History of mathematics (HM) in secondary school mathematics textbook

Abstract The purpose of this study was to investigate elements of the history of mathematics in secondary school mathematics textbooks in Ethiopia. In line with this, the study also identified the extent to which mathematics is seen as a social construct in textbooks. To achieve these four mathematics textbooks from Grades 9 to Grade 12 were selected for this purpose. The document review method used to determine the extent of use of elements of the history of mathematics, the stage in the unit it used, and the learning domains of mathematics it covered in these textbooks are considered. For document analysis purposes Erdoğan et al.’s (2015) classification of elements of the history of mathematics was adopted. This distribution involves historical notes, notes on usage areas of mathematics, applications with historical notes, and historical elements in students’ extracurricular activities. The result has indicated that it has found 26 elements of the history of mathematics and the highest number found in the grade 11 Mathematics textbook. The learning domain algebra in the form of historical notes also received the highest coverage than others. Moreover, the result has indicated most elements of the history of mathematics were used at the beginning stage of the unit. Finally, the study has concluded that elements of the history of mathematics are not sufficiently integrated with the contents of mathematics textbooks. Several elements of the history of mathematics are far from the social context of the learner, as indicated in the textbooks.


Introduction
The history of mathematics could be an investigation into the sources of new discoveries, mathematical notions and methods used in the past (Cajori, 1993).It is a natural question to ask, when the history of mathematics can start.However, there is an indication for which primitive society for instance would have had a general sense of numbers, and instinctively differentiate two things from one (Bell, 2012;Hodgkin, 2005).Which can lead to say that the history of mathematics is as old as the human history.Certain mathematical activities such as counting also regarded as innate behavioural activities.Human infants in the first year of life possess an intuitive sense of number.So that, it is not an exaggeration to trace the historical development of mathematics since antiquity.
It also documented that mathematics helped the advancement of civilization through advancing science, technology and philosophy worldwide.An early man in prehistory used notched bones, cuts of tree and line on the ground to perform counting as have a mathematical concept.Following this, in history of mathematics more advanced mathematical activities noticed in the people of Mesopotamia and Egyptians through their settled agricultural practice.Later, the revolutionary advancement in ancient Greece and its Hellenistic empire provided sufficient evidence regarding the long and impressive history of mathematics (Burton, 2011;Starr et al., 2013).Such presentation informs mathematics as a human product shaped through time in history before it comes in its present form.So that, learning mathematics should include historical elements to show the mathematics that arises from a historical process than teaching it as a finished product.Providing an understanding of implicit motivation by involving the reflective activity of mathematician in the past is necessary for the learning process.On the other hand, several events of nature explained in mathematics (Avital, 1995;Hiebert & Carpenter, 1992;Schoenfeld, 2016;Tzanakis et al., 2002).
Mathematics also helped human being in struggling with life to get an answer to daily problems.Therefore, it is impossible and wrong deed to isolate mathematics education from elements of historical mathematics, culture and daily life activities of learners.Learning mathematics is not only acquiring knowledge of symbols and theories of logical syntax but it also includes sensemaking, meaningful construction, linking new fact with the old and extending and enhancing the existing framework of mathematical concept through time to time.The stated facts are achieved through the integration of school mathematics textbook with EHM (elements of historical mathematics) (Avital, 1995;Hiebert & Carpenter, 1992;Schoenfeld, 2016;Tzanakis et al., 2002).
There is an agreement among researchers that textbooks are the backbone of school mathematics teaching and learning process (Fan et al., 2013;Kajander & Lovric, 2009;Yang & Sianturi, 2017).Due to this, textbook preparation needs attention.Integrating historical elements of mathematics in the textbook helps students to develop knowledge of mathematics and introduce their history and culture.In Ethiopian secondary schools, historical elements are an integral part of lessons in mathematics textbooks.Mathematics textbooks include historical elements to indicate mathematics as a social and cultural product that comes through a long process in history (MoE, 2009).
