SlideShare ist ein Scribd-Unternehmen logo
1 von 20
Downloaden Sie, um offline zu lesen
Essay about Usefulness of Mathematics Education
Usefulness of Mathematics Education
There has been much discussion over the years about the usefulness of mathematical studies.
Everyone seems to have a different viewpoint on the issue. Some believe that mathematics has little
use in the working world and so is not a subject that should be taught at higher levels in secondary
school. Others argue that mathematics does serve a profound purpose, albeit one that is subtle and
not obvious in the vocational world. G. H. Hardy and Underwood Dudley, two great mathematicians
of the twentieth century, have differing views, and our current Secretary of Education Richard Riley
has his thoughts as well. So who is right? Who has a stronger argument? Here we will take a closer
look at what is the...show more content...
Among those that did were the Army, rubber manufacturers, and the nursing profession. Ria and
Burghes' findings showed that these proficiency tests examined the most basic arithmetic skills;
even basic high school mathematics were neglected [5].
Underwood Dudley noted that fully seventy percent of engineers, those persons who are renowned
for actually having to implement mathematics in their daily work, do not need calculus to perform
their work. Dudley's obvious conclusion: if the majority of engineers do not need calculus, then how
many of the thousands of high school and college students who are required to take calculus will
actually use it someday? [1] The answer seems to be minutely few. However, many people use
computer programs daily that have been written using calculus and other mathematics in their binary
code, and numerous jobs require the implementation of mathematical formulas that have been
derived from calculus, such as a formula for the volume of a sphere. Does this mean that the person
using the computer program or the formula needs to know calculus? No. Nevertheless, we must
think once more of the thought process developed by mathematics. A student who has mastered the
techniques of calculus has enhanced their own logical reasoning abilities thus has gained something
from the mathematics.
Michael Wood discusses an aspect of mathematics that is often
Get more content on HelpWriting.net
Essay On Geometry
Is Geometry the Most Fundamental Area of Math?
As the very name implies, Geometry means measuring earth ('Geo' meaning earth and
'metron'meaning measurement). Hence, one can understand how old this branch of Math is and
what importance it should hold among the branches of Math.
What is Geometry?
Geometry is the branch of Math which deals with shapes, sizes, figures and their various properties,
relations and measurements. Doing Geometry with seriousness helps a Math student develop good
mathematical abilities and a precise power of perception.
Origin of Geometry (How old is Geometry?)
Geometry was given importance right from the age of Greeks and most of its concepts were found
in measuring lengths, volumes and areas in their early culture....show more content...
The concepts of Geometry have given rise to Trigonometry with its angles, side angles, right angled
triangles and non–right triangles. Algebraic Geometry is also popular today with its concepts like
coordinates.
You have the emergence ofCalculus from the aspects of Geometry. One can find the root of modern
integral Calculus in Archimedes' ingenuous techniques for calculating areas and volumes. You find
geometric figures like plane curves represented analytically in the form of functions and equations
leading to the emergence of infinitesimal Calculus. Today, you have Topology and differential
Geometry as well.
Overtones of Geometry in various areas of learning
Since Geometry is interlinked with Astronomy and is useful for calculating spatial distances, both
these subjects were learnt together in olden days. Not only that, Geometry has sprinkled its
influence upon various other areas like art, land survey, civil engineering and architecture. You can
find the overtones of Geometry in Science subjects like Physics also. Hence, Geometry has a vast
role to play in the contour of Math learning and makes for successful understanding of related topics
in Trigonometry and
Get more content on HelpWriting.net
Successfully Teaching Mathematics Essay
Successfully Teaching Mathematics
The classroom is a widely diverse environment with many topics to discuss, many discoveries to
make, and many different ways to learn. This wide palette of knowledge potential is a blessing and
a curse to teachers, challenging them to reach each mind, to convey to everyone an understanding of
the world that will improve their lives. The ever–increasing importance of mathematics in the
computer age draws attention to the methods with which we teach it. I think that the most successful
tool that I might have to teach mathematics is the mastery learning method, because it allows
students to move through the many facets of math with great understanding and confidence, allows
heavy use of the powerful...show more content...
I see mastery learning as a solution to this problem. Since the student is not required to move on to a
new idea until they have mastered the first, they have a greater confidence in themselves to
understand what is coming up. Also, by inherent operations of mastery learning, the system will zero
in on problem areas for each student and give them extra exercise in that field until they have a better
understanding, thus able to move on with more efficiency.
The concept behind mastery learning also highlights the use of computers in teaching. Not only do
computers allow students to move at their own pace, they can consistently reinforce correct answers
and good work. Also, creative combinations with the Internet can make up for absences by allowing
students to work at remote locations if necessary.
Finally, I have found it a frequent problem that students pass through a curriculum set without
ensuring the mastery of important basic skills. On the elementary level, poor basic arithmetic
abilities is a common problem. In higher–level mathematics, basic algebra is badly missed. Mastery
learning would guarantee that each student would have these important skills. "No student is to
proceed to new material until basic prerequisite material is mastered." (Bloom, 1987)
In summary, I think that I would most effectively be able to use the mastery learning method
because students would have better
Get more content on HelpWriting.net
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,
Get more content on HelpWriting.net
Observation In The Math Classroom
Observations for Jose took place on his science and math classrooms respectively. At the
beginning of the class, the teacher asked a question to the group, Jose raised his hand to answer.
He remained quiet on his desk while teacher explained the lesson in detail to the whole class.
During the rest of the class, he remained seated on his desk and participated in the discussion at
the proper time. The teacher showed a video to the class and asked some questions, most of the
class tried to answer them, but Jose didn't seem interested as he was with his head down on his
arms. Next Day during the math period, students were working in small groups. Jose actively
participated in the class discussion. He reviewed his paperwork with his peers and asked a few
questions to the teacher's assistant. Jose followed the teacher commands until the class finished.
During the interview process, Jose mentioned that his favorite subjects were reading and science,
conversely the subject that gives him most trouble is English because kids in the class laugh at him.
Jose thinks that learning is natural for him and he can complete assigned works but doesn't feel
being as smart as the other students. When with his friends, he likes to hang out, play games and
soccer. About his other classmates, he stated not getting along with them because they are always
pushing or tickling him. Jose reported having no problems with the teachers or at school in general.
On weekends, he usually enjoys of playing with
Get more content on HelpWriting.net
Reflection On My Math Class
Since starting this class, I feel as though my background knowledge of math would have been
enough for me to feel comfortable in the classroom but, because of the readings and in–class tasks
with my peers I've become more knowledgeable on many terms and practices of math.
It is clear that within the classroom of my peers we all complete a math problem differently. Some
students answer questions the completely different way than I do but, we get the same answers.
For example, when we were asked to add simple math numbers, two of the four of us thought the
same way. While to other people found different ways to get the answer. Amongst the four of us
there were three different ways to solve one simple addition question. This small task opened my
mind completely. I can see that was in my group of four people, there were three strategies to
answer one question. I can only imagine a number of ways a class of 30 students comes up with.
This will enhance my understanding as a teacher because I know that every student does not think
the same and there is more than one right way to solve a question. This class has also shown me
that using manipulatives is one of the best tools to enhance the students understanding. Using
