Isaac Newton Contributions

Isaac Newton Contributions
Sir Isaac Newton was an English mathematician and physicist, considered one of the greatest
scientists in history. He made important contributions to many fields of science. His discoveries and
theories laid the foundation for much of the progress in science. Newton was one of the inventors of
a mathematics called calculus. He also solved the mysteries of light and optics, formulated the three
laws of motion, and derived from them the law of universal gravitation. Newton was born on
December 25, 1642, at Woolsthorpe, near Grantham in Lincolnshire. When he was three years old,
he was put in care of his Grandmother. He then was sent to grammar school in Grantham. Then later
he attended Trinity College at the University of Cambridge. Newton ignored much of the
established curriculum of the university to pursue his own interests; mathematics and natural
philosophy. Proceeding entirely on his own, he investigated the latest developments in mathematics
and the new natural philosophy that treated nature as a complicated machine. Almost immediately,
still under the age of 25, he made fundamental discoveries that were instrumental in his career
science. The Fluxional Method, Newton's first achievement was in mathematics. He generalized the
methods that were being used to draw tangents to curves and to calculate the area swept by curves.
He recognized that the two procedures were inverse operations. By joining them in what he called
the fluxional method,
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Marjorie Lee Browne
In my advance math decision–making (AMDM) class we were encouraged to look up a famous
black mathematics for black history month, so we could see that there were black mathematician in
the field of work. Therefore, I choose Marjorie lee Browne known for her gifted skills in math and
for her electronic digital computer center at North Carolina College.
Marjorie Lee Browne was born in Nashville, Tennessee to Mary Taylor Lee and Lawrence Johnson
Lee on September 9, 1914, but sadly, her mother died 2 years later. Soon her father was remarried to
Mrs. Lottie Lee, a schoolteacher, Marjorie was encouraged to keep up her grades but she still had
time to enjoy sports like tennis. Therefore, during these racial times Browne attended a private high
school that helped black children. When she graduated, she had enough money to go to Howard
University in Washington, D.C., which she graduated from in 1935. ... Show more content on
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and became a professor on campus. When she got her Ph.D. she became the third female African
American to earn a Ph.D. in her field (after Evelyn Boyd Granville and Euphemia Lofton Haynes,
who earned their degrees in 1949 and 1943) .When becoming the chair of the mathematics
department at North Carolina College she build up the computer department and later on received a
$60,000 grant from IBM to orchestrate an electronic digital computer center, 0ne of the first to be in
a minority college. While she leadership North Carolina College was given the title of prized
National Science Foundation Institute for secondary education in the area of mathematics. Browne
continued working which made her travel, then she later on attend Cambridge University thanks to
the Ford Foundation grant. There she studied topology, and modern version of geometry, which
became her

Maths Tutoring Math Research Paper
I write my personal philosophy from the perspective of a maths tutor, as I am yet to engage as a
maths teacher. Ideally, I would love to impart on my students the same love of mathematics as I
have. However, the world is rarely an ideal place.
My ethos in tutoring maths is to remove any fear the student may have in regard to mathematics and
then encourage the student to develop confidence in his or her own mathematical abilities. This
initial object without question is often extremely challenging. However, watching as a student grows
in confidence is one of the most rewarding aspects of being a maths tutor. Furthermore, the
development of mathematical confidence is catalyst for both better understanding and achievements
in the subject.
My focus with senior mathematics is giving the students strong foundations on which they can
build, in everyday life or further studies. Undoubtedly, relaxed and confident students are more
receptive to the, often challenging, content of senior mathematics. Students are strongly encouraged
to be curious and ask as many questions as they need to gain understanding. In addition, they need
to develop a good work ethics and positive approach to their studies. ... Show more content on
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In the current Queensland syllabus, mathematics is a fundamental part of students' general education
and a subject, which is an essential part of developing sound knowledge. Mathematics is recognised
as a subject, which supports many facets of general education and daily life in an increasingly
mathematical society. All of these aspects need to be reflected in "future–oriented" teaching and
learning, in addition to the inclusion of technology in the

Preschool Mathematics Curriculum Paper
Introduction Experimental Evaluation of the Effects of a Research –based Preschool Mathematics
Curriculum (2005) is a research article written by two Distinguished SUNY researchers. Dr.
Douglas Clements and Dr. Julie Sarama focused their study on measuring the effectiveness of a
preschool mathematics programs based on a comprehensive model of developing research –based
curriculum in larger context with teachers and students of diverse background. In this study,
teachers implemented intervention curricula, Building Blocks, and the comparison mathematic
curriculum in preschools in New York State as experimental treatment and its effect on classrooms'
mathematics environment, skills of developing foundation of informal mathematics knowledge, ...
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Further research with larger numbers of teachers should be done to indicate significant relations
between numbers of teachers and scores. This study offers research based evidence on the
effectiveness of a curriculum built on comprehensive research–based principles as well as supports
previous studies showing that organized experiences result in greater mathematics knowledge and
help young children develop foundations. In addition, the researchers suggest that both Building
Blocks and comparison curricula can increase knowledge of mathematical concepts and skills. The
greatest benefit of this study is the conclusion that preschool math curricula can lead to

Race To Calculus In College
Since a public school district's success is determined by state and national assessment, officials in
school systems across the country have sought to make changes to effectively address the academic
deficits of students. A push in education over the past couple decades has been the race to Calculus
and the belief that this path is necessary for a student to succeed in advanced math courses in
college. Although there has been a dramatic increase in the number of students in high school
Calculus, enrollment in Calculus 2 at college has remained relatively unchanged for the last two
decades (Bressoud, 2004; 2009). Many students who have taken Calculus in high school are arriving
unprepared for Calculus in college (Bressoud, 2007).
Middle

Independence and the Development of the American Identity...
During the 1800s, we find the theme of independence, or freedom from outside constraints, in the
development of two different frontiers. We find it in the American West through Manifest Destiny,
freedom from caste, and in the chance that homesteaders had to acquire virtually free land. We find
independence in math through in the building of stronger theoretical foundations, non–Euclidean
geometries, and Cantor's infinities.
Independence involves breaking from the commonly accepted, traditional views in order to explore
the new. It is not necessarily individual people working alone. We can see independence in a
community of thought as well as in the work of a single person.
Independence is an important part of the Western culture as ... Show more content on
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In the 1880s, Hulda Rocell and her daughter Mary emigrated from Sweden to the United States. Abe
Lincoln had just been shot. Mr. Rocell had to stay in Sweden because of his tuberculosis.
Nevertheless, Mr. Rocell said, "Go to the United States. It is strong enough that Lincoln's
assassination will not plummet the nation into chaos." Although he did not place this optimism
under the title of Manifest Destiny, the idea that the United States is strong, and will continue
despite opposition, is a part of this concept.
Hulda married, and her family settled in a sod house in northern Minnesota. Her husband showed
independence and determination for the family to survive by planting fruit trees on the farm. It was
highly unusual to attempt to plant fruit trees that far north.
The family's independent spirit, and courage was a vital part of surviving in the harsh conditions
they encountered. In 1881, there was a terrible blizzard. The snow was so high that it covered the
fence posts. Father tied a rope around his waist and the porch post to tend the animals in a nearby
shed, so that he would not get lost in the blizzard. However, many neighbors froze to death right
outside their own front doors. During the storm, the wind blew the door of the sod house open. The
younger children got in the trundle bed to keep warm, while the parents and older children shoveled
snow out of the house for the rest of the day, so that they could shut the