According to MoE (2009), secondary school mathematics textbooks aim to equip students with solid mathematical knowledge, attitudes and skills that significantly contribute to creating citizens who are conscious of their own country's social, economic, political, historical and cultural realities of Ethiopia.Specifically, to produce students who can actively and effectively participate in the ongoing development process of the country.According to Teferra et al. (2018), the Ethiopian education development roadmap (2018)(2019)(2020)(2021)(2022)(2023)(2024)(2025)(2026)(2027)(2028)(2029)(2030) confirmed that the education system needs to promote nation-building, embrace cultural, religious, and ethnic diversity and give learners shared values and experiences.
According to Gracin (2014), textbooks are concrete tools, widely used by teachers and students, that reflect the history, cultural and educational traditions of particular countries in different forms.In particular, elements of historical mathematics (EHM) have space to integrate with appropriate lessons in the textbooks.In the Ethiopian context, historical elements of mathematics are integrated with textbooks in the form of historical notes by mathematicians, historical notes on usage areas of mathematics, and applications of mathematics with historical notes.Several countries use similar categories to integrate the history of mathematics into students' textbooks.For instance, schools in Turkey, Singapore, Ireland and Canada use similar contexts.Historical biographical information, formula-rule-solution, history of concepts, historical work, tools-equipment, discussion-projects and games are applied to compare mathematics textbooks of Turkey, Singapore, Ireland and Canada (Mersin & Karabörk, 2022).As a result, they found some comparative results, such as Ireland textbooks presenting the highest number of EHM and Al-Khwarizmi and Pythagoras; the most mentioned civilization is Ancient Egypt.
In the Ethiopian education system, the teaching materials, delivery methods and relevance of content in mathematics to link with students' real lives, history and contexts are among quality indicators (MoE, 2010).However, concerning relevance, although the current education policy of Ethiopia emphasizes the contextualization of the curriculum and instruction in schools, not realized in actual term.Moreover, the study has shown the disconnect of school mathematics from students' culture, context and day-to-day activities (Amare, 2009;Bekele & Melesse, 2011;Chernet, 2008).On the other hand, it is well known that Ethiopia is rich in history and EHM that can be included in the student textbook.For instance, Axum Obelisk, La Libel Rock won Church buildings are rich sources of EHM that could be integrated in the textbook.La Libel Rock won Church buildings have rich history in geometry as we can see in Figures 1 and 2.
Rock-hewn churches, Lalibela, Ethiopia, built by Ethiopians around 13th century CE which regarded as sacred geometry.Sacred geometry is the architecture of the universe, which is the eternal visual language wrapped around the root concepts of the manifest universe and it is the unchanging, perfect and timeless geometrical realties springing from Divinity (Dabbour, 2012).In sacred geometry there highly complex variety of spiritual procedures that attributing a cultural or religious value to the graphical presentation of the mathematical relationship and the design of manmade objects that symbolize or represent the mathematical relationships.Sacred geometry defines the nature of space and time.It occurs in very comprehensive and varied ranges of aspects of a person, including changes in their mind's specific parts (De Silva & Amarakoon, 2020).
The rock-hewn Churches of Lalibela are monolithic churches located in the western Ethiopia highlands near the town of Lalibela which perfectly made.The building structure has an element of plane and solid geometry which could be included in solid geometry lesson.Look for instance among different sections of Rock-hewn churches, in Figure 2.
According to Berhe (2015), blocking of Bete Ghiorgis is sculptured from Metatron cube with each having dimension of side length 15 cm width 15 cm and height 15cm.A closer examination of the architect of Bete Ghiorgis shows the basic principles of geometrical pattern which has a pattern of platonic solids to form the entire building.These geometrical combinations go from the floor to the top structure to form a perfect architecture shown in Figure 2.However, the actual construction of the building of Rock-hewn churches is done from top to bottom, that makes the construction unusual.As we know in modern building construction proceeded from bottom to top.