manipulatives will not only help the students, but it will help me as a teacher to understand the
student's steps in solving questions. The best example in class was when my group was given
coloured bears and asked to show 1 as many ways as possible. We decided to
Get more content on HelpWriting.net
Reflection Essay For Math
My thoughts in regards to the course up to this point are indifferent. It is math, and math will
always be difficult for me, but in regards to the instruction process, I do feel like it could be
approached in a different way. I do not feel confident that there is enough focus on processes as
there are on practice problems. Every week I think there is going to be a great explanation of
something, and every week I'm disappointed. It's just "This week is slopes, here is why we use
slopes, now solve it." There isn't a lot of in depth instruction. Or, there is the "What is a real life
slope?" I don't need to know that. I need to know the steps that I will need in the future in order to
solve for slopes, one step at a time, in numerical order....show more content...
A lot of the courses at this institution operate the same way. Perhaps it's me. Perhaps I'm better
suited for a different learning style, but I've never had any problem with learning, nor my grades
until I started with this institution. I feel that there should be more interaction, content, helpful
hints, things to keep, such as diagrams, etc. I feel like I'm paying thousands of dollars to sit
around and Google all day, and at the end of Googling answers for a few years, I will get a fancy
piece of paper. I could sit at home and Google educational concepts for free. Of the five study
strategies from my week one discussion post that I have implemented, 2 and 3 have been the
most useful so far. They have kept me going, emotionally. I have done fairly well with not
becoming discouraged and giving up completely. I have done well with trying to give it some
effort. I am not letting my negative feelings towards math keep me from at least trying. For this, I
am proud of myself. The most interesting concept that has been covered so far in my opinion has
to be breaking down equations. I just like to break things down. It is an easy lesson, but is so
important. It has such significance. The most difficult so far is the current lesson. I honestly have no
idea what is going on with the physics thing. I like physics itself, but I think the example in the
lesson was poorly presented, thus making it difficult to understand. I am not getting a newly found
feel for how much
Get more content on HelpWriting.net
Reflection On Science And Math
Throughout my college experience, there were several things that showed a connection in how
science and math were used to demonstrate my ability to synthesize information on these subjects
and understand different methods of inquiry which were drawn from diverse ways of knowing
about the world and issues that we all face. From these experiences, I was able to use math and
science to communicate how it is implied to the real world and how it can benefit and solve some
of these problems through encouraging healthy lifestyles, equity, and social justice. I was also able
to show how I can turn scientific literature into a creative act of expression and discovery informed
by a scientific article that I translated into an art drawing which was then described in an essay. In a
previous essay that was written in my statistics class I was able to synthesize information on
statistics and understand how its methods were used to real world problems such as the Human
Genome project. The Human Genome Project started in 1990, this project is very beneficial to our
society because it has a positive influence on human health. The project objective is to decode the
DNA sequence and placement of the genes. Researchers collected blood from females and sperm
from males and a total of five people DNA were used for this study. The intentions of the Human
Genome Project were to deliver mapping and sequencing for the human genome and genomes of
model organisms, data gathering and
Get more content on HelpWriting.net
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
Get more content on HelpWriting.net
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
Get more content on HelpWriting.net
The Power Of Maths : The Beauty Of Mathematics
Mathematics is beautiful. It is the basis for any science courses, and math concepts have a deep
relationship with human life. Mathematics concepts have various applications, which brings a lot
of convenience to the whole society. The power of mathematics shows the greatness of God's
power, and reflects the greatness of God' creation. In mathematics field, there are lots of theorems
and axioms. All of them contributes a lot in solving mathematics problems. With these
mathematics theorems, we are able to see the patterns behind a case, and it enriches our
knowledge of thinking. Theorems and axioms are beautiful, because they group mathematics
problems with similar properties and allow us to have a shortcut in solving problems. However,
what are more beautiful than theorems and axioms are proofs that prove the validity of theorems
and axioms. Knowing the basic definitions of theorems and applying them mechanically in solving
questions are not considered learning or knowing math. Everyone can follow a step by step
procedure, but not everyone can come up with a step by step procedure. Therefore, knowing why a
theorem is correct and how a theorem is discovered are the key points of learning the beauty of
math. In my opinion, proofs are the most beautiful part in mathematics. In a proof, we are able to see
a strategy of how to get to the final result, and it guides us to think about the mathematics theorem
and question ourselves, and eventually prove a known statement. Proofs
Get more content on HelpWriting.net
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
Get more content on HelpWriting.net
Reflection On Math Lesson
What? For my second lesson, I taught a math lesson on multiplying decimals with zeros in the
product. I wanted students to be able to show that they could multiply with decimals in the
product and I wanted them to be able to explain how they know where to add the decimal point in
the answer. This lesson was part of the unit over decimals. Students will learn to add them,
subtract, multiply, divide, and then take a test for the unit. I decided to teach this lesson because
this is what my teacher had planned for the day and needed me to teach to keep her on track for
the test. Honestly, I was excited to teach a math lesson because it was a great refresher for me.
Overall, I was very satisfied with the way the lesson went. The students were understanding the
instruction I delivered and were giving the answers I had hoped for. The students were on task
and engaged for the entire lesson and when they weren't engaged, I could draw or mention sticks
and I would get more active participation. Before I asked students to work independently or with a
partner, I modeled exactly what they should be doing and how they should do it. This made a huge
difference from my first lesson because there was no confusion. When I had one students come up
to the board and share their answer, everyone in the class had the same answer. While I was
formatively checking their understanding, this told me that the way I was teaching was working
because they all understood the problem. I really can not think of anything that did not go as I
had planned or that I was not happy with. Although, there was one point where my math was
wrong because I was not thinking logically. I need to make sure I slow down while I am teaching
to check my own work so I am not teaching the students incorrect information! The only change I
would try and make if I taught this lesson again would be to find a way to make it more engaging
and less teaching instruction out of the book. I feel that with math this is sometimes challenging, but
I think it could be done. Even though I did use multiple means of representation by doing a whole
class discussion, partner work, and independent work, I could have found maybe a more "hands–on"
activity for the students to
Get more content on HelpWriting.net
Reflection Paper On Math And Science
1.In the autobiographical statement that I completed at the beginning of this semester, I wrote
about the mostly positive experiences that I have had throughout my schooling and the
importance of math and science. I was lucky enough to have some science and math teachers that
really seemed to care about our success, and made sure to make themselves accessible for help.
The experiences that I have had that were negative in school were typically in middle and high
school with teachers that simply lectured, and failed to guide us in any way. They did not create
an environment that was positive or interactive. Based on my positive experiences as a student, I
have been able to take some of their strategies with me in my own teaching such as being explicit
and creating interactive activities. Our SPED 458 class has really helped to solidify my passion for
math, and has given me a stronger interest in science. We have discussed various strategies to teach
math and science, and make it more accessible for all students through differentiation. Many
members of our class have introduced some interesting do now math problems that involved using
various approaches to solving one problem. There were also many simple science ideas that have
