Fishing For Words Essay

Fishing for Words Essay
Fishing for Words
"Give a man a fish; you have fed him for today. Teach a man to fish; you have fed him for a
lifetime" (http://www.amatecon.com/fish.html). This quote can be applied to illiteracy in America;
basically someone illiterate cannot live on their own until they have been taught the basics, reading
and writing. According to Kozol's essay The Human Cost of an Illiterate Society the government,
administration, and people of high power live by the beginning of the quote (Kozol, The Human
Cost of an Illiterate Society). They help someone illiterate make a living until the person is out of
their control. Yet the government, administrations, and society maintain control through illiteracy.
Illiteracy is spreading like a plague ... Show more content on Helpwriting.net ...
Let us say that a little first grade boy is a hyperactive in class and the school's administration decides
to test the boy for either ADD or ADHD, with parental consent of course. After testing the child is
deemed to be ADD and has to be placed into a classroom where he cannot be a distraction. Can you
imagine being placed into a remedial class for being hyper on day of the year? So now the boy is
learning at a slower pace than his friends are and by the time he reaches fifth grade the
administration decides to retest him. They discover that instead of reading at the fifth grade level he
is reading at the entry level to third grade, so now the boy is classified as mentally retarded because
of the class he was placed into. When to boy reaches high school he is more likely to drop out than
his friends from first grade. The seniority that the administration holds over a child's life is pitiful.
These people are there to provide a positive learning environment yet they ruin a person's life at an
early age. It needs to be pointed out that these administrations entitle a child as illiterate when the
child has not had the chance to learn the basics in school.
To live the American Dream is the motivation for many immigrants to choose to live in the United
States of America. As they arrive their hopes and dreams are shattered. Our society immediately
... Get more on HelpWriting.net ...

What Is Causing America 's Academic Shortcomings? Essay
Nevin Johnson
Chuck Justin
English
21 November 2016
What is Causing America's Academic Shortcomings?
Since the beginning of global standardized testing, American students have been less than
impressive. Numerous other countries consistently score higher than students in the United States.
While comparing the test scores from the Program for International Student Assessment (PISA) and
Trends in International Mathematics and Science Study (TIMSS), two major cross–national studies
of students' scholastic performance, it is true that the United States is nowhere near the top, and is
instead merely mediocre. An exhaustive list of reasons could be compiled in attempting to explain
this phenomenon, but at its core the problem is not that complicated. The prominent issues that
cause American students to lag behind are a result of the nation's multiple separate education
systems, parenting, the curriculum or specifically how it is taught.
In America, the education system is not singular. All education systems in the United States are
loosely regulated under the same federal rules; however, the federal government does not run the
school districts. Instead, districts are operated by individual states, plus the District of Columbia
(Rosales). This means some states preform exceptionally while others preform excessively bad. This
misconstrues the way that the states are being compared to other countries of the world because
comparing U.S. results to the rest of the world is essentially

Jesse Ernest Wilkins Jr.
Jesse Ernest Wilkins Jr. was born on November 27, 1923 in Chicago, Illinois. He was the son of
Lucile Robinson and Jesse Ernest Wilkins Sr. His mother had a Master's degree from the University
of Chicago and was a school teacher. His father was a lawyer, even though he had his Bachelor's in
Mathematics from the University of Chicago, he later became the President of the Cook County bar
association and Assistant Secretary of Labor by president Dwight D. Eisenhower in the Eisenhower
administration, he became the first African American to hold a sub–cabinet position in the U.S.
government. Wilkin's grandfather was also notable for founding St. Mark Methodist Church in New
York City. Living up to his parents' expectations, Jesse Ernest Wilkins ... Show more content on
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He worked there for 10 years. In 1955, he became manager of the Mathematics and Physics
Departments, he later became manager of Research and Development. During this time, Wilkins
was awarded a Bachelor's in Mechanical Engineering from New York University in 1957, three
years later he was awarded a Master's in Mechanical Engineering. In the 60s he worked at the
General Atomic Company in San Diego, in the 70s he was appointed to Howard University as a
Distinguished Professor of Applied Mathematical Physics. He established the first Ph.D. program at
the University and it became the first University to have a program as such. From 1977 to 1984,
Wilkins worked at EG&G Idaho becoming Vice President and Deputy General Manager for Science
and Engineering. Then in 1984 he officially retired as a fellow at the Argonne National Laboratory
of the U.S. Department of Energy in Argonne, Illinois. He remained a consultant at the Argonne
National Laboratory after he retired in 1985. In 1990, he became Distinguished Professor of Applied
Mathematics in Mathematical Physics at Clark Atlanta University. Wilkins published more than 100
papers on a variety of subjects throughout his years the subjects were: Differential Geometry, Linear
Differential equations, Integrals, Nuclear Engineering, Gamma Radiation Shielding and Optics,
garnering numerous professional and scientific awards along the way. In 1994,

Gender Inequalities In America
For 91 years, the United States of America has become the sole superpower of the world by
maintaining its global leadership and competitive position in both military and economic strength.
As jobs and companies are being created around the world to improve their infrastructure and
economy, the United States of America must also be willing to get back on its feet and continue to
become the superpower it is. As the years continue, the future will be different with in advancements
in science, technology, engineering, and mathematics. For the United States of America according to
a 2008 survey by USA Today states that only 26% of the people who were surveyed had a clear
understanding of science, technology, engineering, and mathematics and the United States citizens
ability in math, science, and problem solving has dropped below to ... Show more content on
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Based on an experiment done by two psychologist who are Toni Schmader, a psychologist from the
University of British Columbia, and colleague Matthis Mehl, a psychologist from the University of
Arizona, who up with an innovative way to study the reason to why the gender gap for women and
men is so big. The device they used is it the Electronically Activated Recorder was placed on a few
test subjects to see how they would converse with a person of the opposite gender or the same
gender of different races. These two psychologists found out that when women talk to men, they
already feel a certain discouragement when the other gender talks about work but when talking to
the same gender, women tend to be more engaged into the conversation. Based on this study case,
people of different genders even in the same settings, there seems to be a stereotypical aspect
judging them to make them want to not be the person who they are but instead a different