A Brief Look at George Friedrich Bernhard Riemann
George Friedrich Bernhard Riemann, born in Breselenz, Germany, was a prominent and influential
mathematician during the nineteenth century. At a young age, Riemann was recognized by his
teachers for his swift grasping of complicated mathematical operations. Riemann attended the
University of Gottingen where he developed a strong foundation in theoretical physics from Johann
Listing and other notable professors. Riemann introduced concepts of mathematical importance
such as the complex variable theory, analytic number theory, and differential geometry.
Revolutionizing the field of geometry, Riemann set foundations for theoretical physics, modern
topology, and the general theory of relativity. Riemann spent his adolescent years in a village near
Danneberg, in midst of the Kingdom of Hanover. His father , Friedrich Riemann, was a poor
Lutheran pastor while his mother, Charlotte Ebell, died before Bernhard reached adulthood. While
exhibiting exceptional mathematical skill at a young age, Riemann suffered from nervous
breakdowns and a fear of speaking in public. He attended high school at Johanneum Luneburg,
where he developed a reputation for exceeding his professor's mathematical knowledge. In 1846,
Riemann attended the University of Gottingen, where he initially studied philosophy and theology.
However, Riemann later began studying mathematics and transferred to the University of Berlin,
after receiving a recommendation from Carl Friedrich Gauss. Riemann attended lectures

Writing And Mathematics, Two Vital Mesopotamian Creations
Writing and Mathematics, Two vital Mesopotamian creations
What kind of world would we live in without being able to write or perform mathematic functions?
Writing and mathematics are two of the most indispensable creations crafted by the Mesopotamians
that helped shaped our society as we know it today. The Mesopotamian conception of writing
allowed society to keep records, to document events, and to establish a formal educational system.
With the ability to keep records, a system of mathematics was recorded which assisted in
development of monetary systems, a way to tell time, the ability to build buildings, and the skills to
survey lands. The expansion of knowledge delivered by the creation of Mesopotamian writing and
mathematics was crucial to building the cultural society that has evolved from Meopotamian times
to the present. Cultural and social evolution relys on the understanding of the past and learning from
our successes and our failures. Therfore, record keeping was crucial to the nurturing the evolution of
society. With the importance of record keeping being recognized, the Mesopotamians developed
Cuneiform, the first recognized form of writing.. Initially, Cuneiform, meaning "wedge shaped",
existed as pictographs drawn in clay tablets by a stylus made of a reed. The tablet was baked in the
sun making it practically indestructible. (World History book 7th edition) There were disadvantages
to clay: large documents were heavy and once baked no changes

What Is Wrong With Descartes ' Causal Proof Of God
What is Wrong with Descartes' Causal Proof of God
René Descartes was born on 31 March 1596 in La Haye, France; a city which was later renamed as
"Descartes" in his honor. his early life was not well documented until 1960, but it is known that he
was familiar with mathematics and philosophy (Hatfield). Sometimes described as "The Father of
Modern Philosophy", not only considered a great philosopher, but also a great mathematician,
contributed greatly for both areas – Cartesian geometry, for instance, was named in his honor
(Norman 19). In his Meditations, Descartes uses a causal argumentation to prove the existence of a
perfect being, who he considers to be God; these conclusions are controversial, since problems can
be found in the arguments used (Hartfield). Based on the arguments used to draw his conclusions,
this essay is going to discuss some apparent flaws in Descartes's causal proof of God.
In "Meditations," Descartes discusses the false beliefs he held during his life, and in order to
eliminate them, attempts to deconstruct all of his knowledge and reinvent it with a solid foundation
made only with what is absolutely true. For this, he would deconstruct everything he perceived as
true, starting from his senses ("A Posteriori", or, according to Baehr, something that needs proper
justification through experience), to mathematics ("A Priori", or, according to Baehr, something that
can be known without experiencing) and finally reaching the fundamental truth. Also

Teacher Reflection Paper
Introduction Mathematics is an important part of everyday life and as teachers in the early years, we
are responsible for teaching children the fundamentals of mathematics and helping develop
children's passion for learning mathematical concepts. Knaus (2013) states that "An effective
teacher of mathematics will ask questions to provoke children's thinking and introduce the language
of mathematics to help children see the connections between the world and mathematical concepts
(pg.3). As I progress through my degree and complete each Math unit, I have begun to recognise
mathematical understanding and concepts, I need to develop if I am going to become an excellent
teacher of mathematics. Standard 1.2 of the Australian Association of Mathematics Teachers
[AMMT] (2006) confirms that 'excellent teachers of mathematics understand how mathematics is
represented and communicated, and why mathematics is taught (p.1). The first section of this essay
will reflect on my mathematical understandings followed by a section reflecting of my knowledge
and ability to help children confidently demonstrate and develop mathematical skills and processes.
Lastly a conclusion of how this will benefit me to become an excellent teacher. Mathematical
Understandings After taking the First Five Years Mathematics Competency Test, I could identify
mathematical areas and concepts that I need to develop to enable me to become a better teacher of
mathematics. Once I completed the Competency

Why Is Math Important To Mary W. Shelley's Frankenstein?
In Frankenstein, Mary W. Shelley showed Victor stray from his interest in natural philosophy to that
of mathematics as a result of the unstructured background of his previous study. Victor soon became
aware that his studies were based solely on theories and tossed out the study of philosophy while
stating, "I betook myself to the mathematics, and the branches of study appertaining to that science,
as being built upon secure foundations, and so worthy of my consideration" (Shelley 33). To me, not
only does mathematics provide many societal benefits, but the firm foundation of the subject has
caused me to become obsessed with the study.
My greatest pride has always been my in depth knowledge of mathematics. I first began my
enjoyment for math ... Show more content on Helpwriting.net ...
Constantly, I find people calling me a psychopath due to the constant blabbering of mathematical
terms. I find enjoyment in creating relationships of math to everyday life. When going up a ski lift
in Colorado, I subconsciously created a connection to one of my calculus terms. I felt the desire to
explain the connection between our incline and the first derivative to my father. A look of
displeasure was followed by my explanation. Sadly, I have become accustomed to these responses.
Mathematics can be related to almost anything in the world. Although I have completed all the
available math classes at my school, I still have a thirst for more math–related

