Content uploaded by Gulcin Tan-Sisman
Author content
All content in this area was uploaded by Gulcin Tan-Sisman on Apr 23, 2018
Content may be subject to copyright.
History of Mathematics in the Turkish Middle School Mathematics
Curriculum and Textbooks
Gülçin TAN-ŞİŞMAN a*, Büşra KİREZ a
aHacettepe , ,
Article Info
Abstract
DOI: 10.14812/cuefd.361176
The purpose of this study was to analyze how the history of mathematics incorporated
into Turkish middle school mathematics curriculum (5th-8th grades) and textbooks. The
data were collected through document analysis from the Turkish middle school
mathematics curriculum guide (5th-8th grades) and six Turkish middle school
mathematics textbook series approved by the National Board of Education. According
to the results gathered from the math curriculum, only one reference of the history of
mathematics was found in the sixth-grade learning objectives and a few suggestions
acknowledging the use of the history of mathematics in the learning and teaching
process. No trace of the history of mathematics found in the content and assessment
aspects of the curriculum. Further, the total number of the instances of the history of
mathematics found in the six Turkish middle school mathematics textbooks for 5th-8th
grade is only twenty-seven. Most of the references found in the math textbooks were
placed in the introduction part of the topic. Based on the findings, it is obvious that the
history of mathematics was used like a rarely-found appetizer both in the curriculum
and the textbooks.
Article history:
Received
Revised
Accepted
04.12.2017
05.04.2018
09.04.2018
Keywords:
History of Mathematics,
Turkish Middle School
Mathematics Curriculum,
Turkish Mathematics Textbooks.
Ortaokul Matematik Dersi Öğretim Programı ve Matematik Ders
Kitaplarında Matematik Tarihi
Makale Bilgisi
Öz
DOI: 10.14812/cuefd.361176
matematik
da (5-da
ortaokul matemati
program
incelemesi yoluyla . Ortaokul
6.s
-
ifadeler
. - matematik tarihine
-8.s
tespit
,
, matematik tarihinin hem programda hem
e
Kabul
04.12.2017
05.04.2018
09.04.2018
Anahtar Kelimeler:
Matematik Tarihi,
,
Matematik Ders .
*Author: gulcintans@gmail.com
Vol: 47 No: 1 Sayfa: 188-215
www.cufej.com
- , 47(1), 2018, 188-215
189
Introduction
As a human endeavor and a rich cultural background, mathematics is one of the fundamental school
subjects more than four thousand years of history. While it is widely acknowledged that mathematics is
alive science involving the aspects of daily and professional life, most of the students believe that
mathematics is only about numbers, theorems, symbols, and procedures. One of the reasons behind the
belief that math is a mechanical subject might be due to the ways in which students experience and
engage with mathematics. As McCartney
-
mathematics has a history which is rich in astonishing breakthroughs, false starts, misattributions,
confusions and dead-
concerning the processes of growth and advancements in mathematical knowledge through focusing on
the sources of discoveries in mathematics, the accomplishments, problems, thoughts of well-known
mathematicians (Burton, 2003; Eves, 1990; Katz, 1993; Otte, 2007; Yee & Chapman, 2011).
Focusing on the integration of the history of mathematics, the ignored part of school mathematics,
ffective growth. Fried (2001) argued that history of mathematics (a)
reveals humanistic aspects of mathematics; (b) makes mathematics interesting, more understandable
and approachable; and (c) indicates the origin of mathematical concepts and procedures. Besides,
several research studies on the integration of history of mathematics into mathematics education have
indicated that history of mathematics has potential to promote more positive students attitudes
(Furinghetti, 2000; Liu, 2003; Marshall, 2000; McBride & Rollins, 1977) as well as to facilitate meaningful
understanding of mathematical concepts, procedures and problems through the use of alternative
examples, solution processes, strategies and methods from the history (Helfgott, 2004; Ho, 2008;
Kleiner, 2001). Further, the multicultural nature of mathematics might be enhanced by the integration
studies have not only supported to the use
of history of mathematics in the learning and teaching process and also indicated many benefits for
Hagerty, Smith & Goodwin, 2007;
Jankvist, 2009a; Kaye, 2008; Leng, 2006; Lim, 2011; Liu & Niess, 2006).
Considering a range of well-known arguments in favor of integration of history of mathematics in
classrooms (Fauvel, 1991; Fauvel & Van Maanen, 2000; Jankvist, 2009), the first question might be the
he official document indicating the history of mathematics aimed to be integrated
In this respect, formal curriculum might be considered as an officially-written
document that specifies what/how students are expected to learn and what/how teachers are expected
to teach and assess. The second possible answer for the question raised abov
since they are curriculum materials produced to support curriculum as well as instruction. According to
instructional sources of teachers in many countries. Previous research has clearly indicated that math
textbooks play a central role in translating the intended curriculum into the opportunities to learn in
classrooms ( Fan, Zhu, & Miao, 2013; Reys, Reys, Lapan,
Holliday, & Wasman, 2003; Tan-& Akkaya, 2017; Tyson & Woodward, 1989; Woodward & Elliott,
1990). Valverde, Bianchi, Wolfe, Schmidt, and Houang (2002) conceptualized textbooks by using the
implemented curriculum. In this sense, curriculum and textbooks are considered as the initial parts of
mathematics education and they are one of the primary sources indicating the extent to which history
of mathematics is taken into account by decision-makers and curriculum developers.
