Mathematics is a field of philosophy focused on the principles of pattern, quantity, and structure (Hom and Gordon, 2021). Mathematics is classified into several topics that describe distinct parts of the discipline, such as arithmetic, which deals with numbers, and geometry, which deals with magnitudes. Mathematics has evolved to include more subjects such as probability, calculus, and algebra, among others, as its scope has broadened to include symbols. Clearly, mathematics has progressed from describing simple relationships to more complicated interactions with higher bandwidths over time. As a result, understanding the roots and progress of mathematics requires a look into its history and evolution.
History of mathematics development and its original purpose
Mathematics is thought to have originated with simple counting and is as old as human existence. The Lebombo and Ishango bones are the earliest known representations of mathematics. The Lebombo Bone is where the first mention of people adding up first appears, which dates back to the Upper Paleolithic Age in Africa. This primate fibula is imprinted with 29 cuts throughout its length, which most researchers describe as “tally-marks.” It was discovered in the Lebombo Mountain area and was given the name Lebombo. The 29 markings on the Lebombo bone are thought to be a numerical record. The location could be somewhere between 44,200 and 43,000 years old, according to radiocarbon analysis (Flight, 2019).
The Ishango Bone is much younger but just as spectacular. The Ishango Bone is a baboon’s fibula that Belgian archaeologist Jean de Heinzelin de Braucourt identified in the Democratic Republic of Congo in 1960. While its exact usage is unknown, researchers are nearly unanimous that it exhibits evidence of mathematics. The Ishangoo bone sculptures in patterns are supposed to reveal mastery of mathematical concepts like adding and subtracting, among other things. Approximately 20,000 years ago, the bones were used as tally sticks.
Southern Mesopotamia gradually developed written mathematical concepts. Among the first numbers was π (pi), which the Egyptians and Babylonians were familiar with. The area of a circle was calculated by multiplying three times the radius squared by the ancient Babylonians, yielding pi = 3. A figure of 3.125 for π appears on one Babylonian tablet (about 1900–1680 BC), which is a reasonable predictor. The Rhind Papyrus (about 1650 BC) contains information about ancient Egyptian math. The Egyptians had to use a formula to determine the area of a circle that yielded a figure of 3.1605 for π. Archimedes of Syracuse (287–212 BC), one of the ancient world’s best mathematicians, performed the first computation of π (Exploratorium, 2022).
The Pythagorean theorem, which links the sides of a right-angled triangle, was later discovered by the Babylonians. The intelligence of the Babylonians and Egyptians motivated Pythagoras and Thales, who enhanced Greek mathematics. By applying the Pythagorean Theorem to determine the areas of two separate polygons, Archimedes estimated the area of a circle: the circle’s enclosed polygon as well as the circle’s imprinted polygon. The circle’s area was calculated using the areas of the polygons as minimum and maximum values because the circle’s actual area is halfway between the imprinted and contained polygons’ regions. Archimedes was well aware that he had simply reached an estimation of the figure within those constraints, rather than the actual number.
Pythagoras, an ancient Greek philosopher, is the founder of the Pythagorean theorem. Pythagoras related math to the environment and established a philosophy known as pythagoreanism, which held that numbers were nonexistent actual beings in space and time. The Pythagorean theorem was utilized by ancient Babylonian architects in their architecture, although it was not labeled as the Pythagorean theorem. According to some old stone tablets from Babylonia, the Babylonians developed guidelines for constructing Pythagorean triples some 1000 years prior to Pythagoras. They knew how a right-angled triangle’s sides interacted. They could even calculate an isosceles right-angled triangle’s hypotenuse, resulting in a five-decimal place estimate of the final number. The Egyptians in their construction also used this theory. Many Egyptian pyramids were constructed in this manner.
Supporters of Pythagoras’ philosophy identified irrational numbers. Plato and Socrates responded to Pythagoras’ notion that numbers were realistic in a realm of forms centuries later.
Years later, Euclid established geometrical theory and proposed that prime numbers are infinite. The Egyptians were one of the first to apply geometry to land surveying. At the very foundation of every framework, there are facts that are assumed and cannot be independently verified. Euclid’s “Elements” publications contained the first axiomatic framework. The van Hiele concept has received appreciation from studies in geometry learning and teaching. Two Dutch mathematics teachers created this hypothesis in the late 1950s. They discovered that when kids are studying geometry, they appear to go through the following steps: axiomatic, deduction, relationship, analysis, and recognition.
The idea of infinity therefore picked up steam thanks to Zeno’s discussion of infinity millennia before Euclid. The earliest “solution” to the issue was entirely mathematical. The argument acknowledges that there could be an infinite number of hops to make, but that each successful hop would be progressively smaller than the previous one. As a result, it makes no difference how many pieces you partition it into, provided you can prove that the summation of all the jumps you have to make adds up to a finite value.