NAEYC Affirm Analysis
The NAEYC affirm that high–quality, challenging and accessible mathematics education for 3–6
year old children are a vital foundation for future mathematics learning. The first few years of a
child's life in development is important because teachers are individuals who play the key role to
help children learn, grow and succeed in education. NAEYC and NCTM feel that young learner's
future understanding of mathematic requires an early foundation on a high quality, challenging, and
accessible mathematic education. They feel children's learning within the first couple of years of life
demonstrate the importance of early experiences in mathematics also children start to engage in
early encounters of mathematics developing their confidence in their ... Show more content on
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Children shouldn't suffer from math anxiety or lack confidence in math because they should build
on the child's strength and learning styles to make learning math easier. Some people may feel that
requiring young children to do overly advance work at a young age has a harmful effect on them,
but I feel it prepares them for the next grade level. Achievements in mathematics and other areas
from state to state. The article stated, "Children who live in poverty and who member of linguistic
and ethnic minority demonstrate significantly lower levels of achievement." I don't agree with this
statement because it's downgrading children from low–income families. I don't feel some low–
income children begin school with much less mathematical knowledge than wealthier peers. I feel
children learn among themselves. Children simply make a choice about what they want to do and it
involves on them deciding on their actions and interactions. NAEYC and NCTM feel if children
have a head start in math that children will a long lasting effect of understanding math. Technology
is an important tool that helps improve math because its influences math and enhances students'
learning. In the article it says, "Lack of appropriate preparation may case both preservice and
experienced teachers to fail to see mathematics as a priority." In order for teachers to teach
mathematic to children proficiently, teachers need to see themselves proficient in math. Teachers
should have a basic knowledge of the subject, but if some schools fear the lack of preparation of
math then they should consider a successful program that only early math instructors specialize in
that specific area. For example, the school may designate a teacher to be responsible for teaching
only math to all

Early Childhood Numeracy
Introduction (50 words ) This week learning has focused on how children built their mathematical
understanding in five learning contexts and the importance of numeracy in early childhood. The
learning this week also focused on discussion about setting play experiences which aim to foster and
develop young children's numeracy and place value concepts in mathematics. In relation to teaching
children mathematics what did you learn this week? (100 words) I have learnt that children learn
mathematic by not only playing, manipulating resources or doing things but also by observating,
investigating, communicating, listening, interacting with others, reasoning and thinking what they
have done. Children are involving in mathematic in everyday

Pedagogical Strategies for the Teaching of Mathematics in...
PEDAGOGICAL STRATEGIES FOR THE TEACHING OF MATHEMATICS IN NIGERIAN
PRIMARY SCHOOLS FOR SCIENTIFIC AND TECHNOLOGICAL DEVELOPMENT
BY
AJILEYE, Adewole Mukaila Department of Mathematics
Osun State College of Education, Ilesa
E–mail: ajileye4ever@yahoo.com
Abstract
For a country to be technologically developed there is need for efficient handling of mathematics at
levels of education. The perennial low performance of pupils in mathematics has been attributed
among other things to inadequate knowledge of subject matter content by teachers and poor
instructional techniques. This paper highlighted the basic principles for effective teaching and
learning of mathematics in primary school which is a fundamental stage of child education. ... Show
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The teacher may acquire mastery of the contents but lack skills in the appropriate methods. This
may affect the students understanding of the subjects. There are many approaches to teaching of
mathematics. These include: * Problem solving * Discovery Approach * Expository * Laboratory *
Questioning skills * Individualization group work * Demonstration, etc. (Johnson & Rising,
1972)
All these methods are good but no teaching method could be regarded as superior to the other. In
application, combination of these methods will be desirable. It all depends on the content, objectives
and the nature of the learners.
BASIC PRINCIPLES OF EFFECTIVE TEACHING OF MATHEMATICS 1. Basic stages of
teaching and learning
Fakuade (1981) identifed three significant stages of learning topics in mathematics. These are: *
Concrete materials and demonstration of real life situation stage * Semi–concrete or pictorial studies
stage * Abstraction stage Pupils in the primary schools have the age ranges between 5 and 12. This
is the age period that coincides approximately with the Piaget's concrete operational stage. This is a
transitional stage between the pre–operational period (a period when the child cannot yet perform
any serious operation, a period of intuition when the child's reasoning is not yet quite logical) and
the formal operational stage (a period when the child thought process

Nursery Rhyme Analysis
The book, There were 10 in the bed and other counting nursery rhymes (Press, 2015) offers young
children in the foundation years of schooling an enjoyable way to practice counting using rhyme
and patterns as a tool for remembering the number sequences allowing them to learn how numbers
are used (Siemon, 2011) and was chosen because of its ascetic presentation along with the simple
flow of the rhyming words which make it a pleasant easy to follow book for a young audience to
learn from. The mathematical concept of counting is very clear in this book with all the nursery
rhymes being based on counting with all of them focused on counting. This book, There were 10 in
the bed and other counting nursery rhymes (Press, 2015) can be linked in with ... Show more
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To start the lesson an introduction into counting to ten would be needed and would start with asking
the children if they know how to count to ten and to get them to count with you to ten in order to
demonstrate this ability. Once this has been satisfactorily accomplished the book (press,2015) would
then be introduced to the children and then read aloud to the whole class to enable the children to
hear the rhyme as a whole and to get a feel for how the rhyme flows rhythmically along with the
wording used. The rhyme would be read a few times depending on the students, how they are
feeling about the rhyme and if a few more repetitions are needed for the children to gain a good
understanding of the wording and flow of the rhyme. Once all students are capable of reciting the
rhyme along with the teacher and the book you can then move on to more activities such as creating
a drama play from the text depicting the ten children in the bed with them rolling over and having
one child fall out while reciting the rhyme as they go along following up by asking the children to
explain why they think a child kept falling out during the rhyme and did they think ten children was
too many fit in the bed to start with. This gives the children a chance to gain deeper understanding
of the counting used as they

buisness
Business management, my current major falls under the A.A.S category for degrees. In the
following paragraphs I will explain the differences between the different types of degrees available
at Hudson County Community College. The differences between an A.A, A.S, A.A.S, and A.F.A are
as follows. The Associate in Arts degree (A.A) is given to those who finish programs which
emphasize more on the liberal arts, humanities, fine or performing arts. Somewhat similar to an A.A
is the Associate in Fine Arts (A.F.A); being that students who attain this degree usually transfer to a
Bachelor of Arts or Bachelor of Fine Arts programs at four year schools. The difference is that this
is for students who successfully complete programs that emphasize ... Show more content on
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This type of a degree also leans more to transferring to a higher level of education. The Associate in
Applied Science (A.A.S) degree is granted to students who effectively complete programs which
emphasize preparation in the applied arts and sciences. The difference between this type of degree
and the others is, an A.A.S usually leads to immediate employment. Business management, my
current major falls under the A.A.S category for degrees. In the following paragraphs I will explain
the differences between the different types of degrees available at Hudson County Community
College. The differences between an A.A, A.S, A.A.S, and A.F.A are as follows. The Associate in
Arts degree (A.A) is given to those who finish programs which emphasize more on the liberal arts,
humanities, fine or performing arts. Somewhat similar to an A.A is the Associate in Fine Arts
(A.F.A); being that students who attain this degree usually transfer to a Bachelor of Arts or Bachelor
of Fine Arts programs at four year schools. The difference is that this is for students who
successfully complete programs that emphasize the foundation of studio art study like visual design
principles, art history, art theory and contemporary art. An Associate in Science (A.S) is given to
students who complete programs that focus more

