Introduction
Mathematics has been noted as a significant part of American history since the early centuries. That can be seen from the spread of education in the field of mathematics, which has had notable impacts towards defining the overall shifts experienced concerning this subject. However, Karp & Schubring (2015) argue that people viewing mathematics from the perspective of recent achievements may be tempted to believe that mathematics does not have a history before the twentieth century. That misconception fails to take into account that modern mathematics in American society has been defined by the overall growth of the subject since the early sixteenth century. The history of mathematics helps towards laying down the necessary foundations upon which scholars have been able to build on a constant progression of what it means to reflect on mathematics as a subject.
The focus of this report is to examine the progression of mathematics through the different centuries with the sole focus being towards investigating how the progression has helped in shaping mathematics today. Mathematics is seen as one of the most important subjects today, as it applies in almost every field of study. Consequently, this means that the foundations laid within its historical context have had a notable influence towards changing the way people view mathematics and its importance in the social context. Additionally, the report will seek to examine some of the significant achievements made in mathematics throughout history with the focus being towards investigating how this has helped shape the subject today. That will assist in defining how people can use mathematics today while considering the fact it helps in shaping different areas of the society today.
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Mathematics in the Sixteenth and Seventeenth Centuries in America
Some of the early settlers in America, including British, Dutch, Swedish, French, and Spanish, played a critical role towards defining the importance of mathematics considering that they presented a need for the subject in their day-to-day lives. Most of the early settlers were farmers and artisans that required mathematics for purposes of addition and subtraction, especially in their engagement in trading activities. Although much of the trade may have been considered as being barter, it was important for the settlers to find the use of arithmetic to help in the calculation of the goods that they needed to trade. During this period, mathematics was a skill that was passed on from father to son along with the ability to read simple sentences as a way of ensuring that one would be able to engage with others.
Most of the boys that engaged in trading were expected to have the understanding of simple calculations including addition and subtraction considering that this sought to define their projected understanding of their trading activities. Another critical aspect to note is that mathematics was viewed as being important during the 16 th and 17 th centuries, as it sought to provide navigator with that basic understanding of how to calculate simple angle measurements (Katz, Jankvist, Fried, & Rowlands, 2014). The primary mode of transport during this period was the use of ships, which were used for transportation purposes from one continent to another. The sailors were expected to have a specific level of understanding on mathematics that would allow them to navigate effectively. Consequently, this sought to build some form of curiosity towards the general application of mathematics as a field of study.
The 17 th century in America introduced the need for having to embark on a process that would allow people to subdivide some of the vast tracts of land in the country (Pope & Rogers, 2018). The consequence of this is that it created the need for having to embark on a process of surveying and mapping, which uses mathematics as one of the key ways through which maximize of calculations. Thomas Harriot and Sir Walter Raleigh were among some of the principal persons that helped towards highlighting the importance of mathematics as a technique in surveying and mapping. Harriot, who was from England, helped towards developing some form of interest concerning mathematics, especially algebra, through his report on the American colony. The overall shift in demand for mathematics sought to define the need for in-depth research in the field of mathematics with the focus being towards examining how it can influence society as a critical subject.
The 17 th century also saw an increase in private tutors with an elementary understanding of mathematics, who would offer students with necessary information allowing them to get a clear understanding of what to expect from the subject. The first American college, Harvard, was founded in 1636, which also played a critical role in increasing demand for mathematics as a subject. Harvard was founded fro ofm having to offer training of the clergy with one of the essential areas of consideration during training being mathematics. The colonial government, Britain, sought to give some form of encouragement towards more people studying mathematics, which meant that they attempted to bring scholars from some of the colleges in England including Oxford and Cambridge, who would help in educating the students in Harvard mathematics.
Mathematics in the Eighteenth Century in America
The 18 th century is seen as a pivotal period concerning mathematics as it relates to the American social context, as this was the period where the interest for the different phases of mathematics increased significantly. Gürsoy & Baki (2018) argue that the central aspect that helped in shaping mathematics in the 18 th century was the fact that it has been introduced as a subject of study within colleges in the United States. Although the subject was poorly taught, most of the people found themselves in a situation where their interests were defined by the fact that it has been projected as a subject with the capacity to change the way people viewed the society. Colleges would use mathematics as one of the ways through which to define their students' abilities and capabilities with the focus being towards maximizing on the subject.
Harvard taught a fairly well-known nature of mathematics, in the first half of the 18 th century, which is seen as one of the critical factors that help in shaping how the American people viewed or accepted mathematics. An example of an individual that helped in developing mathematics in Harvard was Isaac Greenwood, who had studied for a specific period in England. Greenwood taught algebra at Harvard and played a critical role towards changing the way people viewed mathematics as a subject while considering that they were able to build on the basic understanding of how mathematics was expected to help them within the different areas of study that they undertook.
Mathematics in the Nineteenth Century in America
As can be seen from the analysis of the first three centuries, it is clear that America was barren regarding achievements in mathematics considering that the subject had not become as popular as may have been expected. However, this changed in the first half of the nineteenth century considering that it portended several notable achievements in the context of the subject, as it created a new approach towards viewing mathematics. In this half of the century, scholars in mathematics were able to engage in in-depth research on the subject with the aim being towards ensuring that they develop the subject extensively. The scholars were able to create a front through which to promote acceptance of the subject not only within colleges and universities but also within different levels of education.