influenced me in a positive way, by making science teaching seem more possible and accessible for
all students through experiments like growing bacteria, acids and bases, and candy science. The
edible car activity and the gumdrop bridges, were great
Get more content on HelpWriting.net
Importance Of Learning Mathematics Essay
Mathematics is the one of the most important subjects in our daily life and in most human activities
the knowledge of mathematics is important. In the rapidly changing world and in the era of
technology, mathematics plays an essential role. To understand the mechanized world and match
with the newly developing information technology knowledge in mathematics is vital. Mathematics
is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the
world. The world cannot progress without mathematics. Mathematics fulfills most of the human
needs related to diverse aspects of everyday life. Mathematics has been accepted as significant
element of formal education from ancient period to the present day. Mathematics has a very
important role in the classroom not only because of the relevance of the syllabus material, but
because of the reasoning processes the student can develop.
The quality of teaching and learning in mathematics is a key challenge for teachers. It is important
for teachers to adopt instructional design techniques to achieve higher accomplishment in
mathematics (Rasmussen & Marrongelle, 2006). Instructional design alone cannot produce better
learning and achievement. The instructional designer must know critical factors that influence
student learning and build a bridge between goals and student performance. Identifying these factors
will help to utilize limited resources including financial resources and time more effectively
Get more content on HelpWriting.net
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
Get more content on HelpWriting.net
Narrative Essay About My Math Class
In my early years of school, I had never taken much of a liking to math. The teachers weren't very
likeable, the classes were rather boring, and the material could be very difficult, not only to learn
and comprehend, but to recall when it was time to take the big tests that were worth huge
amounts of my grade. Despite this, I did relatively well in my math classes. Of course, just
because I was doing well didn't mean I enjoyed the classes, and math quickly became my most
disliked subject. This view began to change in 8th grade. I was in the only algebra class the school
had to offer, along with around twenty other students. When I saw who the teacher was, I was very
surprised. He was the school's main physical education, or gym, teacher....show more content...
He had a way of explaining difficult concepts in a simplistic way, and I found myself
understanding with ease. This was something that had happened only sparingly before, and
certainly not with every concept. For example, he always liked to compare multiple ways of
solving problems to tools in a toolbelt. "Now you have different ways to solve the same problem,"
he would say. "You have all the tools in the toolbelt at your disposal. You have your 'motor oil', your
'ball bearings', and of course, your 'nine–inch gangly wrench.'"
He had a plethora of running jokes and parts of his anecdotes that would come up regularly in class.
Once, he told a story of wanting to take a cab to a well–known area of Akron (I cannot recall exactly
where). When he told the cab driver where he wanted to go, the driver replied, "Never heard of
it!", much to my teacher's shock. From that day forward, "Never heard of it!" became a phrase that
would come up in class on many occasions, drawing laughs every time.
After I had been in his class for a couple months, I began to notice something: I was enjoying it.
What had once been the worst part of my day was now the best. I couldn't believe it, but I was
actually looking forward to going to math class every day. The only reason why this was the case
was because of Mr. Swan. I realized he wasn't just a teacher enamoured by high scores on state tests,
and nothing else. He wasn't just a teacher who handed out worksheets in class, expecting the
Get more content on HelpWriting.net
Personal Statement For Teaching Mathematics
As a prospective mathematics teacher, I want to make thinking visible to my students. I want them to
be able to express their ideas and be able to elaborate on their answers. Two types of thinking I would
like to promote in my classroom are critical and creative thinking because mathematics is a subject
that involves both when it comes to problem solving. Critical and creative thinking promote higher
levels of student engagement and involves opportunities to investigate skills and concepts in a much
wider setting. I want to teach mathematics in a way that has meaning and relevance, rather than
through boring isolated topics. A classroom with a critical and creative thinking environment
provides opportunities for higher–level thinking within authentic and meaningful contexts, complex
problem solving, open–ended responses, and cooperation and interaction. Many students see math as
right or wrong and they don't question or explore more. As a future math teacher, I want students to
learn to question, be critical, and be creative. I want my future students to feel engage in exploration
and investigation. I want to equip my students with higher levels of thinking and engagement and
make mathematics more relevant and meaningful. According to the book "Making Thinking Visible"
students who are engaged in their work are motivated by four essential goals: success, curiosity,
originality, and relationships. Teaching mathematics through critical and creative thinking allows us
to
Get more content on HelpWriting.net
Essay on MAth
Course Project Milestone 2 Interview Guide and Questions Form This is a form to record your
information for this assignment. Review the Course Project Milestone 2: Interviewee Guide and
Questions guidelines and grading rubric in Doc Sharing (Assignments) prior to completing this
form. Review the document in Doc Sharing entitled, NR391 Question Tips. Refer to Appendix A in
your text and select five categories upon which you will concentrate for your interview guide and
questions. Type your answers to the following questions using complete sentences and correct
grammar, spelling, and syntax. Note that the form is expandable. Indeed, you may need more pages
to include the information that is requested in the guidelines for this...show more content...
The categories from which you may choose are listed below. Biocultural Variations and Cultural
Aspects of the Incidence of Disease Communication Cultural Affiliations Cultural Sanctions &
Restrictions Developmental Considerations Economics Educational Background Health–Related
beliefs and Practices Kinship and Social Networks Nutrition Religion and Spirituality Values
Orientation Type the names of the five categories you have chosen in the table below in the column
marked "Categories." 4. Develop one primary question for each of the five categories. Please note
that the questions should be in your own words and designed to elicit meaningful responses, for
example, open–ended or focused format. Use the table to type each question next to its
corresponding category. (60 points) 5. Develop two follow–up questions for each primary question.
Type these next to the corresponding primary questions. (40 points) 6. Indicate reasons for asking
specific questions that relate to culture of origin and healthcare experiences. (50 points) Categories
Primary Question Related to Category Follow–up Questions for each primary question Reasons for
asking questions that are related to culture of origin Category 1: Cultural Sanctions & Restrictions
Help me better understand your culture by explaining the different health care restrictions? 1. What
would
Get more content on HelpWriting.net
Importance Of Learning Mathematics Essay
1.0 Introduction
Mathematics is the one of the most important subjects in our daily life and in most human activities
the knowledge of mathematics is important. In the rapidly changing world and in the era of
technology, mathematics plays an essential role. To understand the mechanized world and match
with the newly developing information technology knowledge in mathematics is vital. Mathematics
is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the
world. The world cannot progress without mathematics. Mathematics fulfills most of the human
needs related to diverse aspects of everyday life. Mathematics has been accepted as significant
element of formal education from ancient period to the present day. Mathematics has a very
important role in the classroom not only because of the relevance of the syllabus material, but
because of the reasoning processes the student can develop.
The quality of teaching and learning in mathematics is a key challenge for teachers. It is important
for teachers to adopt instructional design techniques to achieve higher accomplishment in
mathematics (Rasmussen & Marrongelle, 2006). Instructional design alone cannot produce better
learning and achievement. The instructional designer must know critical factors that influence
student learning and build a bridge between goals and student performance. Identifying these factors
will help to utilize limited resources including financial resources and time more
Get more content on HelpWriting.net

