “Pythagoras was someone, who like that and did something, happened before Christ”
and like that. For example, we always call the Euclidean Theorem. Who is this Euclid, isn’t it?
Here we call the Euclidean Geometry. Well, he must be mentioned in geometry, if not it is
incomplete.” F2
Teachers’ extra
responsibilities 1
“The man (teacher) has the concern of subsistence, does not earn enough money, plus, there is a
lot of burden on him, then he is educator... when come to school, he has to deal with such issues
as making a lesson plans, activities, attending meetings and so on. So teacher is already under
very big burden. If there is no burden and extra loads, it (the use of history of math) would be
possible. However, it's been a big problem since the past, and I don't think it's overcome at the
moment.” F7
Lastly, the faculty members proposed the ways to effectively integrate the history of mathematics in the
teaching and learning process. Their recommendations, as presented in Table 6, focused on mathematics
curriculum, and teacher education.
Table 6. The Faculty Members’ Recommendations for Effective Use of History of Mathematics
Faculty Members’ Recommendations f
Inclusion of the history of mathematics in the curriculum 4
Organizing student-centered learning environment 3
Inclusion of the history of mathematics course in pre-service teacher education program 2
Providing in-service training programs 2
Preparing instructional materials and resources about the history of math 1
Inviting more faculty members having deep knowledge about the history of math to the curriculum development
commissions
1
THE VIEWS OF THE MATHEMATICS TEACHERS REGARDING THE USE OF HISTORY OF MATHEMATICS
The findings revealed that apart from one teacher, all of the mathematics teachers expressed that the history
of mathematics should be used in the learning and teaching process. As given in Table 7, the teachers stated
that using the history of mathematics was a worthwhile effort, with the potential to not only provide
meaningful learning opportunities for students and also enrich teachers’ professional development. Besides,
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the mathematics teachers stated that making use of the history of mathematics might contribute to the
teaching process of mathematics.
Table 7. The Benefits of Using of the History of Mathematics
Benefits for students f
Understanding the process of mathematical knowledge formation 8
Enhancing their learning 6
Being encouraged to do research/science 5
Internalizing the idea that mathematics is a human creation 3
Gaining a rich perspective on mathematics 2
Benefits for teachers f
Enhancing the content knowledge 8
Gaining prestige 5
Improving job satisfaction 2
Enhancing/strengthening communication with students 1
Benefits for teaching process f
Supporting meaningful learning 18
Leading permanent understanding 3
The teachers pointed out the students may benefit from using the history of mathematics in the classroom
as it provides opportunity to (a) understand the process of mathematical knowledge formation, (b) enhance
their learning, (c) being encouraged to do research/science (d) internalize the idea that mathematics is a
human creation, and (e) gain a rich perspective on mathematics. In the Table 8, the results were summarized
with quotations from the teachers’ views.
Table 8. The Students’ Benefits from the History of Mathematics
Students’ Benefits f Middle School Mathematics Teachers’ Views
Understanding the
process of mathematical
knowledge formation
8 “Children want to know how mathematics is discovered. They wonder where will it
work, where did it come from.” T16
“It [the history of mathematics] could be used for explaining why we need mathematics,
such as why it was discovered, what the initial driving forces were in the past.” T25
Enhancing their learning 6 “… a few years ago, when I learned why mathematics emerged and its history, I
realized that I better understood mathematics, so I think that the students could
understand better in that way.” T7
“I think it’s important to lay down the mathematical grounds of the topic.” T23
Being encouraged to do
research/ science
5 “The students sometimes wonder while I am teaching, ‘How did they discover it
teacher?’, ‘Can we discover something, too?’, ‘Is there anything discovered recently?’
they ask. I say ‘Yes you can.” T13
“As a result, when we investigate our own history, students can say: ‘If people like me
did it, I can do it’ and be encouraged.” T18
Internalizing the idea that
mathematics is a human
creation
3 “With the history of mathematics, it is possible to help students to figure out that
mathematics is invented by people, not created in a vacuum, it is the product of human,
and thus can be solved and done.” T11
Gaining a rich perspective
on mathematics
2 “To diversify emergence of numbers, to relate types of numbers… to make feel the
numbers other than the all known classical natural numbers, whole numbers known to
children, I mean they should see the existence of other numbers, they could grow the
thought that these numbers are needed as well, they are used in math indeed.” T5
The middle school math teachers also pointed out that the use of the history of mathematics may help for
teachers to “enhance their content knowledge”, “gain prestige”, “improve job satisfaction”, and
“enhance/strengthen communication with students”. The results on the benefits of using the history of
mathematics for teachers were summarized in Table 9.
