The Enquiry Project Report: History of Mathematics and Teaching

This research report investigates the historical development of mathematics, tracing its evolution from ancient philosophical teachings to its modern applications in education. The study examines how the theories and formulas created by mathematical philosophers have influenced contemporary teaching methodologies. It emphasizes the impact of technology in facilitating the understanding and teaching of mathematical concepts, highlighting how advancements such as videos and animations have simplified complex calculations. The report analyzes the use of mathematical equations in technological advancements, which in turn enhance the comprehension of mathematical principles. Through secondary data collection and qualitative research analysis of research journals, the study explores key literature to provide a comprehensive overview. The conclusion underscores the vital role of ancient mathematics in enabling modern technological progress and its usefulness. The report also looks at the role of technology in the classroom and how it impacts the students.

Running head: THE ENQUIRY PROJECT REPORT
THE ENQUIRY PROJECT REPORT
THE HISTORY OF MATHEMATICS AND HOW IT IMPACTS ON OUR
MATHEMATICS TODAY
Name of the Student
Name of the University
Author Note

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Declaration of Originality
I declare that this assignment script is my own work and has not been
submitted either in the same or different form to this or any other Higher
Education Institution for a degree or other award.
Signature:
Name:
Date:

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Executive summary
This research report deals with study to connect the ancient mathematical teachings
and formulas created by the mathematical philosophers and the impact of the use of
that mathematical study in the modern day teaching pattern to the students of the
world. The modern aspect makes use of technology, which helps in the
understanding, and the teaching of the theories and logic easy to the students. In
this fast-paced world, no one would like to work their whole day to understand
certain small mathematical calculation which would be completed with the help of a
video or animation with a matter of hours. This advancement has also been felt in
the development of the technologies, which makes use of advanced mathematical
equations and formulas to compile the product. The use of these mathematical terms
help in the making of the technologies, which are in turn used to make the
understanding mathematical equations easily. The research has been conducted
with the help of secondary data collection and qualitative research analysis on the
data collected from the research journals. Key literatures has been studied in order
to make the research complete. To conclude it can be said that with the use of the
ancient mathematics it would have been impossible for the mankind to advance to
such a great extent and make use of those theories to make technologies useful for
everyone.

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Table of Contents
Introduction................................................................................................................. 4
Literature Review........................................................................................................5
Methodology................................................................................................................8
Discussion and Critical Analysis................................................................................10
Conclusions and Recommendations.........................................................................13
References................................................................................................................16
ENQUIRY PROJECT CHECKLISTS.........................................................................20

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Introduction
Philosophers have defined mathematics as the study of the relation between
objects and their relations. The word objects in this context can range from a
numerical quantity, structure, space or a change in the form of perception. However,
there is a wide range of views being shared by mathematicians and philosophers on
the prospect of the exact scope of the definition of the word mathematics.
Researchers in the field of mathematics has been seeking out patterns in nature to
find new conjectures to formulate (Chukwuyenum 2013). The researchers work for
the resolving of the truth to find the falsity of the mathematical proofs. It has been
found that the mathematical structures are a good procedural model for the
explanation of the real phenomenon. The mathematical reasoning process can help
in the provision of major insight in the prediction and prediction about the nature of
the work. With the use of abstraction of theory and logical reasoning the
development of the mathematical reasoning helps in the development of the
counting, calculative process and the measuring of the systematic study of the
shapes as well as the motions of the physical objects in the nature (Chukwuyenum
2013). Practical use of the mathematics has been found to be of great use for the
activity of the human nature. This has been in use as far as records exist in the
nature. The research process followed for the topic is for the solving of the
mathematical problems takes many years or in some cases centuries for the finding
of the sustainable inquiry required for the proofing of the theory (Gargiulo et al.
2016).
Mathematics has been used in various field of study with special inclusion in
the field of engineering, medicine, natural science as well as in the field of finance
and social sciences. In the modern aspect of mathematics, the form of applied
mathematics has led to the development of major disciplines in the field (Bangu
2016). The disciplines developed are in the form of game theory and statistics.
Mathematic researchers has been found to be engaged in the pure mathematics
section without the application of the theory in their mind. There has been found to
be no clear line between the application of pure mathematics and applied
mathematics, and practical mathematical use for where the beginning of the pure
mathematics is found. The history of mathematics can be seen in the form of an ever