Similarly, the front elevation plan of Bete Medhanealem is shown in Figure 3, showing the geometrical configuration of consecutive golden proportioned of circles and triangles.Golden proportion arises from the most beautiful number in history of mathematics Phi(Φ≈1.618) which also described in Fibonacci series.More descriptions of Fibonacci series and golden number is found in the later section of this paper.Golden Ratio is a mathematical constant (Phi) which has been applied in art, architecture and music since the foundations of civilisation as it is a primary pattern of the ratios of nature.
In addition to these, Ethiopia has historical symbols for counting, still used in some occasions.It can be included while introducing numeration system in the textbook.Ethiopic numerals are ፩, ፪, ፫, ፬, ፭, ፮, ፯, ፰, ፱ and ፲ used to count from 1 to 10 respectively and ፳, ፴, ፵, ፶, ፷, ፸, ፹, ፺ and ፻ to count 20, 30, 40, 50, 60, 70, 80, 90 and 100 respectively and ""ሺ"" used for 1000 (Assabie & Bigun, 2006).Therefore, considering rich elements historical mathematics we can help students to understand mathematics as a human effort and created by individuals of both genders with their insights and idiosyncrasies.In addition to this, EHM indicates mathematics is found in the cultural heritage of a group or society.It reflects how mathematics is originated in the culture worldwide and the impact of social practices in mathematical study (Jankvist, 2009;JONES, 1969;Liu, 2003).Similarly, EHM also reflected interrelations among the various branches of mathematics and their role in the solution of significant problems that extend the horizons of mathematics.
It is not exaggeration to say human being played a great role in exerting intellectual effort in shaping mathematical knowledge.So that elements of historical mathematics promote learning by giving such experience to learners from the history mathematics.It helps them how to straggle the challenge while solving a particular mathematical problem and give a lesson for solving problem by their own effort.Classroom teachers use EHM as tool for motivating their students (Jankvist, 2009;JONES, 1969;Liu, 2003).
EHM is useful to popularize mathematics, by providing evidence how it influenced the advancement of philosophy, science, technology and helped peoples for better understanding of the world.EHM sharpens learner problem-solving habit, highlights mathematics as social product and lays a foundation for a better understanding of mathematics (Grabiner, 1975;Wilson & Chauvot, 2000).In the history of mathematics, we can indicate how an ancient civilization utilized different number systems to solve their day-to-day activities such as measurements, quantitates performed using tools such as bones, cuts of three and the like (Krantz, 2010).
The study conducted by Ay (2019), Ersoy (2015) and Kaşıkçı (2015) asserts integrating elements of the history of mathematics (EHM) in mathematics textbook have positive impact in increasing learners' attitude towards mathematics and interest to the subject.Moreover, if EHM integrated with the mathematics textbook, it helps the students to acquire a better understanding of the historical development and nature of mathematical fact (Baki & Gürsoy, 2018;Başıbüyük, 2018;Bütüner, 2020;Mersin, 2019;Varol, 2019).
Different empirical studies in document analysis of mathematics textbook found a different number of EHM.Document analysis or document review is a qualitative method that involves evaluating written materials or electronics, which include data on the cases that aimed to investigate in terms of their scope and content (Yıldırım & Simsek, 2013).Document review aims to get an accurate understanding of the contents of the documents and their meaning.It involves interpreting and developing the information they provide to attain the aim.Additional elaboration is given in method section.After analysing seven secondary school mathematics textbooks taught during 2013-2014, Erdoğan et al. (2015) found a total of 27 elements of the history of mathematics, which means an average of 6.3 EHM per textbook.Similarly, Baki and Bütüner (2013) examined three mathematics textbooks taught in grade 6, grade 7 and grade 8 and found 3.9 EHM per textbook or a total of 19 elements of the history of mathematics.An investigation by İncıkabı et al. (2019) in eight secondary school mathematics textbooks taught during 2016-2017, reported a total of 15 elements of the history of mathematics or 1.9 EHM per textbook.
In addition to these other studies, Mersin and Durmuş (2018) performed document analysis on four secondary school mathematics books taught in the same year documented 19 EHM or in average 4.8 EHM per textbook and in their study Şişman and Kirez (2018) found a total of 27 or 4.5 EHM per textbook in six secondary school mathematics taught during 2015-2016.Finally, a recent study by Ceylan (2021) found 27 EHM or 6.8 EHM per textbook after investigating mathematics textbooks taught in 5th, 6th, 7th, and 8th grades based on the Turkish Ministry of National Education designed four years as of 2018.