Why Do We Use Quadratic Equations?
It might seem as if these contributions have no real world applications, however, that would be very
incorrect. Completing the square is very useful for quadratic equations, which we have mentioned
before. The question lies, where do we use quadratic equations? When projectiles are put into
motion they create a parabolic path, to calculate the speed and height at which they travel
completing the square would come in handy. Another example would be traveling by boat, or foot,
or any other method. You would go one way, then probably return to your original location. This
would also be similar to a parabolic path which can be solved by completing the square. Pictured
below is what a parabolic track would look like. Figure 5. Parabolic Graph Without the foundation
that al–Khwarizmi laid out for all mathematicians to come, there would not be the mathematical
field we know today. In every aspect of calculus, geometry and other forms of mathematics, the
methods of reduction, completion and balancing come into play. The combinations that those three
methods have created can be attributed to the many discoveries we have today. Just some examples
are the creation of the World Wide Web, in other words, the internet. Without the algebraic
foundation the strings of Booleans, cannot be translated to create the internet as we know it. Without
the very intricate mathematics we know today, man would have never made it into space. This one,
seemingly insignificant

Ap Human Geography Chapter 1 Summary
Chapter One: Thinking Geographically
Key Issues: How do geographers describe where things are? Why is each point on Earth unique?
Why are different places similar?
Introduction
I. Geographers observe that individuals are being swayed in two directions.
A. Globalization– movement between people, ideas, and cultures. Moves people to interact on a
global scale.
B. Local diversity– unique cultural traditions, unique economics. Individuals interacting with their
local community.
C. Globalization and local diversity lead to conflicts.
II. Three important concepts in HG explain why places on Earth have similar
traditions/cultures/religions.
A. Scale– relationship between a specific place in the world, and the Earth as a whole.
B. Space– Physical ... Show more content on Helpwriting.net ...
III. Connections Between Places
Space–time compression– the reduction in the time it takes for one to reach a place
A. Spatial Interaction
Distance decay– the farther a way two groups are from each other, the less likely that they will
interact.
Technologies have allowed interactions between people that are far away.
B. Diffusion
Diffusion– process by which a characteristic spreads across space from one place to another.
Today, ideas diffuse rapidly across the world.
Hearth– the place from which an innovation originates.
Relocation diffusion– the spread of an idea through the physical movement of people from one place
to another.
Expansion diffusion– the spread of a feature from one place to another in a snowballing process.
Three types: o Hierarchical diffusion– from nodes of authority or power. o Contagious diffusion–
rapid spread of a

Jesse Ernest Wilkins Jr.: The Negro Genius
Jesse Ernest Wilkins Jr. better known as the "negro genius" was the first African–American to enter
into the University of Chicago at the age of 13 and at that time the youngest student ever to register
there. He was born in Chicago on November 27, 1923 to J. Ernest Wilkins, Sr., a lawyer who held a
bachelor's degree in mathematics from the University of Illinois and a law degree from the
University of Chicago. His father was the president of the Cook County Bar Association in Chicago,
Assistant Secretary of Labor in 1954, the first black American to hold a sub–cabinet position and in
1958 he was appointed to the Civil Rights Commission. His mother, Lucile Beatrice Robinson
Wilkins held a bachelor's and master's degrees in education from the ... Show more content on
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In 1965 Wilkins was promoted, first to assistant director of the John Jay Hopkins Laboratory, then to
director of the Defense Science and Engineering Center, and finally to director of Computational
Research. Being as busy bodied as Wilkins was, he moved to Howard University in Washington,
D.C., as a professor of Applied Mathematical Physics leaving General Dynamics in 1970. Dr. J.
Ernest Wilkins, Jr. was elected into the American Nuclear Society (ANS) in 1964 where he held the
position of board of directors from 1967–77 then became the President from 1974–1975. In 1976,
Wilkins was inducted into the National Academy of Engineering and the second black American to
be elected to the National Academy of Engineering (NAE). One of Wilkins' most talked about
achievements was the development of radiation shielding against gamma radiation, emitted during
electron decay of the Sun and other nuclear sources. He developed mathematical models by which
the amount of gamma radiation absorbed by a given material can be calculated. This technique of
calculating radiative absorption is widely used among researchers in space and nuclear science

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

College Algebr A Problem Solving Skill Essay
On the other hand, according to NCTM members, college algebra needs to be implemented in the
school system. Their Standards show that "mathematical power" is required in order for students to
perform effectively in a "variety of authentic settings" (Steen 1992). Algebra looked upon from a
student perspective is known as a problem solving skill meaning a process to seek solutions to
certain problems give. However, looking at algebra from a broad approach we notice that it is very
similar to human stages which are considered to be a baby crawling, walking, and then being able to
run. In order to understand what algebra is we must first look at a problem given to us understand
what the problem is, question ourselves to what is given, and then realize the conditions that are
presented which then helps us plan our strategy to solve a problem. This approach is useful not only
in mathematics, but in other concepts such as in science. In algebra, logical thinking is used this is to
make sense or make connections of a problem in order to find a solution. Algebra is known to be a
part of mathematics that includes general letters and symbols to represent numbers that can be
formulated and found by solving equations. Some students fail to build a solid foundation in
mathematics which is why they are unprepared for college and for work. As future math teachers,
we must encourage students to understand the concept behind college algebra which will help them
excel in their future.