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Table 9. Teacher’s Benefits from Using the History of Mathematics
Teachers’ Benefits f Middle School Mathematics Teachers’ Views
Enhancing the
content knowledge
8 “Although I am a mathematics teacher, I have not done much research on the history of
mathematics. I never questioned where this or that came from. But when we include it in the
lesson, we will inevitably need to get prepared before the lesson. If we are expert in the field
of mathematics, memorizing the formulas is not enough; indeed we should learn its history”
T25
“As a teacher, knowing the history of your own lesson is an important thing. At least, s/he
will be aware of what s/he is doing.” T7
Gaining prestige 5 “…I believe that it makes the teacher more powerful to talk about the history of mathematics
while teaching. Because the student might say ’Look! The teacher knows this, too’. It makes
the teacher stronger.” T3
“…The student considers his/her teacher as a well-equipped with cultural and academic
issues, subject matter expert. In this sense, the use of history of mathematics would be nice.”
T22
Improving job
satisfaction
2 “We did not have the opportunity to practice, because the courses we took at the university
were theoretical. Here, at least I have the opportunity to use some of the theoretical
knowledge that I learned. Saying ‘This is something discovered by this person’, ‘This is
something discovered by that person’ or showing their pictures, I also enjoy.” T4
Enhancing/
strengthening
communication with
students
1 “It also helps to connect or touch with the student. Since we are working hard on numbers,
for instance, we cannot do anything special to touch with student, yet the history of
mathematics offers some ways.” T9
The mathematics teachers participated in the study stated that using the history of mathematics might also
contribute to improve mathematics teaching in terms of meaningful learning and permanent understanding.
In Table 10, the results were summarized with quotations from the teachers’ views.
Table 10. The Benefits of Using the History of Mathematics for Teaching Process
Benefits for
Teaching Process
f Middle School Mathematics Teachers’ Views
Supporting
meaningful learning
18 “If the student knows its history, learns what it is for, then s/he listens more willingly. The lesson
will be more productive. It has a positive effect on my class.” T21
“…It draws attention, for example, when I teach, somewhere during the lesson, I say: ‘While
the Egyptians were building the pyramids, they used similarity.’ or ‘Thales did this and that’
and so on. It draws their [students’] attention…” T3
Leading permanent
understanding
3 “…For example, I taught Thales Theorem about similarity. The students immediately said 'Oh,
this is a Thales question; this is something that Uncle Thales did'. I believe it is more longlasting because they keep in mind in this way.” T4
“I've always questioned my children about why and where they came from, I use the proofs, to
make learning more permanent” T19
On the other hand, some of the teachers emphasized that the use of history of mathematics in learning and
teaching process may turn into disadvantage due to both student-related and teacher-related issues. As given
in Table 11, the student-related issues were expressed as “finding the history of mathematics as boring”;
“not being interested in the history of mathematics because it is not a requirement of the mathematics
course” and “failing to associate the history of mathematics with mathematics”. The teacher-related issue
was stated as “loss of prestige and self-confidence” due to the teachers’ poor knowledge about the history
of mathematics.
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Table 11. The Restricting-issues about Using the History of Mathematics
Student-related issues f Middle School Mathematics Teachers’ Views
Finding the history of
mathematics as boring
6 “Verbal things would be problem for a student who is used to work with numbers. S/he
may not like it very much. Because some students just focus on the numbers while
studying on math. The history of mathematics is not very interesting to them. This may be
a negative thing for them.” T6
“Those who don’t like history or social study lessons might be biased towards the history
aspect of math.” T25
Not being interested in
the history of
mathematics
6 “…Some students see this [the history of mathematics] as a waste of time because they
are used to testing. Sometimes, I show videos about mathematicians, for example, I hear
such voices as ‘Teacher, let’s solve tests’, ‘We have exam, will they be in the exam?' from
students” T27
“It may also seem like a waste of time for the students. They are totally focused on the
exam; it may seem a bit of a waste of time for them.” T10
Failing to associate the
mathematics with its
history
1 “Perhaps the history of mathematics will sound too abstract because they will not be able
to associate it with mathematics much.” T24
Teacher-related issues f Middle School Mathematics Teachers’ Views
Loss of prestige and
confidence
4 “You need to have a strong mastery of the subject matter. If you don't have a mastery of
the history, you can say something wrong in the examples you give. If the student also
reads in a book and claims that this knowledge is not like this but like that, then you may
contradict with the student. Then you will lose his/her trust, as well as your prestige and
self-confidence.” T5
The results related to the teachers’ current use of the history of mathematics in their classrooms revealed
that only three teachers stated that depending on the topic, they integrate adequately the history of
mathematics in learning and teaching process; while the rest of the teachers stated that they rarely use the
history of mathematics due to the reasons given in Table 12.