Weitere ähnliche Inhalte

Ähnlich wie Essays On Math (6)

Ppt on maths (a.k.j)
Ppt on maths (a.k.j)Ppt on maths (a.k.j)
Ppt on maths (a.k.j)
 
Senior Project Research Paper
Senior Project Research PaperSenior Project Research Paper
Senior Project Research Paper
 
Module9
Module9Module9
Module9
 
Effect of technology use on teaching and learning of mathematics
Effect of technology use on teaching and learning of mathematicsEffect of technology use on teaching and learning of mathematics
Effect of technology use on teaching and learning of mathematics
 
Why do some students hate math.pptx
Why do some students hate math.pptxWhy do some students hate math.pptx
Why do some students hate math.pptx
 
Nctm st.louis10272011
Nctm st.louis10272011Nctm st.louis10272011
Nctm st.louis10272011
 

Mehr von Cheap Paper Writing Service

Essay On Travel
Essay On TravelEssay On Travel

Mehr von Cheap Paper Writing Service (20)

Totalitarianism Essay
Totalitarianism EssayTotalitarianism Essay
Totalitarianism Essay
 
Modernization Essay
Modernization EssayModernization Essay
Modernization Essay
 
Thesis Statement For Process Essay
Thesis Statement For Process EssayThesis Statement For Process Essay
Thesis Statement For Process Essay
 
Christopher Columbus Essays
Christopher Columbus EssaysChristopher Columbus Essays
Christopher Columbus Essays
 
Painting Description Essay
Painting Description EssayPainting Description Essay
Painting Description Essay
 
Uc Essay Examples
Uc Essay ExamplesUc Essay Examples
Uc Essay Examples
 
Essays On Indian Economy
Essays On Indian EconomyEssays On Indian Economy
Essays On Indian Economy
 
Essay Health
Essay HealthEssay Health
Essay Health
 
Hometown Essay
Hometown EssayHometown Essay
Hometown Essay
 
Essays On Brave New World
Essays On Brave New WorldEssays On Brave New World
Essays On Brave New World
 
Science Essays
Science EssaysScience Essays
Science Essays
 
What Is A Commentary In An Essay
What Is A Commentary In An EssayWhat Is A Commentary In An Essay
What Is A Commentary In An Essay
 
Sample Memoir Essay
Sample Memoir EssaySample Memoir Essay
Sample Memoir Essay
 
Essays On Autobiography
Essays On AutobiographyEssays On Autobiography
Essays On Autobiography
 