Objective
The purpose of the study is: To investigate the status of elements of the history of mathematics and the use of the history of mathematics in the secondary school mathematics textbooks.

Research questions
The study seeks answer the following research questions: • To what extent does EHM integrate with textbook contents across grade levels?
• At what stage of the program does EHM is integrated with the textbooks?
• To what extent do textbooks include EHM with reference to the learning domains?

Method
The current study examined elements of the history of mathematics (EHM) in the secondary school mathematics textbooks in Ethiopia.Secondary schools are the focus of the current study due to, many of fundamentals of mathematics introduced in these level and university entrance examination in the Ethiopian context covers contents from grade 9 through 12 grades.A qualitative descriptive research design is used as a method to address the problem in this study.Data collected through document review, in particular mathematics textbooks of four-grade levels review.So that, in the study document review approach preferred to answer the research equations stated.It involves access of data on the cases aimed to be investigated both in its scope and content (Yıldırım & Simsek, 2013).Moreover, descriptive analysis employed to make raw data understandable and usable for the readers.Therefore, the result obtained through this analysis is summarized and interpreted based on the predetermined theme (Yıldırım & Simsek, 2013).Based on this mathematics textbook of Grade 9 to Grade 12 is reviewed in this study.There is one standard textbook in Ethiopian context no need of inclusion and exclusion criteria for the selection of the textbooks.No other textbook only one version of textbook standardized and led by Ministry of education of Ethiopia (MoE).
Moreover, in Ethiopian context mathematics textbooks are designed based on the general curriculum framework prepared at ministry of education in Ethiopia (MoE).These secondary school mathematics textbooks objectives, contents, and assessments are designed to attain the aim of teaching mathematics in secondary school.The general aim in the framework for Grades 9, 10,11and 12, stated students to acquire and develop solid mathematical knowledge, skills, attitudes and promoting abilities in applying subject specific and general mathematical methods of thinking and working that significantly contribute to the creation of citizens who are conscious of the social, economic, political and cultural realities of Ethiopia and who can actively and effectively participate in the ongoing process of development of the country (MoE, 2009).So that, the textbooks derived these aims to specific objectives that could be addressed at classroom level.

