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What is Mathematics?

Question:

The History of Mathematics and How It Impacts On Our Mathematics Today.

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 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.

Applications of Mathematics

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.

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 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.

Development of Mathematics

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 more mathematics for the helping in the development of the more significant branch of study (Alpaslan, I?iksal 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.

Philosophy of Mathematics

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).

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:

1. How does the impact of the history of mathematics affect the modern mathematical aspect?
2. Theme 1: What is the historical specification of mathematics?
3. Theme 2: What is the modern aspect of mathematics?
4. 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.

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 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.

Technology in Mathematics Education

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 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:

1. Theme 1: Historical specification of mathematics
2. Theme 2: The modern aspect of mathematics
3. 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.

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 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 images and reflection based on the concept of function rather than taking into concern the modern approach (Adams 2013). On a third level, the theoretical framework of the knowledge of mathematics was shown to the elementary level mathematics teachers and they were able to profit from the study of history of mathematics.

Theme 2:

Looking at the modern aspect of mathematical advancement it can be said that there is a high up rise of the number of researchers in the field of researchable mathematics. Lovász (2013) shows that there is a rise of 50 researchers annually for the domain of mathematics. The author has found that there has been a rapid expansion in materials for study and a rapid downfall for time to be devoted for the teaching of mathematics (Sheffield 2013). This problem cannot be termed as a onetime crisis. The research in the field of mathematics are not showing any visible sign of slowing down. One of the best solution suggested by the author is to leave the recently found theories for the later stages of study so that the learned people to find the best solution for them can approach them (Mumma and Panza 2012). The other suggestion provided by the author is to remove the traditional curriculum for the traditional material that has been deemed as least important. One of the other solution, which can be followed, is to follow the best curriculum created based on the important portions of study material for the students (Gazit 2013). For a better systematic study of the ancient mathematics, which are to be taught at the basic levels, the author has suggested the use of modern technology along with the ancient learnings to provide the students with the help they are to require for the complete understanding of the theoretical approach of mathematics (Maloney, Schaeffer and Beilock 2013).

Following the trend of Lovász (2013), Eyyam and Yaratan (2014) suggest the use of technology in order to make the student’s understand the ancient theoretical aspect of the mathematics. This had been studied with the help of various students, which resulted in a positive result for the use of technology, by the teaching staff to make them understand the mathematical theories, which has been used for a long time. The authors used a method of quasi-experimental design (Vukovic et al. 2013). The method makes use of groups of people without the use of random pre selection. The experiment was conducted on seventh grade students and math’s was taught to them in different format. New topics were taught to them to make the experiment equal for the students. The two groups were controlled group and experimental group. The experimental group was provided with technological aids for their study and the controlled group was made to study on their own. The controlled group was only provided with books and notes (Plato 2013). The authors then used the research study to answer the question of the effect of technology on students when technology was used with the teaching procedure. The experimental students were not to provide with a negative feedback of the study procedure (Clark 2012). The technological teaching procedure helped in the advancement of the traditional method of teaching procedure. The results of the study conducted suggested that the students wanted to be in the class with the presence of technological use, which made them become more successful in class (Cellucci 2013).

Theme 3:

The main literature studied for this research study shows that every researcher has their own insight in the history of mathematics as well as the theoretical knowledge of the theories and its impact on the modern study of mathematics (Gutiérrez 2013). The research is to help in the finding of the connection between the ancient teachings of the mathematician professors and the process in which modern students are being taught the same mathematical proofs with the help of technology. There is a small line of connection between the research of Kilpatrick (2014) and Katz et al. (2014). Lovász (2013) and Eyyam and Yaratan (2014) talk mainly about the working of the mathematics in the modern day aspect. They talk about the use of technology to simplify the study of the ancient philosophers to make the students understand the logic behind the theory easily.

Conclusions

The entire study was focused on the concept of history of mathematics and the successive impact of the history of mathematics in the development of the modern mathematical theories. As cited from the study of the various research journals the authors have a positive feedback for the advancement of mathematics in the development of the modern mathematical calculations and problem solving theories. Mathematics has also helped in the advancement of various other fields of science. These other departments has been able to use the mathematical formulas developed in the field of applied mathematics. The use of technology in the field of mathematical teachings has prompted the students to show new kind of interest in the field of mathematics. The use of various audio video techniques for the teaching of the mathematical techniques to these students attract their attention faster than the use of normal books and written notes. The study has followed the objectives, which were set forward for the completion of this study. The thematic questions developed for the study has the inclusion of both the themes of the research topic: the history as well as the modern aspect of mathematics. The modern aspect of mathematics has followed the use of technology for the teaching and for the advancement in the technology as a part of the research topic.

The history of mathematics is a vast one, but the consecutive research conducted on the topic has provided the readers with the ability of making the theories and the topics of research easy to understand by them. For the modern aspect of the study there is the inclusion of the use of technology to make the study of the mathematical theories easy for the students of  the schools and universities.

Recommendation 1: Based on the findings of the research material that the use of technology for the advancement of the mathematical theories and topics can be useful for the students to understand the advance theories easily and thus speed up the process of learning for them.

Recommendation 2: For an improvement in the field of research, the researchers can make use of the available resources to make the study they are to conduct or are conducting more informative and attractive for the readers to gain their attention.

The study has been limited to the study of very small amount of research journals because the topic of history of mathematics is not one to be taken up by any researcher easily. Latest research journals are not available in abundance. Moreover, the connection between the impacts of the history of mathematics on the modern theoretical approach of study had been hard to find. For the research, the conduction of a secondary analysis has been done and thus the data had to be analyses in a qualitative manner.

For a further scope, in the study of this research topic it can be exploited in a larger amount with the study of various research journals, which has been published long time back. This would be able to provide better insight on the working theory pf the research topic. It would then be complete with the abundance of research data, which would be collected, with the help of secondary data collection and then a successful qualitative analysis is to be done on theat. Moreover, a comparative study of the two aspect of the research topic would help in the understanding of the various steps, which can be included in the research.

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