- , 47(1), 2018, 188-215
190
Although the integration of history of mathematics has continued to receive a great deal of attention
over t
historical dimension of mathematics both in mathematics curriculum and textbooks (Ho, 2008;
Xenofontos & Papadopoulos, 2015). As seen in Table 1, the contemporary studies on history of
mathematics have been conducted with different participants (e.g. middle school students, math
teachers, etc.), various research designs (qualitative, quantitative and mixed) as well as focused on
different aspects (e.g. beliefs, attitudes, knowledge level, etc.).
Table 1.
The contemporary studies on the integration of history of mathematics
Authors & Year
Subjects
Focus of history of
mathematics (HoM)
Method
Findings
2016
4th grade
students
Effects of HoM on
achievement, retention and
motivation
Quantitative
Positive effect on
achievement, retention and
motivation
Ju, Moon, &
Song, 2016
7thgrade
math
textbooks
Analysis of HoM in Korean
math textbooks
Qualitative
Introduction of HoM in a
variety of ways, but limited to
order thinking
Xenofontos &
Papadopoulos,
2015
7th-9th grade
math
textbooks
Analysis of the ways of
HoM integrated math
textbooks of Cyprus and
Greece
Qualitative
Utilization of HoM through
mostly biographical, the HoM
tasks included both lower and
higher cognitive demands
5th-8th grade
math
textbooks
Analysis of use of HoM in
textbooks
Qualitative
Limited use of HoM, only a
few examples supporting
deeper understanding or
analytical thinking
Povey, 2014
Lecturers of
HoM course
Opinions about use of HoM
in initial teacher education
Qualitative
Positive the contributions of
the studying HoM to the
prospective math teachers
Bayam, 2013
6th grade
students
Qualitative
Positive views
Gazit, 2013
Prospective
& Math
teachers
The knowledge level about
the concepts, topics and
characters from HoM
Quantitative
A lack of knowledge about
HoM found in all groups
8th grade
students
Opinions about the HoM
integrated instruction
Qualitative
Positive opinions
& Haser, 2014
Pre-service
math
teachers
Attitudes and beliefs about
the use of HoM and the
level of knowledge of HoM
Quantitative
Positive attitudes and beliefs,
moderate level of knowledge
of HoM
Pre-service
math
teachers
Relationship between
creativeness and attitudes
and beliefs towards HoM
Quantitative
Low level of relationship
between creativeness,
attitudes and beliefs towards
HoM
Baki & ,
2013
6-8th grade
textbooks
The ways of using HoM in
textbooks
Qualitative
Limited use of HoM
Bayam, 2012
6th grade
students
Effect of HoM on
mathematics achievement
and attitudes
Mixed
Positive effect on
achievement, no significant
difference in attitude.
College
students
HoM integrated instruction
Quantitative
Significant difference in
attitude and achievement
- , 47(1), 2018, 188-215
191
Table 1.
The current studies on the integration of history of mathematics (c
Authors & Year
Subjects
Focus of history of
mathematics (HoM)
Method
Findings
11th grade
students
Use of HoM in geometric
proofing
Qualitative
Increase in geometric proof
skills
Panasuk &
Horton, 2012
Math teachers
Perceptions and the factors
related to the integration of
the HoM
Quantitative
A lack of knowledge and
confidence in HoM, time,
testing, resources found as
factors
Clark, 2012
Pre-service
math teachers
Impact of the study of the
HoM on mathematical
knowledge for teaching
Qualitative
Positive impacts on the pre-
pedagogical
knowledge
Yenilmez, 2011
Pre-service
math teachers
Opinions about the HoM
course
Quantitative
Positive opinions about the
course
Burns, 2010
Pre-service
math teachers
and the role of HoM
Mixed
Positive views and changes in
beliefs about incorporation of
HoM in math lessons
Pre-service
math teachers
Attitudes and beliefs about
the use of HoM in teaching of
math
Mixed
Positive attitudes and beliefs
Huntley & Flores,
2010
Pre-service
math teachers
to develop mat knowledge for
teaching
Qualitative
Positive opinions and
contributions
Jankvist, 2010
Secondary
school
students
Reflections about the meta-
issues of mathematics and its
history
Quantitative
The students were capable of
discussing and reflecting upon
meta-issues of mathematics
and its history.
Thomaidis &
Tzanakis, 2009
7th-9th grade
math textbooks
Analysis of use of HoM in
Greek high school math
textbooks
Qualitative
Numerous historical examples
of math, but including errors,
obscurities, or
omissions
2009
Pre-service
math teachers
Experiences related to use of
Dynamic Geometry Program
when solving the quadratic
equation with Khayyam
Method
Qualitative
Positive feelings, recognition
making relations between
era
Smestad, 2008
Math teachers
the curriculum
Qualitative
Different conceptions about
HoM, different use of HoM
with different degrees
yurt, 2008
Senior high
school
students
Opinions about the HoM
integrated instruction
Qualitative
Positive opinions
7th grade
students
Effects of HoM on
achievement and attitudes
Quantitative
Positive effect on
achievement, no significant
difference in attitude
Smestad, 2000
Norwegian
math textbooks
Analysis of HoM in Norwegian
textbooks
Qualitative
A very limited use of HoM
some of them inaccurate,
based on myths.
However, as seen in the Table 1, a few studies were focused on the use of historical foundations of
mathematical thinking in the mathematics textbooks (Baki &
2015; Smestad, 2000; Thomaidis & Tzanakis, 2009; Xenofontos & Papadopoulos, 2015). Besides, the
- , 47(1), 2018, 188-215
192
lines of several reports have also revealed a little effort to incorporate the historical dimension of
mathematics both in elementary and middle school mathematics curriculum and textbooks (Ho, 2008;
Radford, Furingetti & Katz, 2007; Xenofontos & Papadopoulos, 2015). In the light of these issues, the
purpose of the study was to analyze the Turkish middle school mathematics curriculum and
mathematics textbooks in terms of how the history of mathematics was addressed. Indeed, the present
study essentially sought to answer the following questions:
1. How is the history of mathematics addressed in the main components of Turkish middle school
mathematics curriculum, namely, learning objectives, content, delivery, and assessment
process?
