To what extent is math relevant to your life and the lives of others you know and how can it become an even more viable area of knowledge. “In mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the Pure Mathematics.”

Roger Bacon (1214-1294)
Mathematics: the abstract science of number, quantity, and space; a subject considered by many to be useless, a waste of time, and too difficult. “When am I ever going to use in real life?” or “What’s the point of learning all this?” are just some questions people ask when faced with a mathematical problem. So, what is the point of math? Paul Lockhart in his A Mathematician’s Lament stated, “How many people actually use any of this practical math they supposedly learn in school? ... So why do people think it is so important?” It isn’t important, at least from my understanding the “math” taught today isn’t important.

Lockhart says that the math taught in modern day schools is not the math that really is; it is not taught as the art that it is. “I’m sure most people use a calculator for everyday arithmetic. And why not? It’s certainly easier and more reliable. But my point is not just that the current system is so terribly bad, it’s that what it’s missing is so wonderfully good! Mathematics should be taught as art for art’s sake. These mundane “useful” aspects would follow naturally as a trivial by-product.” As a lover of math, I can completely relate to this. I was brought up in a household that valued the reason rather than the answer. It’s great if one has the answer to a question but what’s even better is how one got to that answer, how they came up with the answer and the reason as to why that answer is correct. That, for us, applies to math.

There was no such thing as a calculator in our house, we had to be able to figure things out on our own and not by calculator or memorization of the times tables. We had to...

...Theory of Knowledge
Éanna OBoyle
ToKMathematics
“... what the ordinary person in the street regards as mathematics is usually nothing more than the operations of counting with perhaps a little geometry thrown in for good measure. This is why banking or accountancy or architecture is regarded as a suitable profession for someone who is ‘good at figures’. Indeed, this popular view of what mathematics is, and what is required to be good at it, is extremely prevalent; yet it would be laughed at by most professional mathematicians, some of whom rather like to boast of their ineptitude when it comes to totalling a column of numbers....Yet ... it is not the mathematics of the accountant that is of most interest. Rather, it is ... abstract structures and everyday intuition and experience” (p.173, Barrow).
2.1 Mathematical Propositions
2.1.1 Mathematics consist of A Priori Propositions (theorems)
We know mathematical propositions (or theorems) to be true independently of any particular experiences. No one ever checks empirically that, for example, 364.112 + 112.364 = 476.476 by counting objects of those numbers separately, adding them together, and then counting the result. The techical term to describe this independence of experiences is to say that the propositions are a priori. Therefore we say that mathematical propositions are a priori propositions.
2.1.2 Universality
When...

...
Unbelievably, the study of mathematic is everywhere. Mathematics has become an essential part of daily living, counting money, and even measuring time. In the movie Pi (1998), Max, the protagonist has stated his mathematical theory stating that - Mathematics is the language of nature; everything around us being represented and understood from numbers; and if you graph the numbers in any system, patterns emerge. Max’s theory causes him to believe that there are patterns everywhere in nature.
The four ways of knowing are closely related to mathematics, since without language, we would be unable to communicate or intentions. If mathematicians were unable to communicate with others, then, they would not be able to share and compare their findings. Often, Max is seen communicating with others about his discoveries of the natural patterns found in nature, as well as discussing with his mentor Sol about the potential theories and patters existing in the world.
In the film, Max’s headaches had a great negative reaction towards his emotions. Emotions affect the form in which mathematics will be disseminated in society. This greatly affects the form in which information is transferred to others. For example, if Max was to teach mathematics when he was having one of his “moments” I know I would not have been able to listen and understand everything because I will be more focused on his...

... The perception of human being as to how they view and portray the fact shows the cognitive bias that comes along with anything and everything that can be examined. The Areas of Knowledge that I feel best represent the issue of whether knowledge is attainable without the problem of bias and selections are History and Mathematics.
Mathematics can be clearly defined as the knowledge to know how to solve something which is a form of declarative knowledge which is factual information stored in memory and known to be static in nature. There is no possible way to say that 2+2 is not equal to 4 which is completely unbiased because one cannot reason for the answer being 17 as that is clearly not true. The bias here comes along which deducing the BEST way to attain this value. One student may insist that the use of a calculator is the best way to find that the answer is 4 while another insists that mental math is the best while a third can be set on the idea that writing it down is the way to go. At the end of the day, the knowledge that the answer is 4 and not 17 is cold hard declarative knowledge that cannot really be reasoned to be susceptible to bias. As mathematics becomes more and more complex and many different theories and formulas come in to play, the opportunities for bias come along hand in hand. As in the 2+2 example, we have many different ways to attain the exact same value in these complex problems which allows for the bias...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...experiment.
Third, the way of knowing, reason, which is significantly important in the realm of natural sciences and mathematics, also demonstrate that active experiment and passive observation do produce knowledge. Consider the hypothetico-deductive method, the most widely used method in scientific researches, as an example. Generally, in this model, we form a conjecture based on our passive observations, and then deduce predictions from the hypothesis and conduct active experiments at last. Then, let us take this method into our real life. For instance, we may observe that if we put a full cup of liquid water into a freezer, when the water becomes frozen, the volume of ice may exceed the top of the cup. Afterwards, we may form a hypothesis that temperature influences the density of water. Then, we could deduce such prediction that lower temperature leads to changes on the density of water. Eventually, we could conduct an active experiment to test my prediction. This instance is not unique as the realm of natural sciences abounds with such examples that adopt hypothetico-deductive method. Notable examples include the discovery of the replica of DNA, the plant hybridization experiment by Mendel, the falling objects experiment conducted by Galileo, as well as the decipher method of generic codes. Similarly, one of the most fundamental proof methods in Mathematics, Mathematical Induction presents a similar idea as the hypothetico-deductive...

...MathematicsToK Essay
Prompt: What relationships, if any, exist between mathematics and various types of art (for example, music, painting, and dance)? How can concepts such as proportion, pattern, rhythm, harmony, and coherence apply both in the arts and in mathematics?
Too often math is taken for granted. Most people take math for granted; however, even they encounter math every day, whether it is conscious or unconscious because math can be found in the natural sciences and is encountered in the arts, where it is displayed through artwork, literature, and even building structures. Mathematics is intertwined with nature, and is way of representation, and a formula for beauty. Mathematics is the study of patterns, proportions, numbers, equations, and relationships. Although mathematics may often be a manipulative, tedious, and untruthful, it more frequently allows for society to function and flourish as we see in the sciences and arts.
Math permits magnificence found in both in the arts and the natural sciences. Back in 8th grade, when I was just learning how to draw humans in proportions, my art teacher taught me that the proportions that occur naturally throughout our beautiful bodies. Even “research into attractiveness suggests attraction boils down to how symmetrical one's face is”, showing how important symmetry is in beauty (Welsh). If you measure yourself, your...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....