George Bancroft is seen as one of the key persons that helped in shaping mathematics during the 19 th century, as he was able to introduce European standards that would help towards developing mathematics within the American context. Generally, this meant that the people in America would be able to study mathematics while reflecting on the importance of subject within the European context. Majority of the schools within the United States took up mathematics as a critical subject for their students providing them with primary education on mathematics while ensuring that the people would be examined on the same. The long-term impact that this had on the American social context is that it created an avenue through which people were able to accept mathematics as part of their social system while reflecting on it as one of the essential subjects shaping the society.
However, it must be noted that the progression of mathematics during this period was somewhat slow considering that the number of scholars with information on this subject was very limited in number. Consequently, this meant although the study of mathematics was seen as having being embraced as part of the American social context, it did not change the way people viewed the subject. The outcome of this is that it sought to change the way in which people reflected on the generalized understanding of what to expect concerning the study of mathematics. Colleges and universities were able to advance the knowledge that they passed along to their students concerning mathematics while ensuring that the students would be able to engage in further research on the subject as a way of enhancing their connection to the subject or mathematics.
Mathematics in the Twentieth and Twenty-First Centuries in America
The 20 th and 21 st centuries have seen significant progress concerning the development of mathematics attributed to the fact that a considerable number of scholars in this field of study have been able to embrace research in mathematics as a way of building overall progress towards the subject. An example of a scholar that has helped in shaping mathematics in the 20 th century within the United States is German mathematician Georg Cantor, whose role in developing the understanding of algebra cannot be ignored considering that he played a critical role towards highlighting the rationality in numbers (Furinghetti, 2015). Cantor sought to build on the understanding that indeed number is countable while relying on the understanding of how numbers tend to interact as part of areas that include multiplication and division.
The progression in mathematics during this period has resulted in its introduction within the formal system of education beginning from the lowest level of education to the college or university level. Published books have helped in providing students with a better understanding of how mathematics can be defined within the American social context while taking into account how it helps shape society. Generally, this means that students find themselves in a somewhat effective position through which to engage in mathematics as a subject while reflecting on the generalized understanding of how to use this subject in other fields of study. The continued development of the subject is expected to have serious implications concerning the future of the subject not only within the context of education but also concerning its influence in other areas of study.
Colleges and universities have also been on the forefront towards promoting the progression of mathematics in the 20 th and 21 st centuries by introducing specific courses that focus on mathematics as a subject of great consideration (Wang, Wang, Li, & Rug, 2018). The courses have allowed students to engage in further research on mathematics with the sole intention being towards making notable achievements in the mathematical context. Additionally, they have also helped towards creating a new approach through which students can reflect on mathematics as being key towards allowing people to solve a wide array of problems. The general expectation concerning the uptake of mathematics has been significant considering that the subject is viewed as being important in the education system today. Additionally, it is seen as being a crucial part of other fields of study.
Conclusion
In summary, mathematics has been noted as a significant part of American history since the early centuries. Most of the early settlers were farmers and artisans that required mathematics for purposes of addition and subtraction, especially in their engagement in trading activities. The 17 th century in America introduced the need for having to embark on a process that would allow people to subdivide some of the vast tracts of land in the country. The first American college, Harvard, was founded in 1636, which also played a critical role in increasing demand for mathematics as a subject. The 18 th century is seen as a pivotal period concerning mathematics as it relates to the American social context, as this was the period where the interest for the different phases of mathematics increased significantly.
An example of an individual that helped in shaping mathematics in Harvard was Isaac Greenwood, who had studied for a specific period in England. George Bancroft is seen as one of the key persons that helped in shaping mathematics during the 19 th century. It must be noted that the progression of mathematics during the 19 th century was somewhat slow considering that the number of scholars with information on this subject was very limited in number. The 20 th and 21 st centuries have seen significant progress concerning the development of mathematics. Published books have helped in providing students with a better understanding of how mathematics can be defined within the American social context while taking into account how it helps shape society. Colleges and universities have also been on the forefront towards promoting the progression of mathematics in the 20 th and 21 st centuries.
References
Furinghetti, F. (2015). The History of the Teaching and Learning of Mathematics. In The Proceedings of the 12th International Congress on Mathematical Education (pp. 569-573). Springer, Cham.
Gürsoy, K., & Baki, A. (2018). Does Using History of Mathematics Make Sense? The Views of Teacher Candidates. Journal of Pedagogical Research , 2 (2), 78-90.
Katz, V. J., Jankvist, U. T., Fried, M. N., & Rowlands, S. (2014). Special issue on history and philosophy of mathematics in mathematics education. Science & Education , 23 (1), 1-6.
Karp, A., & Schubring, G. (Eds.). (2014). Handbook on the history of mathematics education . New York, NY: Springer.
Pope, S., & Rogers, L. (2018). Anglo-Danish conference on History of Mathematics in Education: Bath Spa, August 2016. BSHM Bulletin: Journal of the British Society for the History of Mathematics , 33 (1), 62-67.
Wang, K., Wang, X. Q., Li, Y., & Rugh, M. S. (2018). A framework for integrating the history of mathematics into teaching in Shanghai. Educational Studies in Mathematics , 98 (2), 135-155.