2. How the history of mathematics is addressed in the Turkish middle school mathematics
textbooks?
It is believed that the results of this study will be valuable for curriculum developers, scholars, and
teachers who would like to search an example of the mathematics curriculum and textbooks within the
historical perspective. It is also believed that the results may contribute to the ongoing research by
giving an example from the Turkish educational context. Although the focus of the study was not on the
implementation of the curriculum as well as the use of the textbooks in classrooms, the results may also
shed light on the relationship between the intentions about the use of the history of mathematics as
stated in the official curriculum and the indications of the potential learning opportunities related to the
words [2002, p.13]).
Before moving to the next parts, it is believed that the general information about the national setting
of mathematics education in Turkey, where the study stems from, might be useful starting point for a
better understanding. Turkish education system has a highly centralized governance structure and the
Ministry of National Education (MONE) is the main body for planning, programming, executing,
monitoring and controlling all educational services including curriculum development and approval of
textbooks. In 2005, the striking curricular change was made in order to develop a more learner-centered
curriculum and a more constructivist way of learning. In 2012, with the announcement of the new law,
the length of compulsory education was increased from 8 to 12 years and redefined the system into 3
levels (12-years compulsory education covering 4-years elementary, 4-years middle and 4-years high
school). As a result of this structural reform, the MONE had to make the second i mportant curricular
revision. The revised Turkish middle school mathematics curriculum (5th-8th grade) was put into
implementation during the 2013-2014 academic year. The goal of the revised mathematics curriculum is
stated as to provide a learning environment in which students will gain mathematical knowledge and
skills required by the 21st century (MONE, 2013). With regard to the content, there are five main
learning strands, namely, numbers and operations; geometry and measurement; algebra; data analysis;
processing skills (e.g. reasoning, communication, etc.), affective dimensions (attitude, self-confidence,
self-regulation, etc.), and psychomotor skills are highly emphasized issues in the curriculum.
Method
This study was designed to analyze how the history of mathematics occupied in the Turkish middle
school mathematics curriculum and math textbooks. For this purpose, data were collected through
document analysis. The first main data source of the study was the Turkish middle school mathematics
curriculum (5th-8th grades), namely the official curriculum document. The second main data sources
were the Turkish middle school mathematics textbooks approved by MONE during the 2015-2016
academic year. There are totally six approved textbooks and all of them were included in the document
. The detailed information
about the textbooks is provided in Table 2.
- , 47(1), 2018, 188-215
193
Table 2.
The Turkish middle school mathematics textbooks analyzed in the study
Grade
Publisher
Total number of pages
5th grade
MEB
588 (2 volume set)
264
6th grade
264
7th grade
Tutku
354
8th grade
MEB
263
Sevgi
262
Total
6 math textbooks
1995 pages
Before the data analysis process, two frameworks were developed by the researchers. The first
framework, as given in the Table 3, was developed to analyze the official mathematics curriculum in
terms of the main components, namely, learning objectives, content, delivery, and assessment. More
specifically, the attention is here on where (objectives, content, delivery, and assessment) and how
(compulsory or suggested expressions) the history of mathematics incorporated in the curriculum.
Table 3.
The framework for the curriculum analysis
Where is HoM incorporated in the curriculum?
The components of curriculum
Learning Objectives
Content/Strands
Teaching and learning process
Assessment process
How is the HoM incorporated in the curriculum?
The ways of expression
Compulsory (requirement, rule, etc.)
Suggested (recommendations, advice etc.)
The second framework, as given in the Table 4, was developed for the analysis of the math
textbooks. It has two parts as the place of utilization and the way of expression. The former is focused
on where the references to the history of mathematics used in the textbooks (e.g. introduction
activities, explanation of the topic to be learned, closure activities, or off-topic information). The latter
four categories: (1) simple historical/biographical references; (2) solution/proof of a method including
historical pieces; (3) mathematical tasks of purely cognitive elements that require a numerical solution,
explanation or proof and (4) discussion/projects relating the history of mathematics with life outside
mathematics. According to Xenofontos and Papadopoulos (2015), while the references clustered under
the first and second categories just present encyclopedic pieces of information without posing any
question to students, the references under the third and fourth categories present historical dimension
of mathematics through tasks, discussions and/or projects that asked students to produce solutions or
answers.
Table 4.
The framework for the textbook analysis
Where is HoM incorporated in the textbook?
The place of utilization
Introduction activities (e.g. gaining attention)
Presenting topic to be learned
Closure activities (e.g. retention and transfer)
Off-topic information (i.e. not related to topic)
- , 47(1), 2018, 188-215
194
Table 4.
The framework for the textbook analysis (c
How is the HoM incorporated in the
textbook?
The ways of expression
Simple historical /biographical references
Solution/proof of a method/formula
Mathematical tasks
Discussion/project tasks
In order to find out all relevant data (i.e. the references to the history of mathematics), the official
curriculum and the textbooks in each grade level were carefully examined line by line according to the
frameworks. During the analysis process, the researchers coded the data independently and then both
sets of data were compared to establish consistency in the assignment of codes to the same category.
Results
The results gathered from the analysis of the Turkish middle school mathematics curriculum and six
Turkish middle school mathematics textbooks were presented in line with two main research questions.