Example Analysis Essay
Example Analysis EssayExample Analysis Essay
Example Analysis Essay
 
Essay On Travel
Essay On TravelEssay On Travel
Essay On Travel
 
Dialectical Essay
Dialectical EssayDialectical Essay
Dialectical Essay
 
Stereotypes Essay
Stereotypes EssayStereotypes Essay
Stereotypes Essay
 
Wind Power Essay
Wind Power EssayWind Power Essay
Wind Power Essay
 
Cultural Imperialism Essay
Cultural Imperialism EssayCultural Imperialism Essay
Cultural Imperialism Essay
 

Kürzlich hochgeladen

The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
heathfieldcps1
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
ciinovamais
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi  6.pdf1029-Danh muc Sach Giao Khoa khoi  6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
QucHHunhnh
 

Kürzlich hochgeladen (20)

fourth grading exam for kindergarten in writing
fourth grading exam for kindergarten in writingfourth grading exam for kindergarten in writing
fourth grading exam for kindergarten in writing
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111Call Girls in Dwarka Mor Delhi Contact Us 9654467111
Call Girls in Dwarka Mor Delhi Contact Us 9654467111
 
Activity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdfActivity 01 - Artificial Culture (1).pdf
Activity 01 - Artificial Culture (1).pdf
 
microwave assisted reaction. General introduction
microwave assisted reaction. General introductionmicrowave assisted reaction. General introduction
microwave assisted reaction. General introduction
 
A Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy ReformA Critique of the Proposed National Education Policy Reform
A Critique of the Proposed National Education Policy Reform
 
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
Presentation by Andreas Schleicher Tackling the School Absenteeism Crisis 30 ...
 
Introduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The BasicsIntroduction to Nonprofit Accounting: The Basics
Introduction to Nonprofit Accounting: The Basics
 
Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1Código Creativo y Arte de Software | Unidad 1
Código Creativo y Arte de Software | Unidad 1
 
Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3Q4-W6-Restating Informational Text Grade 3
Q4-W6-Restating Informational Text Grade 3
 
social pharmacy d-pharm 1st year by Pragati K. Mahajan
social pharmacy d-pharm 1st year by Pragati K. Mahajansocial pharmacy d-pharm 1st year by Pragati K. Mahajan
social pharmacy d-pharm 1st year by Pragati K. Mahajan
 
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
BAG TECHNIQUE Bag technique-a tool making use of public health bag through wh...
 
Disha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdfDisha NEET Physics Guide for classes 11 and 12.pdf
Disha NEET Physics Guide for classes 11 and 12.pdf
 
The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13The Most Excellent Way | 1 Corinthians 13
The Most Excellent Way | 1 Corinthians 13
 
Grant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy ConsultingGrant Readiness 101 TechSoup and Remy Consulting
Grant Readiness 101 TechSoup and Remy Consulting
 
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"Mattingly "AI & Prompt Design: The Basics of Prompt Design"
Mattingly "AI & Prompt Design: The Basics of Prompt Design"
 
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
Mattingly "AI & Prompt Design: Structured Data, Assistants, & RAG"
 
1029-Danh muc Sach Giao Khoa khoi 6.pdf
1029-Danh muc Sach Giao Khoa khoi  6.pdf1029-Danh muc Sach Giao Khoa khoi  6.pdf
1029-Danh muc Sach Giao Khoa khoi 6.pdf
 
Key note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdfKey note speaker Neum_Admir Softic_ENG.pdf
Key note speaker Neum_Admir Softic_ENG.pdf
 
Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17Advanced Views - Calendar View in Odoo 17
Advanced Views - Calendar View in Odoo 17
 