Rafael developed numbers like I and the concept of positive and negative i in subsequent years, which led to breakthroughs in mathematics. Pierre de Fermat and Descartes contributed to the development of the Cartesian plane, which allowed graphing. Gottfried Leibniz and Isaac Newton eventually utilized the Cartesian coordinate notion to build the calculus. Scientists to explain how planets revolve eventually utilized mathematical concepts. The invention of the number e, which expresses logarithms, as well as the formulation of the logarithmic scale based on Gause’s discovery that the values between prime numbers grow by 2.3, were both significant developments. Plato’s philosophy of mathematics as factual wisdom was beginning to be questioned by the nineteenth century. As a result, philosophers explored techniques to show the reality of math, leading to the development of logicism and formalism.
Peano devised axioms demonstrating that mathematics may be deduced from rational rules like those that the fact that zero is a number. Mathematical structuralism, which determines numbers by their location within mathematical structures, and formalism, which asserts that numbers do not exist, emerge. Philosophers eventually concluded that mathematics is a human invention. Finally, in the contemporary age, mathematics has progressed to applied math, which analyzes mathematical applications that go beyond numbers.
Mathematics contemporary content and purpose
The contemporary world for which learners must be prepared exhibits little relation to the one for which our educational systems were created. In recent years, society has witnessed significant changes that have modified the way math is approached and, as a result, how it must be delivered. People can no longer do many of the procedural elements of mathematics. The statement “you won’t have a calculator with you every day” is no longer relevant since everyone has powerful computers, bookstores, and tutors in their pockets as well as in the cloud. The curriculum, on the other hand, is strongly embedded in its history and tradition, which dates back to the dawn of time. Furthermore, mathematics is a fundamentally self-reinforcing subject; you cannot, for example, skip multiplication and go straight to algebra. Students who do not understand what they are supposed to do at a particular time lag behind, which pushes them to fall further behind.
On the other hand, several jobs that previously did not involve mathematics are starting to include quantitative methodologies in their job requirements (Bialik, Zbarsky, Cardone, and Fadel, 2021). With the same confidence that parents advise eating vegetables before dessert, most mathematicians and certain mathematics tutors will emphasize the need to master the technical intricacies in order to obtain a deeper grasp. Is procedural learning, on the other hand, genuinely a requirement for deeper mathematical understanding? The response is “no,” according to most people.
Programs and curricula aimed at teaching difficult mathematical concepts to young children, like topology and calculus, are surfacing, demonstrating that conventional thinking concerning higher-level arithmetic’s lack of accessibility may be founded on incorrect logic. Besides, in life, one can always use a software or calculator, find the answers online, or seek the advice of a professional. The thing is to identify what to do, what to look for, and who to approach. The conventional, measured approach to teaching mathematics is not only harmful to learners’ perceptions of the profession, but it also fails to reflect the genuine application of mathematics in industry.
Reasons why mathematics is an important part of the curriculum
Excellent for learners’ brains
Employers place great value on analytical and creative skills (Audsley, 2019). Human brains form critical neural connections for interpreting data, so it is no surprise that math is important for brain development and critical thinking abilities. When students work on a mathematical question, they gather data, deconstruct the assumptions, notice the relationships that remain, and systematically solve their sections in a logical manner. Students will be able to prepare their thinking when we face real-world challenges if they can comprehend math and come to rational conclusions. Students can search for the most logical reasoning, explore different answers, and integrate the evidence they have to conclude.
Students’ comprehensive math knowledge will be instantly applied to real-world challenges. If they intend to buy a property in the near future, mastering math fundamentals is essential for handling percentages and property prices. Almost every occupation in the world requires some level of mathematics. It comes as no surprise that if someone aspires to be a CEO, a property manager, a scientist, or even a nuclear engineer, they will use numbers. Students can never be smart enough to avoid mathematics, so they should embrace it and enjoy learning it while their careers are not dependent on it.
Better problem-solving skills
No one can possibly match Alan Turing’s mathematical and problem-solving brilliance. Turing is often regarded as the “Father of Modern Computing.” He was responsible for numerous key mathematical breakthroughs, including cracking the Enigma code used by the Nazis. However, there is no disputing that enhancing one’s mathematical skills and studying them carefully can help students improve their problem-solving abilities. Mathematics clarifies problem solving, and mathematicians have long recognized that problem solving is essential to their career field since there is no math without a problem. In the minds of educational theorists, problem solving has always been a fundamental theme. As a math scholar, you will discover how applied mathematics addresses real-world problems and create better problem-solving techniques.