What Is The Initiation Of An Online Math Program As A...
I propose the initiation of an online math program as a solution. The name of the program would be
BBAM (Becoming Better At Mathematics) and it would be a good fit for the Mathematical
Association of America (MAA) because they are both geared towards the core interest of advancing
student's understanding of Mathematics. Through this program, students will be better able to learn
from their mistakes and apply the appropriate strategies to solve their mathematical problems.
Occasionally, physical or face to face help is not readily available, however, with the
implementation of this online program, students will receive help in a timely manner with little or
no disruptions. The online program would be made in such a way that the teachers ... Show more
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For instance, a summer bridge program offered in a mid–sized public university in the northeastern
USA had a goal to "provide students with academic support in mathematics along with the
opportunity to meet the proficiency requirement during the summer before enrolling for the first
time in the fall semester" (Lesik, 2015). However, the result was that the students who participated
in the program did no better or worse than students who did not participate. Summer bridge
programs are generally designed for students who demonstrate weaker skills in an area, but
sometimes they just do not work. However, other programs have been proven successful. One such
program is the Assistive Technology, which seeks to "offer intervention" and forms of assistance to
everyone who is struggling in a particular area (Lancioni, 2013). Also, another successful program –
the Computer–Assisted Instruction program– "quizzes the student periodically and assess progress
to a mastery level" (Hamilton, 2017). Similarly, the BBAM would operate in this manner as its goal
is to improve the mathematical skills of all students. It is geared towards everyone as it is important
to encourage effective curriculum, teaching, and assessment at all levels, whether students are weak,
intermediate or strong in mathematics. Benefits Henceforth, I propose that the Mathematical

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;

Various Factors for the Downfall of the Public Private...
Jpz777 05/04/2013 Order # 2094371 The construction and maintenance of the vast networks of
infrastructure needed to support cities, states, and the entire nation typically require the collaborative
efforts of both private contractors and public entities to ensure that project design, budget, and
schedule are adhered to in an economically efficient manner. For decades, the private and public
sectors were capable of working in close conjunction through the public private partnership model,
which allowed municipal governments to issue bonds to generate the funding needed for highways,
bridges, hydroelectric dams, power plants, and other essential components of modern infrastructure.
With the nation still struggling to recover from the devastating effects of a prolonged economic
slump known as the "Great Recession," many local governments have experienced severe budget
shortfalls that have forced politicians and the public alike to make extremely difficult financial
decisions. One option which has become increasingly attractive to city managers across America is
the privatization of public assets, a situation which recently occurred in South Carolina when the
state awarded the lease to a 16 mile stretch of interstate expressway, known as the Greeneville
Southern Connector, to the private investment group Connector 2000 Association. Through a
disastrous series of miscalculation and misappropriation, the toll road envisioned by South
Carolina's government to become the state's

The Pros And Cons Of Pseudoscience
What is Pseudoscience? Before this assignment I had no understanding of what defines science as
science and how to pinpoint what is true science and what is fake science, otherwise known as
pseudoscience. According to Jeffrey Lee who published Science and Pseudoscience, pseudoscience
is considered a fake science. It is a collection of assertions that do not satisfy the requirements to
practice true science. The difference being science relies solely on careful observations and
experiments to either confirm or reject a hypothesis. It has to require reproducible results, personal
stories or testimonies are prohibited. As well as arguments are based on logical and/ or mathematical
reasoning. Lastly, there is progress; more and more things are learned and developed over time.
Whereas, Pseudoscience is nothing but the complete opposite of what science represents. It is based
off a hypothesis where the evidence is looked only to support the original hypothesis with little to no
experimentation. Researches focus without skepticism and rely on personal stories and testimonies
to back their belief. After a conclusion is made there is no further progress; nothing new is learned
as time passes. These two very different methods can be the fine line between what is science and
what is pseudoscience. According to Rodney Schmaltz and Scott O. Lilienfeld who published The 7
Ways to Identify Pseudoscience A person can identify what a pseudoscience is by acknowledging
that others will use

Integrated Circuits (Impact on Us History)
Andrew Miller
History 1302 – LaCoco
Monday, May 9, 2011
"Integrated Circuits"
Gordon E. Moore, co–founder of Intel, noted in 1965 that the power of integrated circuits doubles
every two years.[1] This, known as Moore's Law, is the basis for what I believe to have had the most
profound impact on American History. Without integrated circuits, culture changing devices such as
the iPhone would not be possible. These circuits were created in 1958 by Jack Kilby, inventor of the
hand–held calculator and employee of Texas Instruments.[2] By having all the necessary
components made out of the same material on the same chip, integrated circuits make electrical
devices smaller, faster, and smarter.[3] This has greatly impacted the ... Show more content on
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Today's image of America would not exist without integrated circuits, and integrated circuits still
extend to shape tomorrow's image of America. Even though their impact is already great, integrated
circuits continue to shrink in size and lower in price with keeping the same amount of power. "If the
auto industry advanced as rapidly as the semiconductor industry, a Rolls Royce would get a half a
million miles per gallon, and it would be cheaper to throw it away than to park it." – Gordon E.
Moore.
–––––––––––––––––––––––
[1]"Moore's law," Wikipedia, Wikimedia Foundation, Inc., 6 May 2011, 8 May 2011 .
[2]"The History of the Integrated Circuit." Nobelprize.org 5 May 2011 .
[3]"The History of the Integrated Circuit." Nobelprize.org.
[4]"Integrated circuit," Wikipedia, Wikimedia Foundation, Inc., 7 May 2011, 8 May 2011 .
[5]Hall, Edon E., "Integrated Circuits in the Apollo Guidance Computer," klabs.org, 15 Jan 2009, 8
May 2011 .
[6]Mandel, Michael, "Integrated Circuits and the Space Program: A Partial Retraction," Bloomberg
Business Week, Bloomberg L.P., 19 July 2009, 8 May 2011 .
[7]"LGM–30 Minuteman," Wikipedia, Wikimedia Foundation, Inc., 25 April 2011, 8 May 2011 .
[8]"Northrop Grumman E–2 Hawkeye," Wikipedia, Wikimedia Foundation, Inc., 20 April 2011, 8
May 2011 .
[9]"Integrated circuits," Wikipedia.
[10]"Integrated circuits," Wikipedia.
[11]"BASIC," Wikipedia, Wikimedia

Elbert Frank Cox's Major Accomplishments
Born December 5, 1895, Elbert Frank Cox earned his undergraduate degree from the University of
Indiana. In 1925, he became the first African American to earn a Ph.D. in mathematics. He taught
for 40 years at West Virginia State College and Howard University. After he retired, Howard
established a scholarship fund in Cox's name to encourage future Black mathematicians. Elbert
Frank Cox was born on December 5, 1895 in Evansville, Indiana. After graduating from Indiana
University in 1917, Cox served in World War I and then pursued a career in teaching. In 1925, he
earned his Ph.D. in mathematics from Cornell University, becoming the first African American to
earn the degree in the United States and, in fact, the world. After earning his degree, ... Show more
"Year after year, our master's students consistently did much better in departmental oral
examinations on material they'd studied with Cox than on material they'd studied with me or from
our colleagues Woodward, Claytor, and others," Blackwell was quoted as saying in the American
Mathematical Monthly article. At Cox's retirement, Howard University's president noted that the
mathematician had supervised more masters' theses than any other member of the faculty. He
remained a full professor in the department until his retirement in 1966. During his career, Cox
specialized in difference equations, interpolation theory, and differential equations. Among his
professional honors were memberships in such educational societies as Beta Kappa Chi, Pi Mu
Epsilon, and Sigma Pi Sigma. He was also active in the American Mathematical Society, the
American Physical Society, and the American Physics Institute. Cox died on November 28, 1969,
after a brief