Essays On Math

  • 1. Essay about Usefulness of Mathematics Education Usefulness of Mathematics Education There has been much discussion over the years about the usefulness of mathematical studies. Everyone seems to have a different viewpoint on the issue. Some believe that mathematics has little use in the working world and so is not a subject that should be taught at higher levels in secondary school. Others argue that mathematics does serve a profound purpose, albeit one that is subtle and not obvious in the vocational world. G. H. Hardy and Underwood Dudley, two great mathematicians of the twentieth century, have differing views, and our current Secretary of Education Richard Riley has his thoughts as well. So who is right? Who has a stronger argument? Here we will take a closer look at what is the...show more content... Among those that did were the Army, rubber manufacturers, and the nursing profession. Ria and Burghes' findings showed that these proficiency tests examined the most basic arithmetic skills; even basic high school mathematics were neglected [5]. Underwood Dudley noted that fully seventy percent of engineers, those persons who are renowned for actually having to implement mathematics in their daily work, do not need calculus to perform their work. Dudley's obvious conclusion: if the majority of engineers do not need calculus, then how many of the thousands of high school and college students who are required to take calculus will actually use it someday? [1] The answer seems to be minutely few. However, many people use computer programs daily that have been written using calculus and other mathematics in their binary code, and numerous jobs require the implementation of mathematical formulas that have been derived from calculus, such as a formula for the volume of a sphere. Does this mean that the person using the computer program or the formula needs to know calculus? No. Nevertheless, we must think once more of the thought process developed by mathematics. A student who has mastered the techniques of calculus has enhanced their own logical reasoning abilities thus has gained something from the mathematics. Michael Wood discusses an aspect of mathematics that is often Get more content on HelpWriting.net
  • 2. Essay On Geometry Is Geometry the Most Fundamental Area of Math? As the very name implies, Geometry means measuring earth ('Geo' meaning earth and 'metron'meaning measurement). Hence, one can understand how old this branch of Math is and what importance it should hold among the branches of Math. What is Geometry? Geometry is the branch of Math which deals with shapes, sizes, figures and their various properties, relations and measurements. Doing Geometry with seriousness helps a Math student develop good mathematical abilities and a precise power of perception. Origin of Geometry (How old is Geometry?) Geometry was given importance right from the age of Greeks and most of its concepts were found in measuring lengths, volumes and areas in their early culture....show more content... The concepts of Geometry have given rise to Trigonometry with its angles, side angles, right angled triangles and non–right triangles. Algebraic Geometry is also popular today with its concepts like coordinates. You have the emergence ofCalculus from the aspects of Geometry. One can find the root of modern integral Calculus in Archimedes' ingenuous techniques for calculating areas and volumes. You find geometric figures like plane curves represented analytically in the form of functions and equations leading to the emergence of infinitesimal Calculus. Today, you have Topology and differential Geometry as well. Overtones of Geometry in various areas of learning Since Geometry is interlinked with Astronomy and is useful for calculating spatial distances, both these subjects were learnt together in olden days. Not only that, Geometry has sprinkled its influence upon various other areas like art, land survey, civil engineering and architecture. You can find the overtones of Geometry in Science subjects like Physics also. Hence, Geometry has a vast role to play in the contour of Math learning and makes for successful understanding of related topics in Trigonometry and Get more content on HelpWriting.net
  • 3. Successfully Teaching Mathematics Essay Successfully Teaching Mathematics The classroom is a widely diverse environment with many topics to discuss, many discoveries to make, and many different ways to learn. This wide palette of knowledge potential is a blessing and a curse to teachers, challenging them to reach each mind, to convey to everyone an understanding of the world that will improve their lives. The ever–increasing importance of mathematics in the computer age draws attention to the methods with which we teach it. I think that the most successful tool that I might have to teach mathematics is the mastery learning method, because it allows students to move through the many facets of math with great understanding and confidence, allows heavy use of the powerful...show more content... I see mastery learning as a solution to this problem. Since the student is not required to move on to a new idea until they have mastered the first, they have a greater confidence in themselves to understand what is coming up. Also, by inherent operations of mastery learning, the system will zero in on problem areas for each student and give them extra exercise in that field until they have a better understanding, thus able to move on with more efficiency. The concept behind mastery learning also highlights the use of computers in teaching. Not only do computers allow students to move at their own pace, they can consistently reinforce correct answers and good work. Also, creative combinations with the Internet can make up for absences by allowing students to work at remote locations if necessary. Finally, I have found it a frequent problem that students pass through a curriculum set without ensuring the mastery of important basic skills. On the elementary level, poor basic arithmetic abilities is a common problem. In higher–level mathematics, basic algebra is badly missed. Mastery learning would guarantee that each student would have these important skills. "No student is to proceed to new material until basic prerequisite material is mastered." (Bloom, 1987) In summary, I think that I would most effectively be able to use the mastery learning method because students would have better Get more content on HelpWriting.net
  • 4. 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, Get more content on HelpWriting.net
  • 5. Observation In The Math Classroom Observations for Jose took place on his science and math classrooms respectively. At the beginning of the class, the teacher asked a question to the group, Jose raised his hand to answer. He remained quiet on his desk while teacher explained the lesson in detail to the whole class. During the rest of the class, he remained seated on his desk and participated in the discussion at the proper time. The teacher showed a video to the class and asked some questions, most of the class tried to answer them, but Jose didn't seem interested as he was with his head down on his arms. Next Day during the math period, students were working in small groups. Jose actively participated in the class discussion. He reviewed his paperwork with his peers and asked a few questions to the teacher's assistant. Jose followed the teacher commands until the class finished. During the interview process, Jose mentioned that his favorite subjects were reading and science, conversely the subject that gives him most trouble is English because kids in the class laugh at him. Jose thinks that learning is natural for him and he can complete assigned works but doesn't feel being as smart as the other students. When with his friends, he likes to hang out, play games and soccer. About his other classmates, he stated not getting along with them because they are always pushing or tickling him. Jose reported having no problems with the teachers or at school in general. On weekends, he usually enjoys of playing with Get more content on HelpWriting.net
  • 6. Reflection On My Math Class Since starting this class, I feel as though my background knowledge of math would have been enough for me to feel comfortable in the classroom but, because of the readings and in–class tasks with my peers I've become more knowledgeable on many terms and practices of math. It is clear that within the classroom of my peers we all complete a math problem differently. Some students answer questions the completely different way than I do but, we get the same answers. For example, when we were asked to add simple math numbers, two of the four of us thought the same way. While to other people found different ways to get the answer. Amongst the four of us there were three different ways to solve one simple addition question. This small task opened my mind completely. I can see that was in my group of four people, there were three strategies to answer one question. I can only imagine a number of ways a class of 30 students comes up with. This will enhance my understanding as a teacher because I know that every student does not think the same and there is more than one right way to solve a question. This class has also shown me that using manipulatives is one of the best tools to enhance the students understanding. Using manipulatives will not only help the students, but it will help me as a teacher to understand the student's steps in solving questions. The best example in class was when my group was given coloured bears and asked to show 1 as many ways as possible. We decided to Get more content on HelpWriting.net