The History of Mathematics in the Turkish Middle School Mathematics Curriculum
The major focus of the content analysis here was to identify all instances of the history of
mathematics in the Turkish Middle School Mathematics Curriculum (TMMC). Hence, learning objectives,
content, delivery, and assessment aspects of the curriculum were analyzed according to the framework.
The findings gathered from the content analysis are summarized in Table 5.
Table 5.
The instances of the HoM in the curriculum
The components of
curriculum
Instances of the HoM found in the curriculum
The ways of expression
Learning Objectives
1 objective (6th grade)
Compulsory
Content/Strands
No instances found
------
Learning and teaching
process
The use of fam
biographies, and their contributions to the
field
Suggested
Assessment process
No instances found
-------
Considering the learning objectives from 5th to 8th grades, the following sixth-grade objective (see
Figure 1) was the only one
th grade, p. 13). Based on the explanation statement, it can be said
that the way of expression is compulsory. In other words, use of the Sieve of Eratosthenes is the main
requirement for achieving this learning objective.
Figure 1. The objective and its explanation requiring the use of the Sieve of Eratosthenes
(TMMC, 6th grade, p. 13)
- , 47(1), 2018, 188-215
195
With regard to the content, among five main learning strands (i.e. numbers and operations;
geometry and measurement; algebra; data analysis; and probability), no trace of the history of
mathematics was found. As seen in Table 5, the history of mathematics was also reflected in the
learning and teaching process. In the cur
Figure 2), it was acknowledged that providing
the author of the first geometry book written in Turkish as well as introduced the standard units of
measurement. Since these explanations about the integration of history of mathematics with learning
and teaching of mathematics are given in the form of suggestions, the way of expression of learning and
teaching process is not compulsory activities. Like the content aspect of the curriculum, no trace of the
history of mathematics was found in the assessment part of TMMC.
Figure 2. The extract from the Use of Information related to the Development of Mathematics (TMMC,
2013 p. VIII)
The History of Mathematics in the Turkish Middle School Mathematics Textbooks
The aim of the content analysis here was to identify all instances of the history of mathematics in the
six Turkish middle school mathematics textbooks. Totally 1995 pages of the six middle school
mathematics textbooks were analyzed by line by line. The total number of the HoM-related pages for all
grades and all textbooks was found about thirty-five pages. Further, the total instances of the HoM
found in the six middle school mathematics textbooks was only twenty-seven. The results obtained from
the textbook analysis are summarized in Table 6.
Table 6.
The number of the instances of HoM in the textbooks
The place of utilization
The ways of expression
Simple historical
/ biographical
references
Solution /proof of a
method/ formula
Mathematical
tasks
Discussion/
projects
Total
Introduction activities
9
3
2
14
Presenting topic to be learned
3
3
Closure activities
6
1
7
Off-topic extra information
3
3
Total
18
3
4
2
27
- , 47(1), 2018, 188-215
196
Considering the grade levels, the history of mathematics was mostly taken into consideration in the
eighth grade, totally 12 references were found in two different textbooks. Surprisingly, as given in Table
7, no trace of the history of mathematics was found in the seventh-grade textbook. By sixth grade, 8
references and by fifth grade 7 references were determined.
Table 7.
The number of the instances of HoM by grades
According to the findings, the references related to the HoM were mostly placed in the introduction
part of the topic. Figure 3 and 4 are given as examples of the use of the HoM at beginning of the
mathematical topics.
Apart from one reference from the sixth-grade and two references from eighth-grade textbooks,
there was no evidence indicating the history of mathematics used while presenting the topic, concept,
skill, or formula to be learned in the textbook series. Figure 5 indicates that the Sieve of Eratosthenes
was used while presenting the topic of prime numbers that was also explicitly stated in the curriculum.
In Figure 6, a short description about the Pascal triangle and its construction were given.
The place of utilization
Grades
Introduction
Presenting topic
Closure
Off-topic information
5th
7
6th
4
1
3
7th
8th
10
2
Total
14
3
7
3
Figure 3. A short biography of Eratosthenes
(Dikey, 6th grade, p. 39)
Figure 4. A short
contributions to geometry (Sevgi, 8th grade, p. 82)
- , 47(1), 2018, 188-215
197
Besides, only the fifth-grade textbooks included in the references related to the HoM at the end of
the topic. Figure 7 provides example of the HoM placed in the closure part that was related to Wiliam
Playfair and his invention of the bar chart given at the end of the data analysis and interpretation topic.
Another example as given in the Figure 8 provides brief information about the first use of parenthesis in
mathematics by Christopher Clavius in 1608 and by Albert Girard in 1629.
Moreover, the historical dimension of mathematics were also used as off-topic extra information
(i.e. not related to topic or learning objective). According to results, only 3 references were found in the
sixth-grade textbook. Figure 9 indicates the use of the HoM as an off-topic information about Cahit Arf,
a world-famous Turkish mathematician, in the data analysis topic.
The findings concerning how the history of mathematics is integrated in the textbooks indicated that
the history of mathematics was expressed mostly in the way of historical or biographical references. As
seen in Table 8, out of 27 references, 18 of them were expressed in the form of either simple historical
or biographical information.
Figure 5. The Sieve of Eratosthenes
(Dikey, 6th grade, p. 41)
Figure 6. Pascal Triangle
(MEB, 8th grade, p. 78)
Figure 9. Cahit Arf, a world-famous Turkish mathematician (Dikey, 6th grade, p. 151)
Figure 7.
chart
(MEB, 5th grade, p. 127)
Figure 8. The first use of parenthesis in
mathematics
(MEB, 5th grade, p. 61)
- , 47(1), 2018, 188-215
198
Table 8.