Method of data analysis
During data analysis, a mathematics textbook of four levels (9th, 10th, 11th and 12) is examined based on the criteria's stated.It done in line with the distribution of the elements of the history of mathematics (EHM) contents across grade levels, stage of the unit EHM included, usage methods of EHM, and learning domains included in the EHM.The classification used by Erdoğan et al. (2015) regarding elements of the history of mathematics were adapted in the study.The distribution involves historical notes, notes on usage areas of mathematics, applications with historical notes and historical elements in students' extracurricular activities.For EHM distribution by the stage of the learning contents, it considers stage pre-teaching (beginning of the unit), While-teaching (middles of the unit) and post-teaching (at the end of the unit).Moreover, the distribution of EHM by learning domains, Numbers and Operations, Algebra, Geometry and Measurement, Function, Data Processing, Probability and Statistics, and Calculus involved.
Based the classification in Table 2, categorization of EHM included in the textbooks are determined.Some tips of classifications indicated in the following Figures 5,6 and 7.
Figure 5 introduces a briefing on the biographies of George Cantor and provide information of his contribution.George Cantor is the founder of set theory and he is believed a man who themed infinity properly.Such a note is regarded as historical note.
Figure 6 explains about the Pyramids at Giza in Egypt which was perfectly made and have characteristics of solid geometry mathematics, pyramid.So, it counted under usage area of solid geometry which emerged in the historical process.
Figure 7 started by introducing biography of Leonardo Fibonacci and then facts about Fibonacci series.Moreover, it provided a problem which applies Fibonacci sequence or numbers.Historical notes prepared in this way are included in the category of "applications with historical notes".There is a historical element associated with the sequence.As we know Fibonacci numbers are: 1, 1, 2, 3,5,8,13,21,34,55,89,144,233,377 … usually called Fibonacci sequence.There is a connection between Fibonacci numbers and the golden ratio.A ratio is a multiplicative relationship between two numbers.Look ratios of Fibonacci numbers and take the ratio of each term to the preceding one as shown below.The ratios of Fibonacci numbers converge on the golden number Phi(Φ≈1.618).

Notes on usage areas of Mathematics
Notes explaining the various uses of mathematics emerging in the historical process (using primitive number symbols for counting, reading the order in nature with Fibonacci numbers, etc.).

Applications with historical Notes
Explanation of notes on the history of mathematics with various examples or applications (showing how fractions are written, showing how to read number symbols, etc.).

Historical elements in students' extracurricular Activities
Items for extracurricular activities such as projects involving the history of mathematics and performance tasks (examination of a mathematician's studies, research on the history of a concept, etc.)