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increasing series of abstractions (Bangu 2016). The first major abstraction, which
had been found, was in the form of numbers. Most of the complex mathematical
uses has not been found until later in the year 3000 BC.
This research report shows the study of the history of mathematics along with
the advancement of mathematics in the modern world. The modern aspect of
mathematical advancement has helped the students of the newer generation to
understand the theoretical study of mathematics. This form of modern study has
been slowly developed with the help of technology and has provided the modern
world with a better understanding of the working procedure of the ancient theory of
mathematics.
Literature Review
The discussion topic of the development of mathematics from the ancient time
to the impact of the data developed on the modern aspect of the teaching method of
mathematics. Kilpatrick (2014) stated that though mathematics has been taught to
others and consecutively been researched by various mathematical geniuses for the
understanding of the research. Babylonian students were taught to solve quadratic
polynomials on clay tablets but no evidence has been found based on how much
theory was taught to the students to make them understand the working of the
quadratic problems. Kilpatrick (2014) also states that the Chinese ion the year 1115
BC were made to solve an arithmetic examination for the clearing of their civil
service. In the fifth century Plato, a notable mathematician had taught one of his
student that by squaring the sides of one of the square, the result was equivalent to
the area of the square. Kilpatrick (2014) also discusses about the observation of the
teaching of mathematics over the centuries. Teaching of the theoretical mathematics
has offered a reflection about the writing of textbooks developed around the teaching
techniques based on the experience gathered from the teachings (Keeling et al.
2013). As the teachings of the students forwarded, they were able to teach at
universities and colleges, which helped them to identify themselves as a
mathematical scholar.
Katz et al. (2014) says that though there has been a lot of research paper
publication on the topic of science and education as a whole there has been found to

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be very small amount of publication in the field of mathematics. However, this has
not dropped the interest of the mathematics and has continued their work based on
the theory of implementation of mathematics in the modern world (Bartha, Aberdein
and Editors 2013). There has been found to be research particularly in the history of
mathematics and how it came into the world to be of the best quality (Aguirre and del
Rosario Zavala 2013). Most of the papers that are now being published there has
been the discussion about the philosophy of mathematics rather than the history of
mathematics. Katz et al. (2014) also says that there has been signs for the use of the
changing in the situations for a welcoming changes. The philosophy of mathematics
allow a better view of the understanding of the theory of mathematics better than by
understanding the history of mathematics (Aguirre and del Rosario Zavala 2013).
The philosophy helps in learning mathematics in the form of basic nature of
mathematics. Katz et al. (2014) also suggest that a focused study of the theory of
mathematics can help any science educators to understand more about the working
of mathematics in their own department. The paper emphasizes more on the history
of mathematics with the emphasis over the years for the improvement of the flux
(Bronshtein et al. 2015). The teaching of the mathematical ideas is based on the
reporting of their experience using the history sharing with the students. Katz et al.
(2014) also discusses about the considerations to be taken into concern are the
raised theoretical questions about the teaching procedure of mathematics in the light
of the domains history along with the consideration of the philosophy.
Lovász (2013) discusses about the implementation of historical values of
mathematics in the form of theoretical knowledge to be implemented into the study of
mathematics in the form of computer-aided technology. The author also discusses
about the general study of the trends in mathematics. Lovász (2013) says that there
has been an exponential increase in the number of researches in the field of
mathematics. It has been found that the number of researches increase by a number
of 25 every year (Plass et al. 2013). This factor has brought up new possibilities in
the research of the topic that there are no new topics for the researchers to study.
Thus makes the additional problem of the preparation of future researchers in the
field of mathematics. Lovász (2013) also describes that there are new form of
application, which has found new significance like the study of information
technology and science. All areas of human research activity makes use of more and

