The document explores the interplay between mathematics and art, emphasizing the importance of both critical and creative thinking in acquiring knowledge. It discusses the role of a teacher in fostering a positive learning environment in mathematics, highlighting the significance of understanding diverse learning styles and using varied teaching methods. Additionally, it touches upon philosophical contributions to mathematics and the practical applications of mathematics in everyday life.

1. Essay on Mathematics and Art
Mathematics and art are two areas of knowledge that demonstrate different degrees of interaction
between critical and creative thinking. Whether considering mathematics or art, creative thinking
evaluates a new or original idea containing some degree of value. Critical thinking examines
assumptions and challenges a current belief or theory that has previously assumed to be true.
Although general assumptions and creativity may be considered separately when considering
extreme examples of concrete ideas and abstract ideas, the interplay of critical and creative thinking
is one method in which new and validated knowledge is attained.
Mathematics is an area of knowledge that may seemingly appear to be concrete, utilizing reason as its
...show more content...
Reasoning is required to understand all mathematical problems, but knowledge must have supporting
and accepted facts and use reason to justify its formulas or methods. For example, memorizing the
area under a bell curve is very different from understanding how it is derived and what it means.
Mathematics, however, may also be an area of knowledge in which creative thinking is an integral
component. Euclid used the idea of creative thinking in mathematical assumptions in 330 B.C when
he introduced the first systematic discussion of geometry. Euclid proved his theories from a finite
number of postulates, an idea that had previously never been achieved. These concepts remained
unchallenged until the early 19th century when others began using creative thinking to challenge his
theories and describe physical space in a plane. Creative problem solving involving mathematics can
use sense perception as a way of knowing. In these problems, real life situations require that the
student actually understand the concepts rather than memorizing facts from concrete problems.
Sense perception is the active, selective and interpretative process of becoming conscious of the
external world. For example, when trees in a forest are harvested, mathematics can be used to
determine the number of replacement trees by considering the ultimate size of the tree, the preferred
space each tree needs for optimal growth, the percentage of trees that do not grow or die, and the
length
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2. Essay on Teaching Mathematics
Teaching Mathematics
My interest in teaching mathematics came from the experience of helping others. I have always
enjoyed learning math, and I realized that I also like helping other people learn math, especially
those that struggle with it or those who have a disliking for it. As a teacher, I will be able to fulfill
my aspirations; both my students and I will learn together and from one another. I feel that it is
important for me, as a teacher, to stay current and deepen my understanding of mathematics and
mathematics education. My learning will continue from my experiences and interactions as a
teacher, helping me to become a better educator. I must always be willing to learn from the things I
do and use this to better my...show more content...
Also, it is important when teaching to satisfy the needs of all students in the classroom. Everyone
should have the opportunity to learn. However, this can sometimes be a difficult task because
learning happens in a variety of ways. Not all students learn in the same manner; different learning
styles are a given in a class full of diverse students. Every student is an individual, and so they do
not all learn and retain information exactly the same way. Therefore, in order for my students to
succeed in my class, my teaching style will include many different aspects because I believe it is
helpful for students to learn with the aid of such methods as cooperative learning, technology,
manipulatives, and a variety of assessment techniques. Using these different methods will help all
different learning styles from visual to auditory to kinesthetic. Also, these are all very important
because, although lecturing can be effective sometimes, using multiple teaching methods gives
students the opportunity to experience concepts for themselves and keeps them aware of what they
are responsible for knowing and understanding. By learning in this way, students will not only find
class more interesting, but they will have a better perception of the information they are expected to
know.
Finally, most students see school and teachers as an unwanted obligation. They attend school
because they are required to,
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3. Understanding Mathematics Essays
Understanding Mathematics
This paper is an attempt to explain the structure of the process of understanding mathematical objects
such as notions, definitions, theorems, or mathematical theories. Understanding is an indirect
process of cognition which consists in grasping the sense of what is to be understood, showing itself
in the ability to apply what is understood in other circumstances and situations. Thus understanding
should be treated functionally: as acquiring sense. We can distinguish three basic planes on which
the process of understanding mathematics takes place. The first is the plane of understanding the
meaning of notions and terms existing in mathematical considerations. A mathematician must have
the knowledge of what the...show more content...
The only statement characterizing this notion is the remark that understanding is connected with
effort.
The problem of understanding mathematics requires, in my opinion, a short presentation of a more
general issue, that is the issue of understanding as such. I will treat understanding as a kind of
indirect cognition, determined by the perception of the relations between the objects of various
order (y becomes comprehensible for x as a part of the relation xRy, in which y is anobject of a
different order intentionally grasped by x). As it can be seen, I neglect here the problem of
understanding another human being, although it is usually achieved through understanding the
phenomenally accessible human behaviours, i.e. linguistic or extralinguistic creations.
It seems that the Polish philosopher Izydora Dąmbska grasped the problem of understanding
accurately and concisely, stating that this kind of cognition is characterized by the following factors:
1) it refers to the objects connected with the spiritual reality–signs, psychic and psychophysical
creations, logical structures sensu largo etc.
2) it consists in grasping relations which determine the sense of what is to be understood.