David Hilbert: A Biography
David Hilbert was a German mathematician whose research and study of geometry, physics, and
algebra revolutionized mathematics and went on to introduce the mathematic and scientific
community with a series of mathematical equations that have yet to be solved. Furthermore, his
study of mathematics laid the groundwork for a variety of ongoing mathematic analyses, which
continue to influence the world today. David Hilbert was born in Konigsberg, Prussia on January 23,
1862 and went on to pursue a career in mathematics in his mother country before receiving a
doctorate in 1885 for his study and thesis of invariant theory (David Hilbert, n.d.). Hilbert went on
to begin a professional academic career at Konigsberg, where he taught until 1895 when he was
"appointed to the chair of mathematics at the University of Gottingen, a post that he would hold for
the remainder of his life. Hilbert's contributions to mathematics can be divided into five major areas:
invariant theory, which he studied until his transfer to Gottingen; algebraic number field theory,
which he studied from approximately 1984–1899; foundations of geometry and mathematics,
studied from 1899–1903; integral equations, studied from about 1904 to 1909; physics, studied from
about 1912–1914; and foundations of mathematics, studied after 1918 (Kimberling, n.d.). Hilbert's
proofs of Gordan's problem, which dealt with invariant theory, catapulted Hilbert into the spotlight
as a first–class mathematician (Hilbert,

Music And Neuron Analysis
Music and Neuron Networks
The formation of specific nerve cells, named neurons, allows the brain to learn and store
information, communicate, and grow; this ability is called neuroplasticity Urban Child Institute, n.d.
& Harvard University, n.d.). Neuroplasticity is impacted by music due to the all–encompassing
nature that music possesses (Collins, 2014 & Kent, 2006 & Urban Child Institute, n.d.). Due to this,
music can be considered a form of exercise for the brain; as the music passes through the brain, it
causes the neuron networks to communicate through synapses (electrical pulses), the more synapses
that occur in the brain, the stronger the corresponding neuron network is strengthened (Kent, 2006
& Urban Child Institute, n.d.). Neuroplasticity ... Show more content on Helpwriting.net ...
Scientists found that only musicians who had been trained from a young age – in general, 10 and
below – experienced abundant neurological benefits (Kent, 2006 & Wan & Schlaug, 2010). This is
because it is only in childhood that music can create a strong foundation within the brain; due to
neuroplasticity being extremely efficient in childhood, it is the only time when music can have the
most concentrated impact on the brain, resulting in a strong foundation that cannot be formed in any
other point in life (Collins, 2014 & Kent, 2006 & Urban Child Institute, n.d. & Alban n.d. &
Harvard University, n.d.). Therefore, if music, with its all–encompassing abilities, was implemented
before the elimination period, then that would create a strong foundation for future neuron networks
to be built upon (Harvard University, n.d & Urban Child Institute, n.d. & Kent,

Should Mathematics Be Taught In Schools
ABSTRACT
It is generally accepted that learning implies a multitude of factors meant to prepare the children for
life and its challenges. Some of these factors are directly related to the level of knowledge of subject
matter, but others are based on individual feelings, relationships, or capabilities of developing a
sense of belonging and personal worth, confidence, or attitude toward a certain content area. All
these elements together form the foundation of student's future success. On many occasions, certain
factors such as the teaching approaches, encouragement from family members and school personnel,
or past experiences in learning mathematics are important in creating a positive view of
mathematics. From basic arithmetic to the more advanced calculus courses in first years of college,
students build ... Show more content on Helpwriting.net ...
This is a natural process, and it continues throughout our entire life. Unfortunately, for centuries the
traditional education system has discouraged a process of student–teacher interaction. In traditional
classrooms students were not encouraged to ask questions, but instead were supposed to listen and
respond with expected answers. The result was that historically, mathematical aptitude was difficult
to be discovered or addressed in the classrooms, and many students had fewer opportunities to
analyze their attitude or confidence with respect to mathematics. Conversely, it is widely accepted,
as mentioned in the literature (Edwards, Harper, Cox et al., 2014; Nebesniak, Burgoa, 2015) that in
mathematics at least, asking students to memorize facts is not the best approach to education, and
given technological advancements much of this information can be easily accessed. This supports
the idea that students should be engaged not in memorizing information but in inquiry, for asking
questions, while problem solving allows them to learn what to do with the information they can

Marjorie Lee Browne
Marjorie Lee Browne was born on September 9, 1914 in Memphis, Tennessee. She was the daughter
of Mary Taylor Lee and Lawrence Johnson Lee. Marjorie childhood was very rough, her mother
passed when she was two . Right after Marjorie mother passed her father was soonly remarried to
his new wife Lottie Lee so Lottie helped raise Marjorie. Her father was a railway postal clerk, and
stepmother Lottie lee, a school teacher. Growing up Marjorie up into segregation so she went to a
private high school called LeMoyne high school. Even through these times Marjorie parents pushed
her to better and to not worry about going to a all black school. After high school she attended
University of Michigan in 1949 making her the third African– American to earn ... Show more
Outside of her career and achievements she was never married nor have she had kids. Marjorie Lee
Browne died of a heart attack on October 19, 1979 at her home in Durham, North Carolina , at the
age of 65. The Marjorie Lee Browne trusts fund was established by four of her students at the North
Carolina Central University. The Marjorie Lee Browne Distinguished Alumni lecture series are
funded by this trusts. Till this day Dr. Marjorie Lee Browne colloquium is held every year as part of
Dr. Martin Luther King Jr. Symposium in the Department of mathematics, University of Michigan.
Marjorie had a thesis and it was titled On the Parameter Subgroups in certain Topological and
matrix groups, which was written under supervision of G Y Rainich. She was the only person in the
Mathematics Department to have a PhD for 25 years. She taught for 15 hours a week and she also
had 10 masters degrees. She was also the overseer of its installation. She also obtained for the
Department of Mathematics for the first Shell Grant awards to her students. She had a book
published that was called A Note on the classical Groups. It was published in the American
mathematics monthly in 1955. The reason she did it was to set forth the relations between certain
classical