The number of the HoM references according to the ways of expression by grades
Grades
The ways of expression
No question(s) for student(s)
Posing question(s) to student(s)
Simple historical/
biographical references
Solution /proof of a
method/ formula
Mathematical
tasks
Discussion/
projects
Total
5th
6
1
7
6th
5
1
1
1
8
7th
-
8th
7
2
2
1
12
Total
18
3
4
2
27
The examples of the references expressed in the form of simple historical or biographical information
are provided in Figure 10 and 11.
According to the results, a few number of references to the history of a mathematical method or
formula containing a solution or proof without posing any question to student(s) were included in the
mathematics textbooks. Figure 5 (The Sieve of Eratosthenes) and Figure
how the historical references to a method and its solution process used in the textbooks. Moreover, the
findings clearly indicated that the references asking students to interact with the history of mathematics
were rarely included in the textbooks. Only four references related to mathematical tasks of purely
cognitive elements requiring a numerical solution, explanation or proof and two references related to
discussion/project tasks connecting the history of mathematics with life outside mathematics were
found. Examples of these references are shown in Figures 12 and 13 respectively. Figure 12 illustrates an
example of mathematical task that provides short biographical information about Pythagoras and then,
asks stud
Figure 13, an
example of discussion/project tasks, a short historical information about the Ancient Egyptian Number
System and the table indicating what the Egyptian hieroglyphics (symbols) represent in our decimal
system as well as their descriptions are provided. Afterward, students are invited to discuss the
difficulties to perform calculations (addition, subtraction, multiplication, and division) by using Egyptian
hieroglyphics. In order to complete this task, students need to collect information about how Egyptians
carry out calculations.
Figure 10. Abu al-Wafa' Buzjani, a Persian
mathematician and astronomer
(MEB, 8th grade, p. 145)
Figure 11.
mathematician and astronomer
(Dikey, 6th grade, p. 127)
- , 47(1), 2018, 188-215
199
Discussion & Conclusion
In the present study, the findings clearly indicated that both the curriculum and the textbooks are
attentive to the inclusion of historical aspect of mathematics. Considering the learning objectives of the
TMMC, the official curriculum, there is only one objective addressed the history of mathematics
explicitly. In the learning and teaching aspect of the TMMC, the important role of the history of
. Nonetheless, no trace of the history of mathematics was found in the
content and the assessment components of the TMMC. Based on this result, it is obvious that although
the role of HoM in mathematics education is taken into consideration, its integration could not be fully
reflected in the components of the TMMC. In this respect, the results of the present study call for a
mathematics curriculum in which all aspects from learning objectives to assessment are well-balanced in
terms of historical dimensions of mathematics so that students are provided with learning opportunities
to meaningfully engage with mathematics as well as extend beyond rote application of procedures. As
riculum increases
student motivation and achievement by humanizing the subject, emphasizing on the continuous
development of math and foster an appreciation of the multicultural inheritance and culturally
s
1993, p. 461). Towards this aim, the history of mathematics might be connected with all main
dimensions of math curriculum and become more visible and attractive for teachers and textbook
writers.
Furthermore, the findings emerged from the analysis of the six Turkish middle school mathematics
textbooks (for 5th-8th grades) indicated that the total page number of six textbook is 1995 and a middle
school student will meet about 35 pages of history of mathematics during his/her four-year middle
school process. In this respect, the inclusion of the historical dimensions of mathematics in the
textbooks, namely the potentially implemented curriculum, is very limited. Smestad (2000) made a
similar point with respect to the Norwegian math textbooks and found that a student will meet about 36
pages of history of mathematics in his/her ten-year schooling process. Another indicator of limited use
of HoM in the textbooks is the total number of the HoM-related instances that was found only twenty-
seven. Considering the grade levels, no trace of the history of mathematics was found in the seventh-
grade textbook. It might be interpreted that although fifth and sixth graders have little chance to see the
need or rationale behind development of a mathematical concept/theorem/rule through historical
perspective of math, in seventh grade, there is no chance offered for students to continue seeing
mathematics as an organic whole.
Figure 12. The Pythagorean Theorem,
(Sevgi, 8th grade, p. 110)
, (MEB???, 8th grade, p. 145)
Figure 13. The Egyptian hieroglyphics,
(Dikey, 6th grade, p. 15)
, (MEB???, 8th grade, p. 145)
- , 47(1), 2018, 188-215
200
Besides, more than half of the HoM-related references in the textbooks were presented in the form
of encyclopedic pieces of information. Similar results were demonstrated in previous research as well.
of the history of mathematics in the Cypriot and Greek mathematics textbooks. According to Baki and
and pictures of mathematicians in elementary school mathematics textbooks. In this respect, the
findings of the current study clearly indicated that the references that ask students to interact with the
history of mathematics were rarely included in the textbooks. One of the possible reasons behind the
perfunctory attention given to the history of mathematics in the textbooks might be due to the
curriculum itself. Especially such countries as Turkey, having a highly centralized educational system, a
national curriculum is usually embodied in nation-wide unified textbooks. Thus, the extent to which the
historical aspect of mathematics is occupied in the curriculum directly affects the scope of the historical
elements in mathematics textbooks. To sum up, the findings of the present study indicated that
although the TMMC and the middle school math textbooks value the history of mathematics, there are
rather shallow and superficial mentions of the history of mathematics in terms of quantity and quality.
- , 47(1), 2018, 188-215
201
Türkçe Sürümü
Giriş
eri, en temel dersler Matematik
da
de
ve deneyimlerine odaklanarak,
(Burton, 2003; Eves, 1990; Katz, 1993; Otte, 2007; Yee ve Chapman, 2011).
-
- ,
nu
-
(2009)
-
,
Hagerty, Smith ve Goodwin, 2007; Jankvist,
2009a; Kaye, 2008; Leng, 2006; Lim, 2011; Liu ve Niess, 2006).