Table 12. The Reasons for the Rarely-use of the History of Mathematics
Reasons f Middle School Mathematics Teachers’ Views
Lack of historical
perspective in the
curriculum
9 “Because of the curriculum, I mean the history of math is not included in the curriculum. We
follow the curriculum and thus, we do not have to explain or teach.” T11
“The curriculum is lack of the history of math, so there's a comfort due to that. But if it was
included in the curriculum, I would have to mention it; at least I would have to get prepared for,
spend some more time on it. I think I'm taking advantage of not having it in the curriculum.” T22
Teachers’
inadequate
knowledge about
the history of
math
9 “I couldn’t include it [the history of math] in every topic because I don't know that whether the
other topics are related to it frankly. I'm trying to include it in the topics that I know. I don’t
know, if I knew I would include it and maybe use it more effectively.” T3
“If I had mastery on it [the history of mathematics], I would certainly discuss a bit with the
students at the beginning of the lesson. Actually, I do not have much knowledge about the history
of mathematics and also I have not research on it much, though it was my fault.” T21
No room for the
history of math in
exams
7 “The fact that there is no question about it [the history of math] in the exams affects a lot. A
student thinks 'Such questions will not appear in exams, so it doesn’t matter whether I learn it or
not.” T24
“…The system is also built on exam-based approach. Everything is measured by tests or written
exams. Among them, there is nothing about the history of math. So, for students, the number of
correct answers in a text is important. The history of mathematics is not asked in exams.” T15
Time constraint 5 “I already have so much to cover in class, I have no time doing such activities as ‘Wow, who
found it’, ‘Where it came from’ and so on. If we had more time, we could think how we could
spend this time, maybe we could figure out the use of it [the history of math]. But we never have
the chance to do that.” T20
No room for the
history of math in
the textbooks
5 “I don't do anything particularly different from the textbook. The textbook approved by the
Ministry of Education is not included in it, so I think that it is not necessary. In my opinion, if it
is considered as essential, then it will be in the textbook. ” T8
Overloaded
curriculum
2 “There are a lot of content. The curriculum is overloaded, and due to the covering all topics in
the curriculum, we have problems with the use of it”. T16
Students’
inadequate desire
to learn
2 “I mention it [the history of math] only when the students ask ‘What it is used for’… We explain
when the student asks a question but if they ask nothing, we don’t talk about it. We start the
lesson directly.” T9
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Lastly, the middle school mathematics teachers proposed the ways to effectively integrate the history of
mathematics in the teaching and learning process. Their recommendations are presented in Table 13.
Table 13. The Teachers’ Recommendations for Effective Use of the History of Mathematics
Teachers’ Recommendations f
Providing in-service training programs 20
Organizing student-centered learning environment 10
Inclusion of history of math in the curriculum 10
Preparing instructional materials and resources about history of math 8
Inclusion of history of math in textbooks 5
Reducing the intensity of the curriculum 3
Using the history of math in elective mathematics courses 3
Increasing the course hours 1
Inclusion of the history of math course in pre-service teacher education program 1
DISCUSSION AND CONCLUSION
The present study was carried out to investigate the faculty members’ and the mathematics teachers’
perspectives regarding use of the history of mathematics in the learning-teaching process of mathematics.
The findings revealed that almost all of the middle school mathematics teachers and all of the faculty
members believed that the use of the history of mathematics is necessary and important. The result is
consistent with the findings from previous studies in the literature (Baki & Yıldız, 2010; Dejic &
Mihajlovic, 2014; Hatisaru & Erbaş, 2012; Tokay, 2019; Yevdokimov, 2007).
In addition, both teachers and faculty members expressed that the use of the history of mathematics is a
worthwhile effort, since the history of mathematics might help students to understand the process of
mathematical knowledge formation, to enhance their learning, to gain rich perspective on mathematics. The
previous studies in the literature support the findings of the study. For example, Ho (2008) argued that the
history of mathematics helps students to understand the process of mathematical knowledge formation.