Rene Descartes Argument For The Existence Of God
By basing his conclusions on knowledge that has been reasoned to be true through a method
reminiscent of a geometrical proof, Descartes effectively prevents himself from attributing truth to
something that is false. However, the structure of such an argument is built on the assumption that
Descartes's starting point is something undeniably true and, assuming as such, the next truth will
organically stem from it. Descartes uses this type of reasoning in his proof of God's existence and
his reasoning that the soul is inherently separate from the body, both found in Meditations on First
Philosophy. Rene Descartes's argument is multi–layered, formed in such a way that each subsequent
layer depends on that one preceding it, but by being structured ... Show more content on
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Descartes not only uses the methods of mathematical proofs but also uses mathematical concepts
themselves, like geometric shapes, to serve as an example of something both clear and distinct.
However, when translating the method some adjustments must be made to ensure the structure of
his argument. Descartes, in explaining the qualities of a triangle, notes, "I did not see anything in all
[these qualities] to assure me that there was any triangle in the world" (Discourse, 20). However,
there is a fundamental difference between God and triangles. Descartes highlights the differences
with the idea of "infinite perfection" (Discourse, 24). Descartes's argument for the existence of God
is more deeply throughout in Meditations on First Philosophy. He follows the same method, through
starting what is easily known and using that as the foundation for his argument. Descartes starts
with himself declaring himself "[a] thing that thinks" and reinforces that this idea is "obvious" and
"could not be explained more clearly," similar to the concepts of math he touches on earlier in his
work (Meditations,

Comparison of Two Mathematics Curricula
Comparison of Two Mathematics Curricula Math teachers have become increasingly disenchanted
with the traditional materials they are forced to teach due to the existing California standards. The
goal of the teachers is not that they need to change the standards, but there needs to be a better
curriculum to adequately bring students up to those standards. Current curricula follow the letter of
the standards that California has implemented, but they sometimes seem to be based on nothing
substantial which would give credibility to the course of study. If a curriculum is developed to meet
a set of standards, that is exactly what it will do. However, the goal should be to not only meet but
to exceed the stated standards; or, at the very least, give students the ability to go beyond the
standard. In this argument, the California standards are the lowest rung of the ladder that the state
should encourage students to climb. Yes, the student will have a basic understanding of
mathematical concepts if they meet the standard, but they will not have any impetus to reach beyond
that and achieve something more. In this research paper, two different curricula possibilities are
examined for their relative merits; one which is meant to just meet the recommended California
mathematics standard as set forth by the Common Core State Standards Initiative (2005), and one
which is recommended by a practical body, the National Science Foundation (NSF), to encourage
students to achieve a higher,

Career Field Research
Career Field Research: Early Elementary Education and Mathematics A sit–down interview, in the
interviewee's classroom, on April 22, 2017, results in responses from Rachel, a female Elementary
Education teacher at Deerfield Elementary School, in Deerfield, Wisconsin. Containing eight initial
questions and two response follow–up inquiries, this interview represents a 4–year Kindergarten
grade level perspective, and utilizes eleven years of teaching experience. As a University of
Wisconsin–Madison graduate, Rachel began her career in Milwaukee before accepting her current
position of nine years. With extensive knowledge of the field, Rachel qualifies as an excellent
resource, both when actively pursuing plans to become an Elementary Education ... Show more
"Career Field Research: Early Elementary Education and Mathematics." Personal interview. 22 Apr.
2017. Appendix A Career Field Research: Elementary Education and Mathematics; Sample
Interview Questions Name: 1. What are the specifics of any education needed and recommended to
become a teacher? 2. How long have you been teaching? 3. What advice would you give to
somebody considering entering the field? 4. What are some ways you personally use math in your
everyday life (for work or home)? 5. How do you incorporate math into your teaching? 6. Do you
believe critical thinking skills are an important foundation for developing future math skills? Why
or why not? 7. If yes, what are some examples of ways you teach these skills at a 4–year old level?
8. How do you feel about your own math skills? a. Do you wish they were stronger, and if so, why?
b. If you could go back would you do anything different while obtaining your degree to strengthen
these

Math And Numeracy Research Paper
Mathematics and Numeracy go hand in hand. However just because you are good with maths does
not imply your numeracy is good too, as "numeracy is the capacity, confidence and disposition to
use mathematics to meet the demands of learning, school, home, work, community and civic life"
(ACARA, 2009, p.5).
Mathematics is the foundation on which everything is built, however it is not about knowing only
timetables, formulating, calculating, and being able to provide one right answer to every question,
unfortunately this was how maths was taught and enforced with rote and repetition. Rote and
repetition did not promote interconnectedness nor did it promote numerate individuals, therefore
many could see no relevance to maths in their day to ... Show more content on Helpwriting.net ...
Maths learning today is designed for interaction, providing active and open discussion, it makes
connections to nature and to the world around us. Via this type of learning, problem solvers evolve,
those who can use mathematics in a variety of ways to determine the best course of action and
outcome. Thus providing the foundation for strong numeracy skills to develop while enhancing
curiosity, reasoning and creating numerate individuals who know "when to use mathematics,
choosing the mathematics to use and critically evaluating its use" (NSW Department of Education
and Communities, 2011). "Children and young people need to develop their numeracy skills through
learning to read, write and discuss aspects of numeracy within a range of different real–life
contexts" (Teach in
Scotland, 2016). By developing numeracy skills and using them reflectively in life, mathematics
enriches every students life, and gives rise for mathematicians to develop, that may have previously
been lost in the

A Female African-American Philosopher, Janice E. Cook
A female African–American mathematician who contributed to mathematics was Janice E. Cook.
Her birth and death date is unknown, however, she was born in New Orleans. She is one of seven
children of Florence L. Cook and Henry Cook. Growing up, she admired her mother, who was an
elementary teacher, describing her as an inspirational and heroic person in her life. After Janice
completed her studies for the bachelor and masters degree she began a professional career in the
corporate arena, however, she wasn't satisfied. She later realized her true passion was in teaching
mathematics as a teacher at the middle and high school levels. Once she determined her true
educational passion in life, she continued her studies and gained her pre–doctoral