Result
The result of the current study is organized in three themes, namely: EHM distribution across grade levels, distribution of EHM by the stage of learning lessons across grade level and distribution of EHM by the learning domains across grade level.
The result in Table 3 indicated the distribution of EHM from Grade 9 to Grade 12 contents in the students' textbooks.When we see the result across Grade Level, EHM used most is in Grade 11 which accounts for, n = 10.It is in the form of historical notes and applications with historical notes.Namely in unit one lesson in Grade 11 mathematics textbook we get Rene Descartes (1596 -1650) was a philosopher and a mathematician, who assigned coordinates to  describe points in a plane.The x-y coordinate plane is sometimes called the Cartesian plane in honour of this Frenchman.Descartes' discovery of the Cartesian coordinate system helped the growth of mathematical discoveries for more than 200 years.John Stuart Mill called Descartes' invention of the Cartesian plane "The greatest single step ever made in the progress of the exact sciences".This historical note, situated at the beginning of the unit lesson to introduce students about relation and function in coordinate plane.Similar, historical note of John Bernoulli (1667-1748) well known with the method of partial fractions was introduced by John Bernoulli, a Swiss Mathematician who was instrumental in the early developments of calculus.John Bernoulli was a professor at the University of Basel and taught many outstanding students, the most famous of whom was Leonhard Euler, found in unit two while introducing rational expression and rational function.Applications with historical notes like Galileo Galili (1564-1642) in the 16th century Galileo showed that the path of a projectile that is shot into the air at an angle to the ground is a parabola.More recently, parabolic shapes have been used in designing automobile highlights, reflecting telescopes and suspension bridges.Which is found in unit three grade 11, used to show the application of coordinate geometry lessons.Across categories historical notes accounts for largest number (n = 18) Elements of historical mathematics relative to others.Historical elements in students' extracurricular activities are not considered as worthy for the students from Grade 9 to Grade 12.This has great implication for students' practical use of mathematics.In most cases mathematics learning used to pass from one grade to the next.the most achieving students do not utilize mathematics outside the classroom.As a result, we have found mathematics hating generation.At university level students are not willing to study mathematics.Among other reason, engaging students to use mathematics in the form of extracurricular activity is the one.To do this integrating Historical elements in students' extracurricular activities is mandatory.Notes on usage areas of mathematics, is also only included in Grade10 mathematics textbook, which accounts only, n = 2. Which indicates that the curriculum is not emphasizes the relationship of mathematics with daily life.This also needs attention; students need to aspire mathematics is useful.It also necessary, to integrate school mathematics with out of school mathematical activities and other subjects.For this to happen the textbooks need to guide how mathematics is used to explain the world in the past.It is well known that mathematics has helped the achievement of other subjects in history.Albert Einstein studied mathematics, since he wants to explain his discoveries in physics using mathematics.Mathematics served as language of physical sciences in history.
Plane geometry, particularly arcs and circles used to construct "Mona Lisa", the perfect picture ever in history made by Leonardo Da Vinci (ca.1500).Leonardo DaVinci has used the golden ratio to paint "Mona Lisa".Such historical note categorized as notes on usage area of mathematics.However, the fundamentals of geometry in secondary school mathematics use Euclidian Geometry.Therefore, in addition to such historical element on usage areas of mathematics, it could be better to include a very interesting historical note of "Euclid", usually regarded as "the father of geometry".
Table 4 presented EHM in pre-teaching (beginning), while-teaching and post-teaching (end).When we say pre-teaching, it is just the stage that at the beginning of the unit.This stage is especially important to introduce the new concept and used to inspire students towards the unit.while-teaching is to mean that already the unit is started, however some where in the middle there is EHM.This stage is used to strengthening the ongoing concept in the unit.Moreover, EHM post-teaching means it is just at the end of the unit.This stage is used to close the unit lessons and the purpose is to consolidate the learnt concept.
Based on this understanding among 26 EHM 53.8 % are presented at the beginning of the unit and only one used at the end of the unit.Which indicate, in most cases EHM are used at the beginning to start the unit.In most cases EHM is used at the beginning of the unit lesson to inspire  and motivate students towards lesson contents.For instance a historical note of Apollonius of Perga the Greek mathematician who died about 200 B.C. studied conic sections used to introduce the unit lesson of coordinate geometry in grade 10 mathematics.Apollonius is credited with providing the names "ellipse", "parabola", and "hyperbola" and for discovering that all the conic sections result from intersection of a cone and a plane.The theory was further advanced to its fullest form by Fermat, Descartes and Pascal during the 17 th century.This historical note seems used to motivate students to the concept of coordinate geometry and the effort of Apollonius in history for the advancement of mathematics.
The result in Table 5 indicated the learning domain "algebra" received highest number in the EHM.In the rank next to algebra learning domains "geometry and measurement" and "calculus" received relatively higher number of EHM than other domains.In the curriculum framework for Ethiopian education system algebra and geometry and measurement lessons received more emphasis to help students to develop the concept of direction, space, quantity, size and number.According to MoE (2009), "Children will be learning to sort and classify object, to identify common objects around them and to describe their geometric features and positions" (P.12).