Julia Robinson Math Festival Essay
Thanks to your support, the year 2017 has been one of growth and innovation for the Julia Robinson
Mathematics Festival. We continue to reach more and more students across the country and around
the globe in fulfillment of our mission to bring the joy and beauty of mathematics to as many
students as we can through non–competitive, extra–curricular mathematics activities. The reach of
JRMF Festivals is expanding rapidly, while we retain the partners the JRMF team has developed
over the years. This year JRMF and our partners have hosted 50 festivals in 15 states and 5 foreign
countries, reaching more than 5000 students. Of these, 22 festivals were hosted by new partner
institutions. The JRMF teach has also received more than 70 ... Show more content on
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And they are often looking towards the United States for these paradigms. For all the comments and
concerns about American. students' educational achievement, educators in other countries frequently
look to the U.S. for best practices to open up their own pedagogy. JRMF offers exactly these best
practices, in a non–threatening, non–competitive, and non–judgmental context. This work, both
nationally and internationally, is informing our development of new problem sets and activities. It is
also the motivation behind yet another way to leverage the JRMF experience: the development of a
new resource, called "Facilitators' Guides". We are not just writing solutions to our problem sets, but
also collecting experiences and codifying them into documents that seek to give new facilitators a
'leg up' on the problem set and on how to work with students at a Festival. We can look forward to a
time when these facilitators' guides are a direct influence on classroom instruction. We have begun
to visit national meetings and fairs, bringing the JRMF message of the joy of mathematics to a wider
audience. The Young Innovator's Fair in King of Prussia Pennsylvania, and the annual meeting of
the National Association for Gifted Children saw thousands of visitors to our exhibit booths. The
National Math Festival in Washington, DC was a particular success. JRMF organized one

Personal Narrative: White House Math Initiative
I'm looking forward to helping pull together a White House Math Initiative. Are you available to
join a call the week of July 11 (next week) or the week of July 18 (following week) to discuss what
such an initiative might look like? The best time for me would be between 9 a.m. – 12 noon EDT.
After receiving an invitation from Megan Smith in April 2016 to come to DC for the summer to
upgrade math learning for the country, I've been thinking about and brainstorming ideas with about a
dozen math enthusiasts for how to get kids intrigued, engaged, and challenged by mathematics.
After much thought and reflection, I propose having Julia Robinson Mathematics Festivals
(http://jrmf.org/) at or near the White House or at the Mathematical Association of America, and
across the country. Julia Robinson was a great mathematician who, along with two other
mathematicians, was renowned for solving Hilbert's tenth problem.
The Festival problems are designed to inspire students to explore the richness and beauty of
mathematics through activities that encourage collaborative, creative problem–solving. They offer
diverse entry points – arithmetic, hands–on puzzles, card tricks, patterns, coloring – so that students
can wander around the festival and find an activity that grabs their attention. Sample problem sets
can be found online at ... Show more content on Helpwriting.net ...
"Ideally an activity will also illuminate a problem–solving strategy or several strategies, so that kids
begin to see connections among apparently diverse branches of mathematics, as for example when
they use parity to win a game, to prove that a process eventually terminates, to show that a certain
tiling is impossible, and to help assemble a geometric

Agent Based Models ( Abm )
Agents Based Models (ABM) A model is a representation of a real system and thus, it is an
abstraction of the reality 4. "The word "modeling" comes from the Latin word modellus which
describes a typical human way of coping with the reality" (Schichl, n.d.). Models can take various
forms such as mathematical equation, drawing, computer code, etc. However, there is a common
purpose of all designed models, which is to simplify the complexity presented in the real system or
problem. Therefore, models usually contain only the main aspects of the real system (not all details).
Macal and North (2006) believe that ''There is no universal agreement on the precise definition of
the term 'agent', although definitions tend to agree on more points than they disagree''. It seems very
complicated to extract agent characteristics from the literature in a consistent and constant
perspective, because they are utilised in different ways (Bonabeau 2002). Agent–based modelling
(ABM) is able to simulate the individual activities by measuring their behaviour and results over
time for developing models of cities (Crooks 2006). Agent–based modeling and simulation (ABMS)
is a new approach to modeling systems comprised of autonomous, interacting agents. Agent–based
modeling is a new analytical method for the social sciences, but one that is quickly becoming
popular. ABMS promises to have far–reaching effects on the way that businesses use computers to
support decision–making and researchers use

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

Statement of Purpose: Master in Computer Science
Statement of Purpose/Computer Science Master Playing games on my father's computer as a child
fascinated me in the way the computer works, how fast it develops, and now how the computer
helps the world to communicate. It still amazes me in how fast computers change and how
communication across the globe is enhanced with the computer. Computers have drastically
changed how society lives and does business. Even small businesses can do global sales without
leaving their location. With new strategies for business, comes cyber threats of identity theft and
theft of intellectual property that brings information technology security and new laws into play. It is
becoming a fast and ever challenging world. Computer science enables the ability to program
software for protection against these kinds of threats and vulnerabilities. It also enables the ability to
program artificial intelligence into the computer system software to enable society to meet their
needs in more appropriate ways. I have also developed a strong interest in mathematics in the way it
enables problem solving, which is a big part of computer science. It fascinates me in how the
fundamental properties of computational problems are explored with the computational complexity
theory. By approaching the description of the computation, using the programming language theory,
the programming investigates the use of the programming language and complex system. Besides
Information Security, the world of Artificial