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more mathematics for the helping in the development of the more significant branch
of study (Alpaslan, Işiksal and Haser 2014). This poses a problem for the students
who are not able to relate the problem to the actual theoretical statement to apply for
the finding of the solution. The development of new tools like computers and
information technology poses visible new features that help in the introduction of
computers in the education system (Kleiner 2013). However, would the problem be
cleared easily with the use of these technologies for the teaching of the students in a
more productive way? The new form of mathematical activity provides the best
solution for all the problems stated by the author above. The development of
algorithm and modelling techniques help in the writing and lecturing of the
mathematical techniques and theories (Mosvold, Jakobsen and Jankvist 2014). Thus
the problem arises as to which theories to teach the students and which one to wait
for the understanding of the previous ones to proceed with. Lovász (2013) discusses
that the mathematical researchers who are working on their theory would be relevant
by browsing a number of new periodicals. The number of professional workshops
and use of emails are increasing (Fallis 2013). There has been an increase in the
number of multiple researchers, which shows that the mutual personal contact is not
enough to provide sufficient amount of information to the researching community.
Lovász (2013) also says if there is an increasing complexity in the department of
mathematics where the exposition style mathematics has not received any place in
the domain of education. To implement a more expository style teaching there needs
to be a heretical study.
Eyyam and Yaratan (2014) discusses the use of technology in the classrooms
for the teaching of the differ subjects to the students of the schools up to the point of
them passing out from the university. The authors has conducted a study based on
which he has said that there needs to be a better use of technology in the
classrooms for the teaching of mathematics as well as other theoretical subjects
(Linnebo 2013). The authors had taken the help of experimental groups for the
investigation of the preferences and the attitudes of the students who were taught
with the help of technology based instructions. The authors have found that when the
technology is used in a positive manner for the teaching of the departmental
theories, there has been found to be a positive view of the grasping of the knowledge
skills by the students (Karp and Furinghetti 2016).

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The researchers found that the students had a positive outlook to the use of
technology for their teaching. The authors in the journal have discussed the
implications of the curriculum that was designed based in the teaching procedure.
From the study of the above literature the following list of theme questions has
been developed which are to be discussed for the complete understanding of the
research topic:
a) How does the impact of the history of mathematics affect the modern
mathematical aspect?
b) Theme 1: What is the historical specification of mathematics?
c) Theme 2: What is the modern aspect of mathematics?
d) Theme 3: What conclusion can be drawn from the historical specification and the
modern aspect of mathematics?
The literature studied for the paper shows the study based on the analysis of
the history of mathematics (Gutiérrez 2013). The advancement of mathematics
slowly into the theories, which has been developed for the solving of much higher
levels of mathematics, has helped in the slow but a steady advancement of the
theoretical study. This has then been drawn into the modern day aspect of involving
technology into the aspect of modern mathematics has helped for the students to
study and grasp the theoretical values easily and with great interest (Statistics 2013).
Thus, it can be concluded that the use of modern technology for the understanding
of the historical mathematic theories and problems has helped a greater fold in
today’s advancement of teaching methodology of mathematics.
Methodology
There are two kinds of data collection procedure, which is followed in the
development of research methodology. They are primary data collection and
secondary data collection. Primary data collection is the process of collecting first
hand data from real persons. The data is collected with the help of survey forms. The
data’s is to be collected by the researcher on his own (Bråting and Pejlare 2015).
The data is considered to be of the category of real time data and requires vigorous
amount of time for the completion of the data collection procedure. The data is
collected with the help of surveys, observations of environment, experiments

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conducted with the theory in mind, sharing of questionnaire and with the help of
personal interview. The cost for the process of primary data collection has been
considered to be of an expensive quality. The time for the collection of data is long
term and is in a crude form. The data is in the most specific form in regards to the
research topic though has a high level of accuracy (Oecd 2013). The secondary
method of data collection is the process of analyzing of data that has already been
collected by someone else beforehand. The data is of the past reference and no real
data is used in this process. The process has been considered by the researchers to
be of a quick and easy format. The data is collected from various government
document publications, online websites, books, research journal articles and
company related records and publications (Permuth and Dalzell 2013). The process
is considered to be economical as the research can be done by the researcher on
their own without the help of any other person. The time required for the collection of
data is short, as the data has to be only searched from the online resources (Shclick
and Torquato 2013). However, the research data collected from the resources may
or may not be completely related to the research topic. The most important plus point
of this method of data collection is that the data is in the cleanest form however, the
data is of relatively less accuracy.
Apart from the collection of data, there are two types of research
methodology, which is followed, based on the data that has been collected. They are
qualitative research and quantitative research. Qualitative research is based on the
explanation of the research topic (Boaler 2013). It is used for the understanding of
the reasoning and motivations and for the provision of the insight into the problem
topic and help in the development of the idea for the research methodology.
Qualitative research helps in the uncovering of the trends in the opinions and the
thoughts for the understanding of the research topic on a deeper level (Schlimm
2013). The data collection techniques in this process varies from an unstructured
method to a semi structured methodology. The sample size taken for the research is
relatively small and the participants are chosen in such a way so that they are able to
fulfil the quota for the research topic. The next method of data understanding is the
process of quantitative research. In this process, the researcher connects a vast
amount of numerical data, which is then analyzed, with the help of analytical skills to
draw upon a conclusion for the research topic (Rocca 2014). The data collection