Matematik -
gereken -
Posner (1995) resmi/hedeflenen
Mullis, Martin, Foy, ve
,
hedeflenen mesinde
ektedir (Arseven, 2003; Fan, Zhu, ve Miao, 2013; Reys, Reys, Lapan,
Holliday, ve Wasman, 2003; Tan- Tyson ve Woodward, 1989; Woodward ve
- , 47(1), 2018, 188-215
202
Elliott, 1990) yel olarak
uygulanan resmi program
matematik tarihinin karar vericiler ve progra
,
(Ho, 2008; Xeno
.
Tablo 1.
Y
grubu/ veri
Matematik tarihinin (MT)
Ersoy ve
2016
Nicel
Ju, Moon, ve
Song, 2016
Kore matematik ders
Nitel
Xenofontos ve
Papadopoulos,
2015
7-
matematik
matematik ders
Nitel
gerektiren ve
biyografik
MT
ve
5-
matematik
Nitel
Povey, 2014
MT dersi
veren
Nitel
Bayam, 2013
Nitel
Gazit, 2013
Matematik
Nicel
ve
m
Nitel
ve Haser, 2014
Matematik
Nicel
,
u ve
Matematik
Nicel
Baki ve ,
2013
6-
matematik
Nitel
- , 47(1), 2018, 188-215
203
Tablo 1.
Matematik tarihinin (MT)
Bayam, 2012
Karma
olumlu etki
Nicel
olumlu etki
ve
geometrik
Nitel
Geometrik ispatlama
Panasuk ve
Horton, 2012
Matematik
Nicel
yal
Clark, 2012
Matematik
Nitel
O
Yenilmez, 2011
Matematik
Nicel
Burns, 2010
Matematik
Karma
Matematik
Karma
Huntley ve
Flores, 2010
Matematik
MT dersinin pedagojik alan
Nitel
Jankvist, 2010
-
de
Nicel
Thomaidis ve
Tzanakis, 2009
7-
matematik
ders
Yunanistan lise matematik
Nitel
,
ancak hatal
belirsizlik yaratan veya eksik
Baki ve
2009
Matematik
Khayyam Metodu ile ikinci
dereceden denklem
p
deneyimler
Nicel
Smestad, 2008
Matematik
Programdaki MT
Nitel
uygulamalar
yurt, 2008
Nitel
etkisi
Nicel
etki
Smestad, 2000
matematik
Nitel
MT
- , 47(1), 2018, 188-215
204
bilgiler
Ancak, Tablo 1'de de alan da
, tarihsel te Baki ve
2015; Smestad, 2000; Thomaidis ve Tzanakis, 2009; Xenofontos ve
Papadopoulos, 2015) bulu.
, 2008; Radford,
Furingetti ve Katz, 2007; Xenofontos ve Papadopoulos, 2015).
,
1. 2013 Ortaokul Matematik Dersi (5-
2. Ortaokul matematik ders (5- ?
matematik tarihi perspektif ,
akademisyenlere ve matematik
taya
.
-
-
Valverde, ve
2002)
-
Bir sonraki
bir program irme
, izlenmesi ve kontrol edilmesinden sorumludur.
(- ilkokul- ortaokul -
2013- - ortaokul matematik -8.
pro
- ortam
olarak
- ve psikomotor
vurgulanm(MEB, 2013).
Yöntem
2013 ortaokul matematik dersi (5- -
- , 47(1), 2018, 188-215
205
-
--
- MEB devlet okul
matematik ders (5-
Tablo 2.
na
5
MEB
588 (2 cilt)
264
6
264
Tutku
354
8
MEB
263
Sevgi
262
Toplam
6
1995
tirilen
- -
(zor
Tablo 3.
hangi
-
-
ele
Zorunlu
,
a veya ek bilgi olarak)
ise, ders
ul
Xenofonto (1) ; (2) bir
- , 47(1), 2018, 188-215
206
Tablo 4.
lere ders
rs
Bulgular
Ortaokul Matematik Dersi Öğretim Programında Matematik Tarihinin Yeri
Ortaokul yer verilen matematik tarihiyle il
ortaya konul k, ve
Tablo 5.
Zorunlu
------
-
-
-------
5-
- , 47(1), 2018, 188-215
207
veri
ir ifadeye
rastlanma -
olumlu tutum
-duru
Ortaokul Matematik Ders Kitaplarında Matematik Tarihinin Yeri
6 ortaokul matematik ders kita
- sayfadan, matematik tarihine
ortaokul
matematik ders kita tespit edilen
Ders kitaplabulgular
Tablo 6.
Basit tarihi/
biyografik
Matematiksel
projeler
Toplam
9
3
2
14
3
3
Konu sonunda
6
1
7
3
3
Toplam
18
3
4
2
27
- , 47(1), 2018, 188-215
208
Ders
f
7. , mat
Tablo 7.
Konu sonunda
Ek bilgi
Toplam
7
7
4
1
3
8
10
2
12
Toplam
14
3
7
3
27
matematik tarihinin,
.
(Dikey
. 82)
Erastosten Kalburu
(Dikeys. 41)
(s. 78)
- , 47(1), 2018, 188-215
209
e yorumlama konusunun sonunda Wiliam Playfair ve
n on iki
in
veya biyografik bilgiler
basit tarihi veya biyografik
bilgiler
Tablo 8.