Marjorie Lee Brown
In my AMDM class we are learning about black mathematicians for black history month, so for my
presentation I chose the famous mathematician Marjorie Lee Brown. She attended Howard
University, University of Michigan, and for high school she attended in Lemoyne. She was one of
the first African American women to receive a doctorate in mathematics. Her parent names are Mary
Taylor Lee and Lawrence Johnson Lee. Majorie was born September 9, 1914 in Memphis, TN and
she died on October 19, 1979 in Durham, NC. She served as a member of various educational
boards, such as Women's Research Society, American Mathematical Society, International Congress
of Mathematicians, and Mathematical Association of America. The North Carolina Council of
Teachers ... Show more content on Helpwriting.net ...
Under her leadership, the NSF funded a summer institute for secondary school teachers of
mathematics for thirteen years, for which Dr. Browne also authored four sets of lecture notes. The
Marjorie Lee Browne Colloquium was established in 1999 in the Department of Mathematics in
observance of Martin Luther King Day. The colloquium brings a distinguished speaker to campus to
present a talk that highlights their research but also addresses the issue of diversity in the sciences. It
honors the first African–American woman to receive a Ph.D. in Mathematics from UM, She also
retired in 1974. She was inspired and supported by both of her parents, she acquired her math skills
from her father, who himself was popular in his area as the math wizard. During her time at North
Carolina Central University, Browne taught both undergraduate and graduate courses. Her work as
an educator was so adored that she later published four sets of lecture notes for other teachers to
follow. Under her direction, her college became home to a prized National Science Foundation
Institute for secondary education in

Who Is Leonhard Euler?
Leonhard Euler was born on April 15, 1707, in Basel, Switzerland, Leonhard Euler was one of
math's most pioneering thinkers, establishing a career as an academy scholar and contributing
greatly to the fields of geometry, trigonometry and calculus. He released hundreds of articles and
publications during his lifetime, and continued to publish after losing his sight.
Euler showed an early aptitude and propensity for mathematics, and thus, after studying with Johan
Bernoulli, he attended the University of Basel and earned his master's during his teens. Euler served
in the navy before joining the St. Petersburg Academy as a professor of physics and later heading its
mathematics division. In the mid–1740s, Euler was appointed the mathematics director

Role Model: College Nannies And Tutor
1) Since 2014, College Nannies and Tutors, has been a very successful child care/role model/college
tutoring company out of Las Vegas, Nevada. Their appraoch has been specifically geared towards
high moral and values when contributing their expertise to families. Parents have loved the fact that
College Nannies matches the perfect nannies and tutors up with their families.
2) Since 2002, Mathnasium, from Las Vegas, Nevada has helped students (all over the United
States) at every level, reaching up to high school, to improve in math while sticking to a strict plan
of action that teaches them in a way that makes sense to them. Mathnasium has been ranked #86 in
Entrepreneur Magazine's Fast 500 in 2014. Customers' kids have went from hating ... Show more
Certified teachers' goal is to help foster student's fundamental understanding of concepts that are
required to excel in a classroom.
22) Math Dadd Tutoring, out of Las Vegas Nevada, applies learning concepts that helps students
grasp mathematical understandings, while building confidence in the process. Customers have stated
that Math Dadd has been an excellent role model for their kids and have helped them pass both the
ACT and SAT tests with flying colors!
23) "Mostly Math" of Las Vegas, Nevada, offers tutoring support for students and educators – that
may want to invest in academic consulting. Subjects of tutoring interest includes: Math, English,
Science, History, Philosophy and test taking skill development. There goal is to apply the latest
educational research for the betterment of their targeted students and

Education Program For The United Nations Development Program
1. Jim Teicher is Cofounder and CEO of CyberSmart! Education, a digital learning company and
international leader in fostering digital literacy skills. In 2007 Jim founded CyberSmart! Africa–
partnering with The Millennium Villages Project, a joint initiative of the Earth Institute at Columbia
University, Millennium Promise and the United Nations Development Program. The program is
going to provide a sustainable, scalable solution to 21st century learning.
2. Bill Gates is the most influential person in education policy in the last decade. He has contributed
to over $1.2 billion in high school reform efforts. Bill Gates has also helped bring technology into
schools that needed and has had some success with changing the high school system ... Show more
The department's mission covers the following main areas:
Encouraging teaching practices using ICT;
Developing school equipment;
Creating networks;
Teacher training (both initial teacher education and continuing professional development);
Supporting the production and distribution of multimedia resources;
The product and services industry.
2. Agence Bibliographique de l'enseignement Supérieur (ABES)
ABES is the French higher education organisation for bibliographic issues. It has been coordinating
STAR, a management system of electronic theses from all French universities since 2007 and has
now developed a portal for over 60 000 doctoral theses since 2001.
OA mandate: Yes. All universities deposit their theses to this centralised disseminating portal.
3. Centre national de la recherche scientifique (CNRS)
CNRS is Europe's major research organisation working through its 7 institutes of Biological
Science, Chemistry, Ecology and Environment, Humanities and Social Sciences, Information
Sciences and Technologies, Engineering and Systems Sciences, Physics and 3 national institutes:
National Institute for Mathematical Sciences (INSMI); National Institute of Nuclear and Particle
Physics (IN2P3); National Institute for Earth Sciences and Astronomy (INSU)/ Its aim is to
encourage collaborative and interdisciplinary research.
OA mandate: Mandated through the Ministry of Research.
4. Couperin
Academic consortium of over