  • 7. Reflection Essay For Math My thoughts in regards to the course up to this point are indifferent. It is math, and math will always be difficult for me, but in regards to the instruction process, I do feel like it could be approached in a different way. I do not feel confident that there is enough focus on processes as there are on practice problems. Every week I think there is going to be a great explanation of something, and every week I'm disappointed. It's just "This week is slopes, here is why we use slopes, now solve it." There isn't a lot of in depth instruction. Or, there is the "What is a real life slope?" I don't need to know that. I need to know the steps that I will need in the future in order to solve for slopes, one step at a time, in numerical order....show more content... A lot of the courses at this institution operate the same way. Perhaps it's me. Perhaps I'm better suited for a different learning style, but I've never had any problem with learning, nor my grades until I started with this institution. I feel that there should be more interaction, content, helpful hints, things to keep, such as diagrams, etc. I feel like I'm paying thousands of dollars to sit around and Google all day, and at the end of Googling answers for a few years, I will get a fancy piece of paper. I could sit at home and Google educational concepts for free. Of the five study strategies from my week one discussion post that I have implemented, 2 and 3 have been the most useful so far. They have kept me going, emotionally. I have done fairly well with not becoming discouraged and giving up completely. I have done well with trying to give it some effort. I am not letting my negative feelings towards math keep me from at least trying. For this, I am proud of myself. The most interesting concept that has been covered so far in my opinion has to be breaking down equations. I just like to break things down. It is an easy lesson, but is so important. It has such significance. The most difficult so far is the current lesson. I honestly have no idea what is going on with the physics thing. I like physics itself, but I think the example in the lesson was poorly presented, thus making it difficult to understand. I am not getting a newly found feel for how much Get more content on HelpWriting.net
  • 8. Reflection On Science And Math Throughout my college experience, there were several things that showed a connection in how science and math were used to demonstrate my ability to synthesize information on these subjects and understand different methods of inquiry which were drawn from diverse ways of knowing about the world and issues that we all face. From these experiences, I was able to use math and science to communicate how it is implied to the real world and how it can benefit and solve some of these problems through encouraging healthy lifestyles, equity, and social justice. I was also able to show how I can turn scientific literature into a creative act of expression and discovery informed by a scientific article that I translated into an art drawing which was then described in an essay. In a previous essay that was written in my statistics class I was able to synthesize information on statistics and understand how its methods were used to real world problems such as the Human Genome project. The Human Genome Project started in 1990, this project is very beneficial to our society because it has a positive influence on human health. The project objective is to decode the DNA sequence and placement of the genes. Researchers collected blood from females and sperm from males and a total of five people DNA were used for this study. The intentions of the Human Genome Project were to deliver mapping and sequencing for the human genome and genomes of model organisms, data gathering and Get more content on HelpWriting.net
  • 9. 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 Get more content on HelpWriting.net
  • 10. 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 Get more content on HelpWriting.net
  • 11. The Power Of Maths : The Beauty Of Mathematics Mathematics is beautiful. It is the basis for any science courses, and math concepts have a deep relationship with human life. Mathematics concepts have various applications, which brings a lot of convenience to the whole society. The power of mathematics shows the greatness of God's power, and reflects the greatness of God' creation. In mathematics field, there are lots of theorems and axioms. All of them contributes a lot in solving mathematics problems. With these mathematics theorems, we are able to see the patterns behind a case, and it enriches our knowledge of thinking. Theorems and axioms are beautiful, because they group mathematics problems with similar properties and allow us to have a shortcut in solving problems. However, what are more beautiful than theorems and axioms are proofs that prove the validity of theorems and axioms. Knowing the basic definitions of theorems and applying them mechanically in solving questions are not considered learning or knowing math. Everyone can follow a step by step procedure, but not everyone can come up with a step by step procedure. Therefore, knowing why a theorem is correct and how a theorem is discovered are the key points of learning the beauty of math. In my opinion, proofs are the most beautiful part in mathematics. In a proof, we are able to see a strategy of how to get to the final result, and it guides us to think about the mathematics theorem and question ourselves, and eventually prove a known statement. Proofs Get more content on HelpWriting.net
  • 12. 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 Get more content on HelpWriting.net
  • 13. Reflection On Math Lesson What? For my second lesson, I taught a math lesson on multiplying decimals with zeros in the product. I wanted students to be able to show that they could multiply with decimals in the product and I wanted them to be able to explain how they know where to add the decimal point in the answer. This lesson was part of the unit over decimals. Students will learn to add them, subtract, multiply, divide, and then take a test for the unit. I decided to teach this lesson because this is what my teacher had planned for the day and needed me to teach to keep her on track for the test. Honestly, I was excited to teach a math lesson because it was a great refresher for me. Overall, I was very satisfied with the way the lesson went. The students were understanding the instruction I delivered and were giving the answers I had hoped for. The students were on task and engaged for the entire lesson and when they weren't engaged, I could draw or mention sticks and I would get more active participation. Before I asked students to work independently or with a partner, I modeled exactly what they should be doing and how they should do it. This made a huge difference from my first lesson because there was no confusion. When I had one students come up to the board and share their answer, everyone in the class had the same answer. While I was formatively checking their understanding, this told me that the way I was teaching was working because they all understood the problem. I really can not think of anything that did not go as I had planned or that I was not happy with. Although, there was one point where my math was wrong because I was not thinking logically. I need to make sure I slow down while I am teaching to check my own work so I am not teaching the students incorrect information! The only change I would try and make if I taught this lesson again would be to find a way to make it more engaging and less teaching instruction out of the book. I feel that with math this is sometimes challenging, but I think it could be done. Even though I did use multiple means of representation by doing a whole class discussion, partner work, and independent work, I could have found maybe a more "hands–on" activity for the students to Get more content on HelpWriting.net