Marjorie Lee Browne Biography
A Mathematical Genius: Marjorie Lee Browne Marjorie Lee Browne was a extrusive mathematician
right from her childhood. Dr. Lee Browne was mostly inspired by both her parents. Though most of
her math genius was acquired from her father, who himself was popular in his area as a "math
wizard" and passed on his love for the subject to his daughter. Thus, in 1949, she became the third
African–American women who graduated with a Ph.D in her field becoming a pioneer for African
American women in mathematics.
In Dr. Lee Browne's early life, born in Memphis, Tennessee, her father Lawrence Johnson Lee often
encourage Dr. Lee Browne to take mathematics seriously, for she usually liking the subject and
working very well with numbers. Despite the racial ... Show more content on Helpwriting.net ...
For instance, in the early 1950s, she was awarded a Ford Foundation grant and help her attend
Cambridge University, where she studied topology (a modern version of geometry) and matrix
groups which became her specialty. Thus, her paper, "A Note on the Classical Groups," was
published in The American Mathematical Monthly, June–July 1955, 424–427. This paper later set
forth some topological properties of and relations between certain classical groups. For example,
Browne wrote in the paper that "while much of the material included here may be known to a few,
the main interest of this paper lies in the simplicity of the proofs of some important, though
obscured, results." In addition, other grants also allowed her to attend University of California at
Los Angeles and Columbia University. In 1975, Browne received an award, where she was
recognized with the first W.W. Rankin Memorial Award for Excellence in Mathematics Education,
which lauded her for "helping to pave the way for integrated organizations" , an honor handed out
by the North Carolina Council of Teachers of Mathematics. Thus, overall Browne served as a
member of numerous organizations: Women's Research Society, the American Mathematical
Society and the Mathematical Association of America. She also served as one of the first African–
American women as a member of the advisory council to the National Science Foundation.
Works Cited
Marjorie Lee Browne. Web. 30 June 2017.
"Marjorie Lee Browne." Biography.com. A&E Networks Television, 02 Apr. 2014. Web. 30 June
2017.
"Marjorie Lee Browne." Browne Biography. Web. 30 June 2017.
"Who Is Marjorie Lee Browne? Everything You Need to Know." Childhood, Life Achievements &
Timeline. Web. 30 June

The Importance Of The Early Years Learning Framework
The Early Years Learning Framework is an essential tool for educators, it allows us to understand
that there are many foundations for early childhood development, and are essential for children's
success in learning. The foundations for these competencies are built in early childhood. (EYLF
page 38) As Hill & Rowe (1998) state in 'Teaching Mathematics: Foundation to Middle Years' there
has been research and it has discovered that the teaching is one of the main contributors to how
effectively our children learn. So the way we teach has a significant difference on how effective
education actually is. As teachers, we have an extremely influential role in the way children learn.
Ensuring we are providing them with appropriate learning experiences. As Siemon states in
'Teaching Mathematics: Foundation to Middle Years' that there are strong connections between
teaching and mathematics learning, and in the end ensuring we have effective mathematics teaching.
To understand what it means to be an effective mathematics teacher, you need to have confidence in
your own understandings, having conceptual connections among various mathematical topics.
Ensuring educators are creating and providing meaningful learning opportunities for children. As
educators, we need to understand that setting the scene is also a key role in developmentally
appropriate experiences, As the EARLY YEARS LEARNING FRAMEWORK states on page 14,
that there is an importance on "physical and social learning

Gödel's Incompleteness Theorems
Gödel's incompleteness theorems were mathematically proven results but they had broad
philosophical consequences. They were proofs that would show that there are certain true
propositions that are improvable. They were epistemological truths, meaning they dealt with the
nature of knowledge itself by proving an absolute limitation on what we can mathematical prove.
(Goldstein 2013)
To assess the effects of Gödel's results, the theorems themselves will be outlined, as will the three
schools of logicism, formalism and intuitionism, then the effects of the theorems on the schools
shall be considered. To appreciate the consequences of the incompleteness theorems there is a need
to explain the key terms of consistency and completeness and ... Show more content on
Helpwriting.net ...
(Struik 1987, 203). Logicism disagrees with Intuitionism as it asserts that we do not create
knowledge but simply reveal existing truths (Brown 2008, 125). Since in intuitionism 'abstract
entities are admitted only if they are man made' (Snapper 1979, 209). Brouwer's criticism of
Logicism is that they use the principles of finite sets and their subsets as a form of logic beyond and
prior to mathematics and used it to reason about infinite sets (Kleene 1952, 46–7).
Intuitionism was developed as a reaction to Cantor's set theory and its paradoxes. Intuitionists
sought to rebuild mathematics from the 'bottom–up'. They saw Mathematics as 'an activity';
Mathematicians do not access pre–existing knowledge but construct knowledge (Brown 2008, 121).
Brouwer saw logic as an unreliable basis for mathematics and therefore Brouwer's intuitionism sees
mathematics as having its foundations with 'Ur–Intuition, a basic intuition of the natural numbers'
(Struik 1987, 202, Palmgren 2009). Its fundamental and defining characteristic is its analysis of
what it means for a statement to be true. In Brouwer's original intuitionism he demands 'truth though
constructivity' (Struik 1987, 202). This means that he only allowed entities that had a clear and
definable method of construction. For example, in this way Brouwer would accept the idea of
possible infinitely, as it required a continuous set of constructions and 'remains forever in the

Professional Math Project
Professional Math Project
I'm interested in psychology, and in its research and applications. So, when we received this
assignment I took it as an opportunity to explore the importance of mathematics in psychology. My
brother is actually a social worker, with his masters in social work and a bachelor in psychology.
There are many similar demands between work in psychology and social work, including in terms
of training and the required mathematical foundation. As a result, I decided to talk to my brother.
My belief that math's importance extends to the field of psychology was most certainly confirmed.
I already knew that math plays an important role in both experimental and clinical psychology. It is
necessary to both those conducting research ... Show more content on Helpwriting.net ...
It is necessary for psychologists and social workers in analyzing input from clients, making relevant
connections with all of their training, and wisely applying information, skills and methods gleaned
from psychological research. Critical thinking allows them to process information intelligently, to
see how things fit together, and to consider what outcomes their clients might achieve as a result of
applying certain methods. Guiding clients through this sort of problem solving is essential in clinical
psychology and social work and takes a great deal of skill. It is also necessary for psychologists and
social workers to be able to think critically in reflecting on their own approach, and best application
of knowledge and tools in working with a client. Being able to take complex concepts and research
and to make it relatable and applicable in real life is important and

How Transformational Change The Common Ideologies And...
transformative change in the common ideologies and understanding of society as well as the
natural world. Through new developments in fields like astronomy, mathematics, physics,
chemistry, and biology, new discoveries and ideas fundamentally changed how ordinary people
perceived and interpreted the world around them through a non–religious perspective. With this
newfound knowledge, fields of modern science and mathematics were established through
which questions about the natural world were answered through observations that were concrete,
quantified, and unaltered by opinion. In doing so, these newfound ideas and discoveries
challenged the Catholic Church's power to dictate knowledge to people of all standing in society
through the Church and the Bible's perspective. Scholars like Galileo and Francis Bacon
revolutionized how knowledge was gained by approaches such as the Scientific Method; this
new problem solving process involved one observing and questioning using reasoning to gain
new knowledge instead of blindly taking in information as given by the Church. Innovations like
Galileo's work, the use of mathematics, and Bacon's Scientific Method gave rise to modern
science, a secular way of understanding society as well as the natural world. As a result, an
intellectual revolution began in the West during the Early Modern period as people pursued an
understanding of society and the world independent of the Church's authority.
model of