3) it enables the reconstruction and the application, in other conditions, of what we understand.
The essence of this kind of cognition, which we call understanding, decides about the hypothetical
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4. Philosophy in Mathematics Essay
Philosophy in Mathematics
Mathematics has contributed to the alteration of technology over many years. The most noticeable
mathematical technology is the evolution of the abacus to the many variations of the calculator.
Some people argue that the changes in technology have been for the better while others argue they
have been for the worse. While this paper does not address specifically technology, this paper rather
addresses influential persons in philosophy to the field of mathematics. In order to understand the
impact of mathematics, this paper will delve into the three philosophers of the past who have
contributed to this academic. In this paper, I will cover the views of three philosophers of
mathematics encompassing their...show more content...
At this time it was customary for men of his stature to choose from church or army, which he would
serve. Choosing the latter position, Descartes joined the army in 1617.
In an event of chance, Descartes stumbled upon Isaac Beeckman, head of the Dutch College at Dort,
who would translate a sign off the streets. This sign was in actuality a challenge to anyone to solve a
geometrical problem (Wilkins, D.). Within a few hours, with help from Descartes' respect and
appreciation of mathematics, he found a solution and a friendship was formed between Beeckman
and Descartes. This unexpected turn of events fueled Descartes' contempt of his life in the army;
but due to family influence and tradition, he remained a soldier until 1621 (Wilkins, D.). Descartes
was 25 years old.
The next couple of years found him relocated all around Europe until he settles in Paris in 1626. In
the five years from when he left the army until his alighting in Paris, Descartes had devoted his life
to the study of pure mathematics. There, in Paris, Descartes would live for two years until Cardinal
de Berulle, founder of the Oratorians, urged on Descartes the duty of "devoting his life to the
examination of truth." (Wilkins, D.). Now 1628, Descartes moved again, this time to Holland, to
secure himself from interruption. He would spend the next twenty years in Holland, focusing on
philosophy and mathematics.
His time in Holland
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5. Mathematics in Everyday Life Essay
Mathematics is possibly one of the most underappreciated sciences. It everywhere in our lives,
mathematics runs our computers, flies our aircraft, and protects our information. But for such a
major part of our lives, very few people can say that they know how it is done, how the RSA
encryption protects their e–mail, or even that 21 squared is 441 without going into tedious mental
calculations or reaching for their calculator. Contrary to popular belief, mathematics has a wide
range of useful applications. Those who would ask whenever they would need algebra, both linear
algebra and calculus is used extensively in computer programming and engineering. The fact is that
mathematics is integrated into almost every profession, and every...show more content...
There are some issues with this system. For example, imagine that both Person A and Person B
want to include a third person in their correspondences, Person C. First they would need to give
Person C a key, through some sort of secure system, preferably a face–to–face meeting. But what if
Person C lives in Alaska and both Person A and Person B don't have the time, money, or desire to
travel to Alaska to give Person C the key, nor does Person C want to travel to Person A or B. This
is a key weakness of the symmetric key system. In an asymmetric key system, Person A sends
many open locks to Person B, these locks can be put on messages and only Person A has the key
to them. Person B does the same thing, now if they wish to include Person C all Person C need to
do is send open locks to Person A and Person B. In real life, there are usually two keys, one for
encryption and one for decryption, and these keys are in fact, usually numbers which determine
how the message is encoded. Now we are going to work off a common example, your credit
company. Most public key cryptography will have your encryption key public, anyone can view it,
and use it, but only you can decrypt it. So if someone wanted to send you a message, they would
take your key, encrypt your message, and leave it in your mailbox, you would then use your
decryption key, to decipher the message. The main problem with public key cryptography is that no
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6. Teaching Mathematics Essay example
When teaching mathematics to children the teacher's enthusiasm can determine whether or not the
child's math experience is negative or positive. For instance if you do not like math chances are, it
will show up in the activities that you prepare for the child, as well as the way you go about a
question because the children will sense your frustration that you have for math. If a teacher likes
math on the other hand the activities will be well thought out, and the children will be able to ask
questions without having the feeling that the teacher is frustrated because they are giving off a
positive attitude. This is what shapes the person's feelings towards math, how good of a math teacher
one is, and how whether or not the person's...show more content...
This usually resulted in me forgetting how to do the math problem, and getting the answer wrong
when I clearly knew the answer, and how to do the problem. In college I had good math
professors who liked what they were doing, and were excited to teach us the material that was
being taught. They also made time for us to help us during their office hours. On the other hand, I
felt like because of my previous experience with math, and teachers not spending time with me I
had a negative outlook for math which made me think it was worse then it was. As a teacher of
mathematics for young children I can see myself as someone who will have a positive impact on
them. The reason for this is that I have had a bad experience in math with teachers who were not
passionate, nor excited in what they were teaching. Therefore, I don't want the children I am
teaching to feel the same way I do. I mean even though I don't like doing math I can still teach it in a
positive way, and be an effective teacher by helping the children when needed without giving them a
negative attitude. I also would not move onto a different topic until everyone has understood the
previous topic. I believe that doing this would give children a positive attitude towards math and
show them that I am willing to help them and teach them the math until they understand it. Areas of
math that I feel would be challenging when
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