  • 14. Reflection Paper On Math And Science 1.In the autobiographical statement that I completed at the beginning of this semester, I wrote about the mostly positive experiences that I have had throughout my schooling and the importance of math and science. I was lucky enough to have some science and math teachers that really seemed to care about our success, and made sure to make themselves accessible for help. The experiences that I have had that were negative in school were typically in middle and high school with teachers that simply lectured, and failed to guide us in any way. They did not create an environment that was positive or interactive. Based on my positive experiences as a student, I have been able to take some of their strategies with me in my own teaching such as being explicit and creating interactive activities. Our SPED 458 class has really helped to solidify my passion for math, and has given me a stronger interest in science. We have discussed various strategies to teach math and science, and make it more accessible for all students through differentiation. Many members of our class have introduced some interesting do now math problems that involved using various approaches to solving one problem. There were also many simple science ideas that have influenced me in a positive way, by making science teaching seem more possible and accessible for all students through experiments like growing bacteria, acids and bases, and candy science. The edible car activity and the gumdrop bridges, were great Get more content on HelpWriting.net
  • 15. Importance Of Learning Mathematics Essay Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop. The quality of teaching and learning in mathematics is a key challenge for teachers. It is important for teachers to adopt instructional design techniques to achieve higher accomplishment in mathematics (Rasmussen & Marrongelle, 2006). Instructional design alone cannot produce better learning and achievement. The instructional designer must know critical factors that influence student learning and build a bridge between goals and student performance. Identifying these factors will help to utilize limited resources including financial resources and time more effectively Get more content on HelpWriting.net
  • 16. 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 Get more content on HelpWriting.net
  • 17. Narrative Essay About My Math Class In my early years of school, I had never taken much of a liking to math. The teachers weren't very likeable, the classes were rather boring, and the material could be very difficult, not only to learn and comprehend, but to recall when it was time to take the big tests that were worth huge amounts of my grade. Despite this, I did relatively well in my math classes. Of course, just because I was doing well didn't mean I enjoyed the classes, and math quickly became my most disliked subject. This view began to change in 8th grade. I was in the only algebra class the school had to offer, along with around twenty other students. When I saw who the teacher was, I was very surprised. He was the school's main physical education, or gym, teacher....show more content... He had a way of explaining difficult concepts in a simplistic way, and I found myself understanding with ease. This was something that had happened only sparingly before, and certainly not with every concept. For example, he always liked to compare multiple ways of solving problems to tools in a toolbelt. "Now you have different ways to solve the same problem," he would say. "You have all the tools in the toolbelt at your disposal. You have your 'motor oil', your 'ball bearings', and of course, your 'nine–inch gangly wrench.'" He had a plethora of running jokes and parts of his anecdotes that would come up regularly in class. Once, he told a story of wanting to take a cab to a well–known area of Akron (I cannot recall exactly where). When he told the cab driver where he wanted to go, the driver replied, "Never heard of it!", much to my teacher's shock. From that day forward, "Never heard of it!" became a phrase that would come up in class on many occasions, drawing laughs every time. After I had been in his class for a couple months, I began to notice something: I was enjoying it. What had once been the worst part of my day was now the best. I couldn't believe it, but I was actually looking forward to going to math class every day. The only reason why this was the case was because of Mr. Swan. I realized he wasn't just a teacher enamoured by high scores on state tests, and nothing else. He wasn't just a teacher who handed out worksheets in class, expecting the Get more content on HelpWriting.net
  • 18. Personal Statement For Teaching Mathematics As a prospective mathematics teacher, I want to make thinking visible to my students. I want them to be able to express their ideas and be able to elaborate on their answers. Two types of thinking I would like to promote in my classroom are critical and creative thinking because mathematics is a subject that involves both when it comes to problem solving. Critical and creative thinking promote higher levels of student engagement and involves opportunities to investigate skills and concepts in a much wider setting. I want to teach mathematics in a way that has meaning and relevance, rather than through boring isolated topics. A classroom with a critical and creative thinking environment provides opportunities for higher–level thinking within authentic and meaningful contexts, complex problem solving, open–ended responses, and cooperation and interaction. Many students see math as right or wrong and they don't question or explore more. As a future math teacher, I want students to learn to question, be critical, and be creative. I want my future students to feel engage in exploration and investigation. I want to equip my students with higher levels of thinking and engagement and make mathematics more relevant and meaningful. According to the book "Making Thinking Visible" students who are engaged in their work are motivated by four essential goals: success, curiosity, originality, and relationships. Teaching mathematics through critical and creative thinking allows us to Get more content on HelpWriting.net
  • 19. Essay on MAth Course Project Milestone 2 Interview Guide and Questions Form This is a form to record your information for this assignment. Review the Course Project Milestone 2: Interviewee Guide and Questions guidelines and grading rubric in Doc Sharing (Assignments) prior to completing this form. Review the document in Doc Sharing entitled, NR391 Question Tips. Refer to Appendix A in your text and select five categories upon which you will concentrate for your interview guide and questions. Type your answers to the following questions using complete sentences and correct grammar, spelling, and syntax. Note that the form is expandable. Indeed, you may need more pages to include the information that is requested in the guidelines for this...show more content... The categories from which you may choose are listed below. Biocultural Variations and Cultural Aspects of the Incidence of Disease Communication Cultural Affiliations Cultural Sanctions & Restrictions Developmental Considerations Economics Educational Background Health–Related beliefs and Practices Kinship and Social Networks Nutrition Religion and Spirituality Values Orientation Type the names of the five categories you have chosen in the table below in the column marked "Categories." 4. Develop one primary question for each of the five categories. Please note that the questions should be in your own words and designed to elicit meaningful responses, for example, open–ended or focused format. Use the table to type each question next to its corresponding category. (60 points) 5. Develop two follow–up questions for each primary question. Type these next to the corresponding primary questions. (40 points) 6. Indicate reasons for asking specific questions that relate to culture of origin and healthcare experiences. (50 points) Categories Primary Question Related to Category Follow–up Questions for each primary question Reasons for asking questions that are related to culture of origin Category 1: Cultural Sanctions & Restrictions Help me better understand your culture by explaining the different health care restrictions? 1. What would Get more content on HelpWriting.net
  • 20. Importance Of Learning Mathematics Essay 1.0 Introduction Mathematics is the one of the most important subjects in our daily life and in most human activities the knowledge of mathematics is important. In the rapidly changing world and in the era of technology, mathematics plays an essential role. To understand the mechanized world and match with the newly developing information technology knowledge in mathematics is vital. Mathematics is the mother of all sciences. Without the knowledge of mathematics, nothing is possible in the world. The world cannot progress without mathematics. Mathematics fulfills most of the human needs related to diverse aspects of everyday life. Mathematics has been accepted as significant element of formal education from ancient period to the present day. Mathematics has a very important role in the classroom not only because of the relevance of the syllabus material, but because of the reasoning processes the student can develop. The quality of teaching and learning in mathematics is a key challenge for teachers. It is important for teachers to adopt instructional design techniques to achieve higher accomplishment in mathematics (Rasmussen & Marrongelle, 2006). Instructional design alone cannot produce better learning and achievement. The instructional designer must know critical factors that influence student learning and build a bridge between goals and student performance. Identifying these factors will help to utilize limited resources including financial resources and time more Get more content on HelpWriting.net