It helps almost every career
Mathematical understanding, as well as its intricacies, can be beneficial in nearly every profession. Mathematics and its applications are used to establish and improve indispensable jobs in the sciences, commerce, economics, production, telecommunications, and engineering, among other fields. Engineers, software developers, actuaries, statisticians, mathematics tutors, and even company directors are among the vocations and professions that gain from a degree in mathematics. All of these occupations tend to be distinct, They all require a well-developed mathematical set of skills, which is something they all have in common.
It helps me understand the world better
Students gain a greater understanding of the world when they study mathematics. This may seem self-evident, but understanding the subtleties of how math operates can widen their perspective and enable them to see the world from a different perspective. For instance, Einstein’s relativity theory (which states that the force of gravity is caused by the bending of time and space and that elements like the earth and the Sun affect this geometry) has enhanced our knowledge of the world (Audsley, 2019). This concept demonstrated that space and time have a give-and-take interaction and that the bendy, shifting “space-time” fabric is made up of these two elements. This approach to thought prompted Einstein and others to look more closely at the symmetries of the universe, or all the unique approaches someone can twist, spin, and pass across it while keeping the proximity between events or objects the same.
The purpose of mathematics content serves relation to the opposition between knowledge and ideology
Math content is vital in helping education transfer. To begin with, there is a transfer of higher education from western nations to eastern and “developing” economies. International branding and remote education programs in the native countries, as well as research at institutions in the supplying nations, are used to attract students to participate in academic research and study. Scholarships funded by the scholars’ native countries, self-funding for individuals from privileged families, and, less frequently, funding from “developed” nations like Commonwealth Scholarships help to encourage this. As a result, “developed” nations are receiving net inflows of capital, while “developing” countries are receiving net inflows of skills and knowledge. The ideological effect is the intellectual direction or absorption that occurs as information and knowledge move to ‘developing’ nations. For the purposeful absorption of knowledge, skills, experience, and research procedures, a collection of latent norms, as well as cognitive and ideological orientations, is always present. These may substitute or cohabit with the receiver’s personal orientation, but they cannot be completely dismissed if the receiver is to be effective in getting and implementing the knowledge and competence.
Secondly, math content helps in seeking international opportunities. Instructional academics and researchers are recruited and mobilized abroad for work, consulting, and research initiatives. This encompasses the importation of knowledge and experience from the West or “developed” nations in the form of permanent or fixed-term contracted staff, such as scholars and team members, as well as bought-in consulting firms for higher education institutions’ faculties, who operate as external evaluators, employees’ instructors, and so on. Since other qualified professionals must inexorably convey their ideological orientations with them, one of the ideological effects of this flood of expert knowledge to “emerging” nations is the ideological orientation impact. Excursions by scientific research employees paid by “developed” nations to do research in “developing” nations are also included in the migration of personnel.
Math content also serves the dominance impact. The main sources of the dominance impact are international journals and other scholarly articles in math, science, and technology learning. This literature review, which includes periodicals, texts, guidebooks, dissertations, and internet sources, is mainly based in northern and “developed” nations and is predominantly Anglophone at the high-end. Despite the fact that numerous countries are represented on publication boards and conference panels, the center of authority remains solidly Eurocentric. This, like the Eurocentricity of global research teams and seminars noted above, intensifies the ideological effect. Furthermore, the research literature is promoted internationally, resulting in an increase in knowledge as well as a flow of cash into “developed” nations.
In conclusion, the tale of mathematics is unfinished since it continues to progress and may continue indefinitely. Mathematics is now a well-established man-made concept that is universally accepted and has evolved into a universal language for all people everywhere. Civilization continues to affect and transform mathematics, opening up new avenues for mathematical progress. Mathematics has become an indispensable component of human life and is still regarded as such. More mathematics problems will emerge, which will serve as the foundation for future mathematics advancements, this cycle will continue as mathematicians improve to meet human needs, and as long as human needs change, new problems will emerge for mathematics to address. As a result, the evolution of mathematics is inextricably linked to shifting human demands.
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Bialik, M., Zbarsky, E., Cardone, T. and Fadel, C., 2021. [online] Curriculumredesign.org. Available at: <https://curriculumredesign.org/wp-content/uploads/Mathematics-for-the-Modern-World.pdf> [Accessed 1 May 2022].
Exploratorium, 2022. A Brief History of Pi (π) | Exploratorium. [online] Exploratorium. Available at: <https://www.exploratorium.edu/pi/history-of-pi> [Accessed 1 May 2022].
Flight, T., 2019. 20 Mind-Blowing Facts from African History that Made Us Rethink Our World History Lessons. [online] HistoryCollection.com. Available at: <https://historycollection.com/20-mind-blowing-facts-from-african-history-that-made-us-rethink-our-world-history-lessons/> [Accessed 1 May 2022].
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