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

Birth Of Algebra Research Paper
How Much Do You Know about the Birth of Algebra?
Jiawei Xue
Azusa Pacific University Abstract
Typically, Arabic civilization had significant contribution to algebra we use today. On the other
hand, the famous Arab mathematician Al–Khwarizmi own the title the father of algebra. However,
there is evidence that the ancient Babylon had stone tablet where looks like people exploring
fundamental idea of algebra around 2000BC. Additionally, there are other civilizations and
mathematicians such as Egyptian, ancient Greek, and Chinese also made significant contributions to
algebra we use today. The concept of algebra was used is widely used by different civilizations.
Overall, the evidences shows that the birth of algebra was not created by ... Show more content on
Helpwriting.net ...
(n.d.). Elementary number Tnheory and its applications. The
Mathematical Gazette, 162–162.
Boyer, C., & Merzbach, U. (1991). A history of mathematics (2nd ed.). New York: Wiley.
Connor, J. & Robertson, E. Abu Ja'far Muhammad ibn Musa Al–Khwarizmi. Retrieved from
http://www–history.mcs.st–and.ac.uk/Biographies/Al–Khwarizmi.html Greenberg, M. (2008).
Euclidean and non–Euclidean geometries: development and history
(4th ed.). New York: W.H. Freeman.
Helm, C. (1977). The Muslim contribution to mathematics. Atlantic Highlands, N.J.: Humanities
Friberg, j. & Marzahn, j. A chain of trapezoids with fixed diagonals. Retrieved from
http://www.worldscientific.com/doi/pdf/10.1142/9789812708847_bmatter Kvasz, l. (2004). The
invisible link between mathematics and theology. Perspectives on Science and Christian Faith,
Vol.56, pp.111–116
Merzbach, U.C. & Boyer, C.B. (2011). A history of mathematics (3rd ed). Hoboken, NJ: John
Wiley & Sons, Inc.
Sesiano, J. (2009). An introduction to the history of algebra: Solving equations from
Mesopotamian times to the Renaissance. Providence, R.I.: American Mathematical Society.
Shid, R. (2009). Al–Khwārizmī: The beginnings of algebra. London:

Conflict and Labeling Theory Essay
Conflict and Labeling Theory Labeling theory is concerned less with that causes the onset of an
initial delinquent act and more with the effect that official handling by police, courts, and
correctional agencies has on the future of youths who fall into the court system. Labeling theory
states that youths violate the law for a number of reasons; these reasons are poor family
relationships, neighborhood conflict, peer pressure, psychological and biological abnormality and
delinquent learning experiences. Cesar Lombroso was called the father of Modern Criminology,
originally came up with the labeling theory. (Labeling Theory) Cesar Lombroso classified criminals
into four major categories: born criminals, insane criminals, occasional ... Show more content on
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(Horton the elephant is a criminal :) The criminal justice system and criminal law are operating on
behalf of rich and powerful social elites, with resulting policies controlling the middle–lower class.
The criminal justice establishment aims at implementing standards of morality and good behavior
created by the whole of the society. Focus is on separating the just from the once that would steal
from others protecting themselves from physical attacks. In this process the legal rights of the lower
class are ignored. The middle class are also actively involved in the community thinking they might
themselves rise to the top, by supporting their status. Street crimes that covered minor monetary
crimes are routinely punished, while large scale financial and business crimes are treated much more
leniently. (Horton the elephant is a criminal :) Radical criminology is a branch of conflict theory,
using Marxist ideals. (Critical Perspectives on Crime) In his speeches, Carl Marx indicated the
criminal justice system's specific role in keeping the system in place. From his point of view, certain
types of crime transform with a different character. Stealing could be seen as an attempt to take
away from the rich, yet the law enforcement community followed a different path in which police
officers concentrated on civil rights protesters. Modern capitalist societies are

Women In Mathematics 1900-1860
Many women have achieved in the mathematics field since the 1900's. Especially women of color.
No matter how young or old, these women have taken their careers in mathematics to an inspiring
degree. Take the following women as examples, for they have created history in mathematics
forever.
Euphemia Lofton Haynes
In 1943, Euphemia Lofton Haynes was the first African American woman to earn a Ph.D. in
Mathematics. Ms. Haynes attended the Catholic University in Washington, D.C. Ms. Haynes father,
Dr. William S. Lofton, was a prominent black dentist and financier of black business in the area and
her mother, Lavinia Day Lofton, was active in the Catholic church. She was married to Harold Appo
Haynes who was a principal and deputy superintendent ... Show more content on Helpwriting.net ...
In 1932, Williams was born in Warri, Nigeria. She received her education at Queens College in
Lagos, University Colllege at Ibadan and the University of Vermont, before receiving a Ph.D in
mathematics education from the University of Chicago in 1963. She made history as the first
Nigerian woman to be awarded a doctorate. Dr. Williams returned to Nigeria for a couple of years
postdoctoral work at the University of Ibadan before joining the University of Lagos in 1965 as a
faculty member.
Dr. Williams continued interest in mathematics education was originally sparked by her stay in the
United States, which coincided with the Sputnik phenomenon. Working with the African
Mathematics Programs in Newton, Massachusetts, under the leadership on MIT professor Ted
Martins, she participated in mathematics workshops held in various African cities. Her courses
covered basic concepts in mathematics, working in concert with leading mathematicians and
educators. She spent a decade directing the Institute of Education, which introduced innovative no–
degree programs and certificate recipients working as elementary teachers. She is currently a
Professor of Mathematics at the University of

Agent Based Models ( Abm )
Agents Based Models (ABM) – Introduction to ABM A model is a representation of a real system
and thus, it is an abstraction of the reality 4. "The word "modeling" comes from the Latin word
modellus which describes a typical human way of coping with the reality" (Schichl, n.d.). Models
can take various forms such as mathematical equation, drawing, computer code, etc. However, there
is a common purpose of all designed models, which is to simplify the complexity presented in the
real system or problem. Therefore, models usually contain only the main aspects of the real system
(not all details). Macal and North (2006) believe that ''There is no universal agreement on the
precise definition of the term 'agent', although definitions tend to agree on more points than they
disagree''. It seems very complicated to extract agent characteristics from the literature in a
consistent and constant perspective, because they are utilised in different ways (Bonabeau 2002).
Agent–based modelling (ABM) is able to simulate the individual activities by measuring their
behaviour and results over time for developing models of cities (Crooks 2006). Agent–based
modeling and simulation (ABMS) is a new approach to modeling systems comprised of
autonomous, interacting agents. Agent–based modeling is a new analytical method for the social
sciences, but one that is quickly becoming popular. ABMS promises to have far–reaching effects on
the way that businesses use computers to support decision–making and