Basit tarihi/ biyografik
Matematiksel
projeler
Toplam
6
1
7
5
1
1
1
8
-
7
2
2
1
12
Toplam
18
3
4
2
27
Matematik tarihinin basit tarihi veya biyografik bilgiler
(MEBs. 127)
(MEB, s. 61)
Cahit Arf (Dikey, s. 151)
, (MEB, . 145)
Dikey, s. 127)
- , 47(1), 2018, 188-215
210
da de
bir matematiksel
ispat gerektiren tespit
edilirken; matematik tarihi ile in
matematikse
Tartışma ve Sonuç
Matematik tarihinin, ortaokul matematik dersi (5-
ders (5-
bulgular, hem program hem de ders kitaplar
sadece tek bir a
-
tam Bu
mlar matematik tarihinin dengeli
bir .
nin .
vurgu yapacak ve
l boyutunun .
matematik tarihinin,
hale ge.
,
(Sevgi,
(Dikey,
- , 47(1), 2018, 188-215
211
, elenen 6 toplam sayfa
ortaokul lerinin
Bunlara ek olarak, tespit edilen toplam
temelleri matematik tarihi perspektifi an deneyimleme
olarak tespit edilen
Xenofontos ve
Papadopulos (2015), , matematik
tarihinin benzer
elde
ni deneyimlemesi ve
nadiren .
matematik
matematik tarihine
hem program yer verilme durumunun nitelik ve nicelik
yetersiz
- , 47(1), 2018, 188-215
212
References
Effects of history of mathematics integrated instruction on mathematics self-efficacy
and achievement. Unpublishe
-
mathematics and their attitudes and beliefs towards using history of mathematics in mathematics
education. Science & Education, 23(1), 159-183.
Arseven, A. (2003).
. Unpublished master thesis, Hacettepe University, Ankara.
and attitudes towards history of mathematics and their creativeness level. Journal of Research in
Education and Teaching, 2
Teaching mathematics
and Its Applications, 28
Baki, A., & th, 7thand 8th grade
mathematics textbooks. Elementary Education Online, 12(3), 849-872.
. (Unpublished master thesis). Middle East Technical University, Ankara
The use of mathematics history in mathematics courses:
and Babylonian method sample. Unpublished master thes
Bayam, S., B. (2012). The impact of a knowledge of the history of mathematics on primary school student
mathematics achievement and attitudes. Unpublished master thesis, Kastamonu University,
Kastamonu.
Bayam, S., B. (2013). The views of students aged 12 about activities for history of mathematics included
in mathematics curriculum. Paper presented at Eighth Congress of European Research in
Mathematics Education, Antalya, Turkey.
Bellomo, C., & Wertheimer, C. (2010). A discussion and experiment on incorporating history into the
mathematics classroom. Journal of College Teaching & Learning, 7
Bidwell, J., K. (1993). Humanize your classroom with the history of mathematics. Mathematics Teacher,
86, 461-464.
Burns, B.,
teaching of high school mathematics. Issues in the Undergraduate Mathematics Preparation of
School Teachers: The Journal, 4, 1-9.
Burton, D., M. (2003). The history of mathematics: An introduction (5th ed.). New York, NY: McGraw-Hill.
Clark, K., M. (2012). History of mathematics: Illuminating understanding of school mathematics concepts
for prospective mathematics teachers. Educational Studies in Mathematics, 81(1), 67-84
Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics
textbook affected two teachers' learning. The Elementary School Journal, 103(3), 287-311.
Ortaokul matemat
yeri: ekolojik bir analiz. , 42(42),
239-259.
Ernest, P. (1998). The history of mathematics in the classroom. Mathematics in School, 27
etkileri. , 15(2).
- , 47(1), 2018, 188-215
213
Eves, H. (1990). An introduction to the history of mathematics (6th ed.). San Francisco, CA: Saunders.
Fan, L., Zhu, Y., & Miao, Z. (2013). Textbook research in mathematics education: Development status
and directions. ZDM, 45(5), 633-646.
Fauvel, J. (1991). Using history in mathematics education. For the Learning of Mathematics, 11(2), 3-6.
Fauvel, J. &Van Maanen, J. (Eds.) (2000). History in mathematics education-The ICMI study. Dordrecht:
Kluwer Academic.
Fried, M. N. (2001). Can mathematics education and history of mathematics coexist? Science &
Education, 10, 391-408.
Furinghetti, F. (2000). The history of mathematics as a coupling link between secondary and university
teaching. International Journal of Mathematical Education in Science and Technology, 31 (1), 43-51.
Gazit, A. (2013). What do mathematics teachers and teacher trainees know about the history of
mathematics? International Journal of Mathematical Education in Science and Technology, 44(4),
European
Journal of Science and Mathematics Education, 1(3), 125-136.
history of mathematics in mathematics teaching. Unpublished master thesis, Karadeniz Technical
University, Trabzon
Hagerty, G.W., Smith, S. & Goodwin, D. (2007). The unique effects of including history in college algebra.
Convergence: Where Mathematics, History and Teaching Interact, 4.
Helfgott, M. (2004). Two examples from the natural sciences and their relationship to the history and
pedagogy of mathematics. Mediterranean Journal for Research in Mathematics Education, 3(12),
147164.
Ho, W. K. (2008). Using history of mathematics in the teaching and learning of mathematics in
Singapore. In Proceedings of 1st RICE (pp. 1-38), Singapore: Raffles Junior.
Huntley, M. A., & Flores, A. (2010). A history of mathematics course to develop prospective secondary
PRIMUS: Problems, Resources, and Issues in
Mathematics Undergraduate Studies, 20, 603-616.
, N. (2007).
attitudes towards mathematics and their success on it. Unpublished master thesis,
University, Van.
education. Educational Studies in Mathematics, 71(3), 235-261.