Theories of Cognitive Development in Relation to...
Introduction:
In order to survive the world around us that is fully designed on mathematical notions, young
children need to acquire mathematical knowledge. Hence, this aspect when attained effectively
places them in the right position to face the distinct real world of mathematics. Therefore, it is
essential to acknowledge how these children obtain numeracy skills and their capabilities through
the theories of cognitive development presented by many influential theorists. The following essay
elaborates a chosen theory of cognitive development in relation to mathematical knowledge with a
link to the Australian Curriculum to demonstrate how the document chosen allows for scaffolding of
children's learning for kindergarten students. ... Show more content on Helpwriting.net ...
He saw that "scaffolding provides an effective way to reach potential levels of development" (Eddy,
2010). Therefore, children can easily learn and develop numeracy concepts when the teacher uses
discussion and think in a loud voice with students as well as, when teachers are "encouraging
collaborative group work, peer assistance and discussion" highlighted by Westwood (2008, p30).
Also, through identifying the child's level of understanding and capabilities to offer guidance that
assist the child to progress more. Thus, the (ACMSP011) stresses upon children answering "yes/no
question to collect information", this help children interpret data and develop reasoning skills.
Comparison of cognitive development theories:
On the other hand, Jean Piaget and Jerome Bruner have also offered theories about cognitive
development for foundation year children. First, Piaget mainly approved on the interaction between
the child and his environment. He believed the child can only learn when regularly interacting with
his environment through "making mistakes and then learning from them" (Eddy, 2010). He saw the
child as the only scientist who learns from his own experiences. Whilst, Bruner saw that young
children are able to learn mathematics by exploring and discovering on their own. As well as,
through interacting creatively with well–informed adults and peers who can offer

Scientific Revolution: Absolute Truth
The Scientific Revolution mangled all scientific theories, which previously was viewed as absolute
truth. Aristotle was the "grandfather" of science. His theories were law, and science could only build
upon his foundation. However, Copernicus began to shatter those theories, now proclaiming that the
geocentric view of the world was no longer correct. Instead, he proposed a heliocentric worldview.
Although he presented the world with a new theory, he never lived long enough to convince others
that his theory had truth. After Copernicus' death, Tycho Brahe became a leading astronomer.
Contrary to Copernicus, Brahe still believed in the geocentric view. Brahe prophesized that
everything revolved around the sun, but that the sun revolved around ... Show more content on
Helpwriting.net ...
Isaac Newton was a well–known scientist as well as a fantastic theologian. Through combining
math and science he produced the Law of Gravity, the Nature of Light, the Laws of Motion, and
suggested universal gravitation rather than crystalline spheres. Following Newton was Sir Francis
Bacon and Renee Decart. Bacon believed that all science should be open. Everything should be
questioned, examined, and tested until proven one–hundred percent true, and that we should never
trust the theories of those before us without testing it ourselves. Decart is famously known for, "I
think therefore I am." But beyond that, he is known for pronouncing that "Mathematics plus Science
plus Reason equals Order." However, he never truly witnessed how right he was. Subsequent to that,
not only were the walls of science and mathematics forced to crumble, but the walls of medicine
were also demolished. With the help of Andreas Vesalius and William Harvey medicine was fully
reinvented and the belief that everything could be explained by an imbalance of humors was
eradicated. In the end, all medieval beliefs were destroyed and replace with new theories,
mathematics, and

Technology in the Mathematics Classroom Essay
Technology in the Mathematics Classroom
In today's society, technology is advancing at such a rate that on can hardly stay ahead. Technology
surrounds every person in civilization. To not use the technology that is readily available would be
absurd. The same idea applies to technology in the classroom. Calculators, in particular, are
becoming more readily available in the classroom, but technology should not stop there. Many
inspiring computers programs, such as Geometer's Sketchpad,
Math Success, Fathom, Maple, and Minitab greatly enhance the mathematical teaching and learning
that can take place in a classroom. With these types of programs, teachers can cover required more
in–depth, and addition material more
closely ... Show more content on Helpwriting.net ...
The myths include:
1. "Calculators are a crutch: They are used because students are too lazy to compute the answers on
their own; they do the work for the student."
2. "Because calculators do all of the work for the student, he/she will not be stimulated or
challenged enough." 3
3. "If I didn't need to use technology to learn math, then neither does my child. After all, I turned out
just fine."
4. "The use of calculators prevents students from effectively learning the basic mathematics they
will need when they enter the workforce."
5. "People will become so dependent on calculators that they will be rendered helpless without one.
(e.g.:
What if the battery dies or the student has to perform a computation when no calculator is
available?)" (Waits pg. 6–8)
Waits gives reasons why these myths are in fact false and why it is important for the myths to be
overcome by the public in his essay. In conjunction with the importance of parents and teachers
fostering technology is the importance for students to foster technology in the classroom.
Students should be taught to use technology as a tool for learning and not a "crutch." As noted in the
NCTM
Principle, "Technology should not be used as a replacement for basic understandings and intuitions;

Effective Instructional Strategies to Ensure Fifth Grade...
Effective Instructional Strategies to Ensure Fifth Grade Mathematics Readiness
Literature Review
The purpose of this literature review is an exploration into effective instructional strategies to ensure
fifth grade mathematics readiness. This two–part study investigates what teachers consider to be key
elements in instructional design and implementation to support mathematics curriculum across the
elementary grade levels. It will also investigate specific mathematics skills that teachers believe
should be taught and reinforced each year from kindergarten through fifth grade.
Due to the constant changes to the national and state education programs, there has been an increase
in the focus on language objectives and literacy skills in ... Show more content on Helpwriting.net ...
Unless a learner enters a grade with a full proficiency of the skills learned in prior years, that learner
must be retaught or face the very real risk of falling even further behind.
While reteaching is seen in a negative context, one in which students need remedial instruction to
help them become proficient in heir current grade level skills, it is also seen as an effective
instructional tool in the mathematics classroom. Incorporating curriculum review in daily instruction
assists educators in finding deficiencies in foundational mathematics skills and addressing those
needs in a timely manner.
Early Numeracy in the Lower Elementary Grades Standardized testing has become a controversial
topic. Contrasting opinions either support or oppose the use of standardized testing to truly measure
a learner's proficiency. These tests base their content on what a learner should know by their
respective school year. When a learner reaches the end of the fifth grade year, but is performing
below average on their state's standardized test, one cannot help but wonder where the breakdown
has occurred. The natural response is to want to locate the disconnect in a student's learning pattern
and correct this for future students. By beginning early numeracy skills in early elementary grades,
specifically kindergarten and first grade, students are beginning the scaffolding they need to
successfully transition to subsequent grade levels. Using student–centered instructional