The Development Of Advanced Students
Luis Contreras
Lit Review The focus of my study is on the development of advanced students. I feel so much time
is focused on the development of struggling learners, that we as educators lose focus on developing
our most advanced students. Analyze–Write–Pair–Share–Apply is a modified version of Think–
Pair–Share I use in my pre–calculus classes. My pre–calculus classes are composed of mainly 11th
and 12th graders. Aside from students thinking about a problem and sharing their ideas, I added the
component of having them write down and apply their knowledge to similar problems. I am
interested in conducting this study to see how the Analyze–Write–Pair–Share–Apply strategy,
impacts my most advanced students' understanding of the content. I plan on collecting information
through interviews, observations, and surveys. Through my study I hope to gain some insight into
how the Analyze–Write–Pair–Share–Apply strategy will influence my current and future advanced
students. Locke high school is a title 1 charter high school located in Los Angeles, California.
Eighty–eight percent of the students were eligible for reduced or free lunch. The school is composed
of 45% females and 54% males. The majority of the students who attend Locke are Latino 69.0%,
26.0% are African America, and 3% are multiracial. Students at Locke High School are at an
economic

Media Portrayal of Mental Illness in America
Media Portrayal of Mental Illness in America The media in American society has a major influential
impact on the minds and beliefs of millions of people. Whether through the news, television shows,
or film, the media acts as a huge database for knowledge and instruction. It is both an auditory and
visual database that can press images and ideas into people's minds. Even if the individual has no
prior exposure or knowledge to something, the media can project into people's minds and leave a
lasting impression. Though obviously people are aware of what they are listening to or watching,
thoughts and assumptions can drift into their minds without even realizing it. These thoughts that
drift in are extremely influential. The massive impact it ... Show more content on Helpwriting.net ...
This advocated knowledge, education, and social support in hopes of erasing the stereotypes of
mental illness that was installed in society from the beginning. Also, this led to the final reform
movement, which began in 1975 and still continues today. This "community support" era views
mental illness in terms of social welfare. Some problems include education, employment, housing,
and governmental assistance (Surgeon General's Report on Mental Health, as cited in Morrison and
Goldman, 1984). Table 2–10. Historical reform movements in mental health treatment in the United
States Reform movement Era Setting Focus of Reform Moral Treatment 1800–1850 Asylum
Humane, restorative treatment Mental Hygiene 1890–1920 Mental hospital or clinic Prevention,
scientific orientation Community Mental Health 1955–1970 Community mental health center
Deinstitutionalization, social integration Community Support 1975–present Community support
Mental illness as a social welfare problem (e.g., housing, employment) Sources: Morrissey &
Goldman, 1984; Goldman & Morrissey, 1985. In addition to the historical aspect, confusion about
mental health is another reason leading to the perception of the mentally ill. The Surgeon General's
Report on Mental Health, (1999), dispels any confusion by making detailed analogies and
information. Mental health and mental illness are not opposites; they are like two points on a
continuum. The value of mental health is

David Blackwell
David Harold Blackwell was born on april 14 1919 he grew up in Centralia , Illinois , on the Mason
Dixson Line . He was raised by a family which expected and supported working hard and a little
faster than most . Blackwell says he was fortunate to attend a mixed school rather than the all black
school . While he was growing up . Illinois was probably fairly racist . But he was not even aware of
these problems he had no sense of being discriminated against . As a schoolboy Blackwell did not
care for algebra and trigonometry , Blackwell loved Geometry . His junior year he took an
elementary analysis course and really fell in love with mathematics. Dr. Blackwell was appointed a
Postdoctoral Fellow at the Institute for Advanced Study from 1941 for a year . At that time members
of the Institute were automatically officially made visting fellows of Princeton University , and thus
Blackwell was listed in its bulletin as such . This caused considerable ruckus as there had never been
a black student much less faculty fellow , at the University most ... Show more content on
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In 1979 , Blackwell won the John von Neumann Theory Prize from the Operations Research Society
of America and the Institute of Management Sciences. Blackwell mentored 65 Ph.D. students ,
wrote two books and published more than 80 papers during his career . He held 12 honorary degrees
, including from Harvard , Yale , Carnegie Mellon and Howard universities and from the National
University of

Algebra, Logical Thinking, Or Prerequisite For Future...
In order to understand what algebra is we must first look at a problem given to us understand what
the problem is, question ourselves to what is given, and then realize the conditions that are presented
which then helps us plan our strategy to solve a problem. This approach is useful not only in
mathematics, but in other concepts such as in science. In algebra, logical thinking skills are used to
make sense or make connections of a problem in order to find a solution. Mathematicians create
universal analogies to certain topics. For instance, while students might use numbers as tools, they
seek to discover how much there is to know about this world. Even the simplest observations one
might make about this world might even turn to be directly analogous to at least some aspects of the
real world. According to the Mathematical Association of America, algebra is considered to be the
"first subject where students develop logical thinking" (2012). For mathematicians, algebra is
considered the basics or prerequisite for future courses such as pre–calculus, geometry, calculus,
linear algebra, statistics, and advance mathematical courses. Moreover, algebra is known to be a part
of mathematics that includes general letters and symbols to represent numbers that can be
formulated and found by solving equations. Some students fail to build a solid foundation in
mathematics which is why they are unprepared for college and for work. As future math teachers,
we must encourage students to

Human Gender and Mathematics Essay
Human Gender and Mathematics
Is there a difference in the mathematical ability between men and women? Historians have no
precise method of quantifying or comparing their individual accomplishments (Olsen). Not only in
mathematics, but also in many other career areas in the past, women were looked upon as inferior to
their male counterparts. Women were not encouraged to pursue a career in mathematics.
Historically, women were seen working around the home, cleaning the house, taking care of the
children, and cooking the food. Even if they did pursue a career in mathematics, their research was
sometimes viewed as questionable. I will defend the fact that, "Women have the same capabilities of
achieving in mathematics than men do." ... Show more content on Helpwriting.net ...
Hypatia was born in 370 in Alexandria, Egypt. Hypatia was known as a mathematician, scientist,
and philosopher. She was credited with the invention of the astrolabe, a device used in studying
astronomy. However, she was better known for her work in mathematics, primarily for her ideas on
conic sections. Her concepts developed ideas on hyperbolas, parabolas, and ellipses. Hypatia was
the first woman to have such a profound impact on the survival of early thought in mathematics
(Scott). Maria Gaetana Agnesi was born in Milan on May 16, 1718. By the age of twenty, she began
working on her most important work, Analytical Institutions, dealing with differential and integral
calculus. Analytical Institutions also deals with the analysis of finite quantities, problems of
maxima, minima, tangents, inflection points, the analysis of infinitely small quantities, and
differential quantities. She is also known for the curve called the "Witch of Agnesi," which states
that the x–axis is always horizontal and that the y–axis is always vertical (Scott). Maria Gaetana
Agnesi
Sophie Germain was born in Paris on April 1,1776. She collected most of her information from the
Ecole Polytechnique, where women were not allow to enroll. She was first noticed when she
submitted an analysis to J. L. Lagrange under the pseudonym of M. LeBlanc. Lagrange was
surprised when he met LeBlanc, finding out that LeBlanc was really Sophie