Jankvist, U. T. (2009a). Using history as a goal in mathematics education. Unpublished doctoral
dissertation, Roskilde University, Roskilde.
JanEducational Studies in Mathematics
Education, 74(1), 53-74.
Ju, M. K., Moon, J. E., & Song, R. J. (2016). History of mathematics in Korean mathematics textbooks:
Implication for using ethnomathematics in culturally diverse school. International Journal of Science
and Mathematics Education, 14 (7), 1321-1338.
Katz, V. J. (1993). A history of mathematics: An introduction. NY: Harper Collins.
Kaye, E. (2008). The aims of and responses to a history of mathematics video conferencing project for
schools, In Proceedings of the British for Research into learning mathematics, 28 (3).
Kleiner, I. (2001). History of the infinitely small and the infinitely large in calculus. Educational Studies in
Mathematics, 48, 137-174.
- , 47(1), 2018, 188-215
214
Leng, N. W. (2006). Effects of an ancient Chinese mathematics enrichment programme on secondary
International Journal of Science and Mathematics
Education, 4
Lim, S. Y. (2011
achievement, In Proceedings of AAMT-MERGA Conference 2011 Mathematics: Traditions and New
Practices, 455-463.
Lingard, D. (2000). The history of mathematics: An essential component of mathematics curriculum at all
levels. Australian Mathematics Teacher, 56(1), 40-44.
Mathematics Teacher, 96(6), 416-421.
Liu, P., & Niess, M. L. (2
a historical approach calculus course. Mathematical Thinking and Learning, 8(4), 373-406.
Marshall, G. L. (2000). attitudes toward
mathematics. (Unpublished doctoral dissertation), Illinois State University, Normal, IL.
McBride, C. C., & Rollins, H. J. (1977). The effects of history of mathematics on attitudes toward
mathematics of college algebra students. Journal for Research in Mathematics Education, 8
61.
McCartney, M. (2012). History of mathematics in the higher education curriculum. Maths, Stats and OR
Network and HESTEM project report. http://uir.ulster.ac.uk/22942/1/HistoryofMaths.pdf
MONE, (2013). Turkish national middle school mathematics curriculum (5th-8th grades). Ankara: MONE
Mullis, I. V. S., Martin, M.O., Foy, P., & Arora, A. (2012). TIMSS 2011 International results in
mathematics. Chestnut Hill, MA: Boston College
Otte, M. (2007). Mathematical history, philosophy and education. Educational Studies in Mathematics,
66(2), 243-255.
proof skills. Procedia Social and Behavioral Sciences, 4681.
Panasuk, R. M., & Horton, L. B. (2012). Integrating history of mathematics into curriculum: What are the
chances and constraints? International Electronic Journal of Mathematics Education, 7
Porter, A. C., & Smithson, J. L. (2001). Are content standards being implemented in the classroom? A
methodology and some tentative answers. In S. H. Fuhrman (Ed.), From the capitol to the classroom:
Standards-based reform in the states (pp. 60-80). Chicago: University of Chicago Press.
Posner, G. J. (1995). Analyzing the curriculum (2nd ed.). New York: McGraw-Hill .
Povey, H. (2014). Walking in a foreign and unknown landscape: Studying the history of mathematics in
initial teacher education. Science & Education, 23(1), 143-157.
Radford, L., Furinghetti, F., & Katz, V. (2007). The topos of meaning or the encounter between past and
present. Educational Studies in Mathematics, 66(2). pp. 107-110.
Reys, R., Reys, B., Lapan, R., Holliday, G., & Wasman, D. (2003). Assessing the impact of" standards"-
based middle grades mathematics curriculum materials on student achievement. Journal for
Research in Mathematics Education, 34(1), 74-95.
Smestad, B. (2000). History of mathematics in Norwegian textbooks. In Ninth International Congress on
Mathematics Education, Tokyo, Japan.
conceptions of history of mathematics. Retrieved on 12, March, 2016,
from http://home.hio.no/~bjorsme/HPM2008paper.pdf
Tan-Sisman, G. & Akkaya, G. (2017). The appropriateness of the ninth grade mathematics textbooks
- , 47(1), 2018, 188-215
215
Pamukkale University Journal of
Education [], 42, 1-14.
Thomaidis, Y. & Tzanakis, C. (2009). The implementation of the history of mathematics in the new
curriculum and textbooks in Greek secondary education. Dins: Working group, 15, 139-151.
The perceptions of senior high students regarding the lessons, in which activities
chosen from history of mathematics are used on the subject of numbers learning area. (Unpublished
master thesis). Gazi University, Ankara
from textbooks. Educational
Leadership, 47(3), 14-17
Valverde, G. A., Bianchi, L. J. , Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the
book. Using TIMSS to investigate the translation of policy in to practice through the World of
textbooks. Dordrecht: Kluwer Academic Publishers.
Woodward, A., & Elliott, D. L. (1990). Textbooks: Consensus and controversy. Chicago: National Society
for the Study of Education.
Xenofontos, C., & Papadopoulos, C. E. (2015). Opportunities of learning through the history of
mathematics: the example of national textbooks in Cyprus and Greece. International Journal for
Mathematics Teaching & Learning, 1-18. Retrieved on 9 November, 2017, from
http://www.cimt.plymouth.ac.uk/journal/xenofontos. pdf
Yee, L. S., & Chapman, E. (2011). Using history to enhance student learning and attitudes in Singapore
mathematics classrooms. Education Research and Perspectives, 37, 110-132.
tics
course. Pamukkale University Journal of Education, 30, 79-90.
Acknowledgements or Notes - This is the extended version of the paper presented in the 13th
International Congress of Mathematics Education (ICME-13), Hamburg, Germany on 24-31 July, 2016.