Calculus As A Part Of Modern Mathematics Education
Calculus (from Latin calculus, literally "small pebble used for counting")[1] is the mathematical
study of change, in the same way that geometry is the study of shape and algebra is the study of
operations and their application to solving equations. It has two major branches, differential calculus
(concerning rates of change and slopes of curves),[2] and integral calculus (concerning
accumulation of quantities and the areas under and between curves);[3] these two branches are
related to each other by the fundamental theorem of calculus. Both branches make use of the
fundamental notions of convergence of infinite sequences and infinite series to a well–defined limit.
Generally, modern calculus is considered to have been developed in the 17th century by Isaac
Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and
economics[4] and can solve many problems that elementary algebra alone cannot.
Calculus is a part of modern mathematics education. A course in calculus is a gateway to other,
more advanced courses in mathematics devoted to the study of functions and limits, broadly called
mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or
"infinitesimal calculus". Calculus (plural calculi) is also used for naming some methods of
calculation or theories of computation, such as propositional calculus, calculus of variations, lambda
calculus, and process calculus.
Contents [hide]
1 History
1.1

How Did Calculus Contribute To The Development Of Europe
There was an unexpected explosion in the math and science world in the 17th century across
Europe, known as the Age of Reasoning. Scientists such as Galileo, Brahe and Kepler continued to
increase our knowledge on mathematics and science, especially the solar system which led to
Kepler's laws of planetary motion. Isaac Newton also discovered the laws of physics explaining
Kepler's Laws, and brought together the concepts now known as calculus. The invention of the
logarithm by John Napier contributed to the advances of science and astronomy and was one of the
most significant developments of this time. Rene Descartes development of analytical geometry and
Cartesian coordinates allowed the orbits of the planets to be plotted. Other mathematicians such as
Fermat and Pascal formulated theorems which extended our knowledge on number theory. Pascal is
most famous for his Pascal triangle even though similar figures had been done by the Chinese and
Persian mathematicians before him. Newton and Leibniz revolutionized mathematics by developing
infinitesimal calculus. Much more credit should be given to many other mathematicians at this time,
but as said before, this was a time of severe increase in mathematics and these are only a few of the
most important discoveries. (15) ... Show more content on Helpwriting.net ...
This period, however, was dominated by Bernoulli. He was responsible for further developing
Leibniz's calculus as well as Pascal and Fermat's number theory. Leonhard Euler was another
notable mathematician of this time. He worked in all field of mathematics and was able to find links
between these different fields. He also proved multiple theorems and wrote many

What I Learned In Mathematics Class
Remember being taught something new in a mathematics class and thinking to yourself, "when am I
ever going to use this in life?" Sure, not every mathematical theory taught in class will be used in
your career, but from my experience, many of the skills learned in mathematics are frequently
utilized each day. While mathematics may not be everyone's favorite subject, I found it to be not
only the subject I use the most outside of school, but the one that I enjoy the most, which is why
mathematics is my favorite subject. As a mathematics major, the concept that most people overlook
is that I did not choose to study mathematics because I do well at it; I chose to study mathematics
because it makes me smarter. In fact, all throughout junior high and high school I was in remedial
mathematics classes and worse, I did not even place into a freshman year mathematics class in high
school. I had to re–take 8th grade mathematics. However, something about mathematics excited me.
Maybe it was the fact that mathematics never came easy to me and I wanted to prove to myself that
not only could I pass mathematics classes, I could actually understand and excel at them. For me,
mathematics is not about the arbitrary numbers, trivial solutions, meaningless formulas, or repetitive
computation: it is about the progress of knowledge and human understanding. I believe that there
are two different ways in which the world develops; the first is through the advancement of history
and human

How Did Galileo Invented The Telescope
Some people will see Galileo as a regular person who invented the telescope. But I'm here to show
you that Galileo was a crucial part in advancement in modern technology. He was the foundation of
astronomy. Without him being alive during that time period it's possible we wouldn't even have
telescopes. This has all begun in a city where Galileo was born named Pisa. For the time Galileo
was very smart, while he lived in Pisa he attended a private tutor and learned about Medicine and
Math and English. Then he moved to Florence to attend a college to learn more in Mathematics and
Physics. Sadly before he was able to get his diploma he had to drop out forced to money issues, so
he moved back to Pisa. While he was back in Pisa he stopped learning about medicine so he could
focus more on mathematics. "In 1589, at age 25, Galileo was given the position of lecturer in math
at the University and was selected as the Chair of Mathematics." "Galileo (1564–1643)" During this
time Galileo was starting to challenge different theory's like Aristotle, trying to find a problem in it.
Most of the students in his classes thought he was insane for doing so. When he finally found
something, he tried to get the respect of his students back by showing them, that everything drops at
the same rate. ... Show more content on Helpwriting.net ...
The church convicted Galileo of heresy and incarcerated him but thankfully he got his sentenced
lowered to just house arrest. For his final years alive he spent them under house arrest studying
mathematics with some help from several of his students throughout the last years of his life. After
his death more people started to study the starts and acknowledge what he has said to be actually
true! Without Galileo we wouldn't be as advance as our society is today. Like most likely we would
have telescopes but for 100% sure we wouldn't be this advance in Astronomy. He was and always
will be the foundation to Astronomy, he made his

Understand Current National and Organisational Frameworks...
Understand current national and organisational frameworks for mathematics 1.1 Explain the aims
and importance of learning provision for numeracy development. Numeracy development is
important for all children as maths is an important part of everyday life. The way in which maths is
taught has changed greatly over the years. When I was at school we were taught one method to
reach one answer. Now, particularly in early primary phase, children are taught different methods to
reach an answer, which includes different methods of working out and which also develops their
investigation skills. For example, by the time children reach year six, the different methods they
would have been taught for addition would be number lines, ... Show more content on
Helpwriting.net ...
They use a variety of ICT resources as tools for exploring number, for obtaining real–life data and
for presenting their findings. Much of their work will be oral. They develop their use and
understanding of mathematical language in context, through communicating/talking about their
work. They ask and respond to questions, and explore alternative ideas. They use appropriate
mathematical language to explain their thinking and the methods they use to support the
development of their reasoning. They develop a range of flexible methods for working mentally
with number, in order to solve problems from a variety of contexts, checking their answers in
different ways, moving on to using more formal methods of working and recording when they are
developmentally ready. They explore, estimate and solve real–life problems in both the indoor and
outdoor environment. They develop their understanding of measures, investigate the properties of
shape and develop early ideas of position and movement through practical experiences. They sort,
match, sequence and compare objects and events, explore and create simple patterns and
relationships, and present their work in a variety of ways At Key Stages, learners build on the skills,
knowledge and understanding they have already acquired during the Foundation Phase. They
continue to develop positive attitudes towards mathematics and extend their mathematical thinking
by solving

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