Similarly, according to Liu (2003), students can better understand that mathematics is a constantly
developing discipline with the use of the history of mathematics. Also, Siu (1993) stated that it can help
students to gain a rich perspective of mathematics. Moreover, Tözlüyurt (2008) found out that mathematics
lessons involving the activities selected from the history of mathematics can provide students to gain
different perspective of mathematics. Similarly, the studies of Dickey (2001), Awasonya (2001), and
Nataraj and Thomas (2009) also supported that the history of mathematics can support better understanding
of mathematics. Besides, the study revealed that the use of history of mathematics may provide internalizing
the idea that mathematics is a human creation for students. This result was also in compliance with Kaye’s
(2008) study. Hence, it can be concluded that the both teachers and faculty members appreciate the
importance of the history of mathematics for offering more meaningful and enriched learning experiences
to students. In other words, they seem to be aware of the potentials of integrating history of mathematics
into learning and teaching process in designing well-qualified and rich mathematics learning environments.
Moreover, the middle school math teachers and faculty members stated that the history of mathematics may
help for teachers to enhance their content knowledge. Besides, the teachers expressed gaining prestige,
improving job satisfaction and enhancing communication with students as the strengths of the use of history
of mathematics, while the faculty members emphasized the student-centered instruction. In the literature,
it is pointed out that teachers, while blending their qualified knowledge about the history of mathematics
with in-class activities, can develop their creative skills and acknowledge the reason for teaching each
specific topic. As a result, their teaching skills might improve (Furinghetti, 1997; Liu, 2003; Nataraj &
Thomas, 2009; Pengelley, 2002). Furthermore, it is asserted in the literature that if the teachers are
interested in the history of mathematics and integrate it in the learning-teaching process this may improve
their knowledge, skills and attitudes about mathematics (Panasuk & Horton, 2013; Tymocsko, as cited by
Liu, 2003). Similarly, in Ulusoy and Girit-Yıldız’s study (2019) it is also found that the history of
mathematics is necessary in order to enhance teachers’ content knowledge and prestige. Besides, the middle
school math teachers stated that the history of mathematics could support meaningful learning and lead
permanent understanding and these results were supported with many research studies in the literature
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(Fauvel & Maanen, 2002; Ness, as cited by Fried, 2001; Rickey, 1995). The previous studies also reported
that the use of the history of mathematics in learning and teaching process could increase students’ interest
and curiosity towards mathematics and thus, it could support meaningful learning (Ersoy, 2015; Hatisaru
& Erbaş, 2012; Tong, Loc, Uyen & Thi Y, 2019). In this respect, it can be said that the mathematics teachers
who participated in the study were aware of the importance of the history of mathematics in the learning
and teaching process of mathematics.
Besides the strengths, the participants mentioned some limitations about the use of the history of
mathematics in classroom. The middle school mathematics teachers associated these limitations with both
student- and teacher-related issues; while the faculty members linked them to only teacher-related issues.
Both agreed on that teacher could lose their prestige and confidence if they have poor knowledge of the
history of mathematics. In addition, some of the faculty members stated that if a teacher has poor knowledge
on the history of mathematics, s/he has to deal with extra workload to comprehend and understand it. In
this respect, it is concluded that teachers’ poor/lack of knowledge was one of the reasons preventing
teachers from integrating the history of mathematics in their class. The findings of the present study indicate
similar patterns with the literature (Baki & Yıldız, 2016; Başıbüyük, & Şahin, 2019). Unlike the faculty
members, the middle school math teachers stated that the student-related issues, namely finding the history
of mathematics as boring, not being interested in the history of mathematics and failing to associate the
history of mathematics with mathematics, also affected their decision-making process whether to use the
history of mathematics or not. There are some studies that underline the similar student-related factors
affecting the use of history of mathematics in teaching process. For instance, in the Siu’s list (1998) of
negative effects of the history of mathematics on students, it was stated as “…find the history no less boring
than mathematics” and “lack of assessment” (as cited by Tzanakis & Arcavi, 2000, p. 203). Hence, the use
of history of mathematics in the learning and teaching process might be affected by students’ characteristics
(e.g. beliefs, attitudes towards math, readiness level, etc.) as well as the teachers’ characteristics (e.g.
pedagogical content knowledge and skills, etc.).