Discussion
The current study investigated the extent to which elements of historical mathematics in a secondary school mathematics textbook.Moreover, the study examined the stage of the lesson in the unit that EHM, usage methods of EHM, and the learning domains involved in EHM in 4-grade levels mathematics textbooks.
During document analysis, the study identified, a total of 26 EHMs on the four textbooks.In other words, per the textbook, 6.5 EHM is identified.However, across grade level grade 10 accounted for the highest number (10) of EHM.Which is a minimal number as compared to the importance of EHM and the number of units covered in the textbooks.There are a total of 34 units covered in four textbooks.So that there are several units that did not have EHM.The result nearly aligns with While Baki and Bütüner (2013) found 6.3 EHM per textbook and Ceylan (2021) found 6.8 EHM per textbook.
In the study, it is significant to note that EHM in the context of "historical elements in the students' extracurricular activities" never given in any of the four textbooks.However, MoE (2010) emphasized school mathematics contents need to link with students' day-to-day activity.The curriculum required contextualization based on the culture of learners.Students need to practice classroom mathematics in their daily life activities.Textbooks under this study did not include historical elements in the students' extracurricular activities, indicating the disconnection of school mathematics with out of school practice indicated by Bekele andMelesse (2011), Chernet (2008) and Amare (2009).According to Krantz (2010), with the history of mathematics, it is possible to show how ancient civilizations utilized different number systems.For instance, to meet their dayto-day activities such as measurements quantitates performed using bones and cuts of three and the like.Başıbüyük (2018) indicated the need to include EHM in school mathematics textbook it helps the learner to develop positive learning attitudes if the mathematics of Babylonian, Egyptian, and Maya Civilizations, Chinese, Indian, Greek, and Islamic societies incorporated based on their grade level.
The distribution of EHM also examined based on the stage in the unit, as pre-teaching, whileteaching and post-teaching.The result indicated that the majority of EHM presented at the beginning of the topic in the textbooks.On the other hand, only one used at the end of the unit.It indicates, in most cases, EHM is used at the beginning to start the topic to motivate, retain students' attention and introduce the unit lessons with a practical concept.The result is consistent with the study conducted by Baki and Bütüner (2013), Erdoğan et al. (2015).Regarding, the importance of EHM to motivate, seek students' attention and seek students' attitude towards mathematics is supported in the study made by Ersoy (2015), Kaşıkçı (2015), Mersin (2019) and Ay (2019).
The result on the distribution of EHM based on the learning domain indicated that three for Numbers and Operations, six items for Algebra, 5 for Geometry and Measurement, four-item for Function, 1 for Data Processing, 2 for Probability and Statistics and five-item for Calculus.Algebra received the highest number.However, an interesting historical note of "al-Khwarizmi" usually regarded as the father of algebra not mentioned.Moreover, something related to "Euclid's" who usually regarded as "a father of geometry" not mentioned as a historical note among the five items of the Geometry and Measurement domain identified.Especially Euclid known by his book "The Element" in history in it he stated five postulates before he proofs 32 propositions.

Conclusion
Based on the findings, the study concluded that the history of mathematics not sufficiently integrated with secondary school mathematics.EHM has a significant contribution to mathematics education.It uncovers mainly mathematics as a social and cultural product.It helps the learner to understand mathematics is not a finished product but changeable through time.However, in this study, the status of EHM in the textbook does not help to achieve its pedagogical purpose.It identified the number relative to content coverage, appropriateness of EHM, the balance of the stage it used and learning domains of mathematics it addressed.

Implication
The finding of this study has policy implication.During development of textbooks at secondary school it is required to consider EHM as mandatory criteria not as optional.In this regard the results of the current investigation have shown the existing textbooks gaps incorporating EHM appropriately.Moreover, the findings inform curriculum practitioner like teachers to effectively utilize EHM included in mathematics textbook in secondary school.

Recommendation
Improving the use of EHM in mathematics textbooks of secondary schools is required in the way that meets its purpose.To attain the aims of the mathematics curriculum in Ethiopian education system, it required including sufficient EHM in the textbooks.Contextualizing school mathematics in the cultural context of student is one of the quality measures for mathematics in the curriculum framework.Revisiting the appropriateness of elements of historical mathematics is also other demanding issue.In the study findings indicated some elements of historical mathematics are vague or inappropriately situated.Furthermore, Great historical note that shows "Euclid's" work needs to include since many of Euclidian Geometry introduced at secondary schools.Students can learn and inspired through the work of Euclid in the history of mathematics.

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Figure 4. Mathematics student text books reviewed in this study.

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Figure 5.An item taken as historical note (George Cantor: Grade 9 mathematics textbook, p. 16).

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Figure 7.An example of application with historical note (Leonardo Fibonacci: grade 12 mathematics textbook, p. 8).

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Figure 6.Pyramid of Giza in Egypt item taken as notes on usage areas of mathematics (grade 10 mathematics textbook, p. 269).