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process is much more structured in this type of research methods. The data is
collected with the help of online surveys and interviews from various participants by
the researcher.
For this research, the process of secondary data collection has been
conducted due to the unavailability of any kind of numerical data. However, it has
been found that there is a high abundance of theoretical research journals. This
helped in the collection secondary data collection from the journals and make use of
them in this research report. The process of qualitative research methodology is to
be followed for the analysis of the data for the topic. This has been chosen because
the amount of numerical information for the research topic is almost negligible. The
topic chosen is much more of a research topic rather than a survey related topic.
For a more deeper understanding of the research topic a thematic analysis
has been done on the research topic. The following theme questions have been
developed for the research based on the research topic of this project:
a) Theme 1: Historical specification of mathematics
b) Theme 2: The modern aspect of mathematics
c) Theme 3: Conclusion from the historical specification and the modern aspect of
mathematics
The thematic analysis emphasizes on the pinpointing and then following the
analysis of the pattern in the data that is to be collected from the data collection
procedures (Panasuk and Horton 2012). The thematic analysis is conducted on the
research journals with the help of six steps for the clearing of the research topic
along with the pattern of the topic. With the help of thematic analysis the theoretical
aspect of the research topic can be easily divided up and the analysis can be
conducted easily.
Discussion and Critical Analysis
Theme 1:
Kilpatrick (2014) says that mathematicians have used mathematical problems
and theories in the field of research since long time. As the theories of the research
topic was advancing periodically, there was a slow advancement of the theories and

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the proofs related to the theories already known. The proofs helped in the
understanding of the knowledge used for the mathematical problems easily.
Mathematics has often been chosen as a form of academic advancement filed where
the researchers are able to work on the topic to understand their depth easily
(Hodgson 2013). Kilpatrick (2014) observed that the countries of Europe where most
of the students try to take up education in the form of science. This scenario has
been considered to be equal to a preparatory seminar for the teachers and a medical
schools for physicians. The author also found that the early researchers in the field
of mathematics wanted to learn how mathematics was being done in the world
(Carvalho and Dassie 2012). A questionnaire was shared among 100
mathematicians to understand how they were to work on their mathematics. The
report on the survey was compiled into several journals and was published between
the years 1905 to 1908. A commission was formed named International Commission
on the Teaching of Mathematics (ICTM) by the Fourth International Congress of
Mathematicians in Rome. The purpose of this commission was to look after the
teaching standard of mathematics at school level in the world (Kilpatrick 2014). The
researcher on requiring to make their field into a more of a scientific format worked
on the making of an educational psychologist for the improvement of the natural
science. Many of the mathematicians were looking for a field of science where they
would be able to make use of science as a model (Panasuk and Bolinger 2013). A
psychologist named Edward L. Thorndike did one of such education in the early
years of the twentieth century. The study was conducted with the help of a control
group and an experimental group. Thorndike was able to conclude that the
experimental group had a problem with the judging of the size of rectangles to that of
squares. This study proved that only theoretical study was not enough to make a
student fully aware of the study and problem.
Again Janet Barnett, Jerry Lodder and David Pengelley said that a long
standing methodology has been in the teaching department of mathematics at the
university level courses with the help of various framework for the various theoretical
framework for the role of mathematical history (Kjeldsen and Blomhøj 2012). The
second portion of the study was the study of the secondary level school study of
mathematics with the help of theoretical framework. Tinne Hoff Kjeldsen and Pernille
Hviid Petersen conducted this. This helped in proving the students concept of