Moreover, the majority of the teachers stated that they rarely used the history of mathematics in their
classes. Lack of historical perspective in the curriculum, teachers’ inadequate knowledge about the history
of mathematics, no room for the history of mathematics in the exams, time constraint, no room for the
history of mathematics in the textbooks, overloaded curriculum and students’ inadequate desire to learn
were the reasons of rarely-use of the history of mathematics in the learning-teaching process stated by the
teachers. Besides, all of the faculty members expressed that the use of the history of mathematics in the
classes was limited because of the teachers’ inadequate knowledge about the history of mathematics, examoriented education, MoNE’s uninterested approach, overloaded curriculum, lack of historical perspective
in the curriculum and teachers’ extra responsibilities were the factors affecting the use of the history of
mathematics in learning-teaching process. In this respect, the present study clearly revealed that both the
teachers and the faculty members perceived the history of mathematics as complementary part of
mathematics teaching, but they also underlined such dynamics as education system, curriculum,
instructional materials, time dedicated to math lessons, etc., that undoubtedly affect teachers’ decision on
whether to integrate the history of mathematics or not. The findings of the present study coincide with the
related literature. For instance, Fried (2001, p.394) stated that “Teachers must complete a great number of
topics in a very short time…it is not surprising that teachers should resist introducing a program of history
of mathematics despite its virtues.” Similarly, Siu (2007) pointed out that it might be difficult to use the
history of mathematics in learning-teaching process if teachers have inadequate knowledge about it and
also the history of mathematics does not affect the students’ grade. In addition, Sözen’s (2013) study
indicated that teachers are challenged while using the history of mathematics in their classes because of
having inadequate knowledge about the history of mathematics. In the study of Baki and Yıldız (2016), the
most important factors that seem to prevent teachers from using the history of mathematics in their classes
are the poor quality of the historical parts in the textbooks, inadequate numbers of course hours and the
pressure of the central exam. Similarly, Panasuk and Horton (2012) found that teachers avoid using the
history of mathematics due to lack of adequate knowledge on the history mathematics as well as not
knowing how to use it in their classes.
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Furthermore, providing in-service training programs, organizing student-centered learning environment,
inclusion of history of mathematics in the curriculum, preparing instructional materials and resources about
history of mathematics and inclusion of the history of mathematics in pre-service teacher education
programs are the recommendations stated by both middle school mathematics teachers and faculty
members. In addition, teachers proposed some other ways to effectively integrate the history of mathematics
into learning and teaching process such as inclusion of the history of mathematics in textbooks, reducing
the intensity of the curriculum, using the history of mathematics in elective mathematics courses and
increasing the course hours; while faculty members emphasized that inviting more faculty members having
deep knowledge about the history of mathematics to the curriculum development commissions for using
the history of mathematics effectively in learning and teaching process. As a result, it can be concluded that
organizing the pre-service and in-service teacher education and mathematics curriculum are priorities for
integration of the history of mathematics into learning and teaching process. In other words, it is clear that
both the teachers and the faculty members in the study give priority in their suggestions to increasing
teachers’ level of knowledge about history of mathematics and improving the aspects of the curriculum.
The present study is a phenomenological research focusing on the use of history of mathematics from the
perspectives of the mathematics/mathematics education faculty members and the middle school
mathematics teachers. Overall, as given the Figure 1, the findings of the current study clearly answered the
following questions “Why the history of mathematics should be integrated in teaching and learning of
mathematics?”, “What is the current situation of the use of the history of mathematics in classrooms?”,
“What are the reasons for rare-use of the history of mathematics?” and “What should be done to use the
history of mathematics effectively?”.
Figure 1. The history of mathematics from the perspectives of faculty members and teachers
According to the Figure 1, both the teachers and the faculty members who took part in the study stated that
the history of mathematics should be used, yet the most-agreed reasons avoiding the use of history of
mathematics are teachers’ inadequate knowledge about history of mathematics. In this respect, the results
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call for the improvements in teacher education programs (pre- and in-service) in order to equip teachers
with the knowledge of the historical side of mathematics as well as how to integrate it in mathematics
teaching. Moreover, the issues related to the current mathematics curriculum (e.g. no place for the history
of mathematics, time constraint, etc.) should be solved. It is recommended that stakeholders (e.g.
curriculum development experts, textbook authors, decision-makers, etc.) should improve both the
curriculum and textbooks by considering the possible contributions of the history of mathematics for
students, teachers and learning-teaching process pointed out by the teachers and faculty members in this
study. Lastly, the results of the present study were only based on the views of the faculty members and
mathematics teachers gathered from the qualitative data collection method. Thus, there is a need for additional
research to get a wider picture about students’ opinions and experiences of the history of mathematics in actual
classroom practices.
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