Mathematics Is That Of Pi ( Π )
PI (π) One of the oldest and most commonly known and used concepts in mathematics is that of Pi
(π). In the earliest of know human civilizations, people realized the importance of finding the exact
value of π for practical reasons. Even by todays standards, we still only need to know the exact
value of π to a few decimal place values, although that hasn't stopped mathematicians from pursuing
a more accurate representation for its value throughout time.
The earliest know approximations for the value of π have been identified on ancient clay tablets,
dated 1900–1650 BC, from the Babylonian civilization which states the value of π as (25/8) = 3.125.
and from the Egyptian civilization, from the Rhind Papyrus(1650BC), which approximates the value
of π to be (16/9)^2 = 3.1605. Although these earliest of approximations have been proven to be
within 1 percent of todays actual know value, it marks the point of obsession for mathematicians to
find an exact value for π.
The next advancement in determining a more accurate value didn't occur for more than another 1000
years. Around 250 BC, the Greek mathematician Archimedes developed an approach using
circumscribed and inscribed polygons to prove that the value of pi to be between (223/71) < π <
(22/7) (3.1408 < π < 3.1429). This geometrical approach was predominantly used by
mathematicians for the next 1000 years, were in 1630 an exact value of π was found to 39 decimal
palaces.
Sometime around the year 1425, a new approach

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

Chapter 1: Introduction. Professional Development Refers
CHAPTER 1: INTRODUCTION Professional development refers to the development of a person in
his or her professional role. According to Glattenhorn (1987), by gaining increased experience in
one's teaching role they systematically gain increased experience in their professional growth
through examination of their teaching ability. Professional workshops and other formally related
meetings are a part of the professional development experience (Ganzer, 2000). Professional
development for new and veteran teachers rests on the premise that teacher content knowledge and
pedagogical content knowledge, or PCK (Shulman, 1986), directly and positively affects both the
teachers practice and student learning. The National Council of Teachers of ... Show more content
on Helpwriting.net ...
Majority of the research have been case studies, involving a maximum of 10 teachers, a repeated
trend was 2–3 teachers. Generally, the researchers concluded teachers with a moderately weak
conceptual understanding of mathematics have a tendency to use a step–by–step approach to
instruction and only allow students to practice the math computationally. As anyone might expect,
these teachers could only offer limited assistance to students for building up comprehension in what
they were learning (Ball, 1991; Leinhardt and Smith, 1985). When the teachers tried to give an
clarification or explanation, they were not equipped to do so (Borko, Eisenhart, Brown, Underhill,
Jones, Agard, 1992). In some studies, their deficient in conceptual knowledge caused them to teach
incorrect math procedures (Leinhardt and Smith, 1985; Putnam, Heaton, Prawat, and Remillard,
1992.). A portion of these studies contrasted the low level of teaching practices with the teaching
practices of teachers who had greater understanding of math. These studies indicate that a strong
grasp of mathematics made it possible for teachers to understand and use constructively students'
mathematical solutions, explanations, and questions (Ball, 1991; Fernandez, 1997.) Several
researchers found, however, that some teachers with strong conceptual knowledge did not
necessarily use that knowledge to understand their students' mathematical explanations, preferring
instead

Mathematics Is Essential For Life
Mathematics is essential in life. College algebra is a mathematical concept that is currently being
used in biomedical, mathematical, physics, and computer science degrees. This subject is considered
the foundation for advanced mathematical courses. Students typically pursue a University degree in
order to get a decent job after graduation; however, once hired, they are deficient in able to solve
complex problems. This is due because of their lack of ability to use logical thinking. College
algebra may be complex for some, but if one trains our brain to solve complex problems we will be
able to succeed in the real world. From personal experience, college algebra is known to be a basic
in order to receive a mathematical degree. With that said, without the rules of exponents and
algebraic property, we would not be able to solve problems in our future math classes. Society must
be taught algebra concepts as a basic course in the University in order to be able to solve higher
order thinking problems within their life, not just within math itself. In recent studies, students were
interviewed to see how Algebra influenced their attitudes towards mathematics in their careers.
According to Joe Champion, a study was made to "identify the degree to which college algebra
students value mathematical skills" in their future careers (2010). Besides content knowledge in
mathematics, the following skills: inquiry, critical and creative thinking, are necessary to understand
quantitative

Piaget and Vygotsky
Introduction
Cognitive development is interpreted as the gradual orderly development of thinking, understanding
and reasoning processes from birth to maturity. The aim of primary school is to build the knowledge
and the skills children need to have for further cognitive development. Therefore, the constant
development of coginition is very important to young children, because it gives them the basic
understanding towards themselves and the world. As a result, in order to assist and support
children's early cognitive development, teachers apply the ideas of educational theorists such as Jean
Piaget and Lev Vygotsky in teaching.
Review of Literature
Jean Piaget and Lev Vygotsky are two of the most influential ... Show more content on
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Furthermore, in mathematical center, it involved large numbers, it equipped children with numeracy,
logical thinking and problem solving skills. In learning center, all children's motor skills have
developed, especially for Down's syndrome child Hilly, her fine motor skills has developed through
finger painting. For children who are into game making by using blocks, their thinking process
become more organized and strategic.
In conclusion, most of children are in preoperational stage, but heading to concrete operational
stage, they gradual gain more logical thinking skills and reversibility through game making,
discovering and problem solving. Nevertheless, Troy and Tim are likely functioning in concrete
operational stage. Troy and Tim both have more logical and organized thinking process than others,
since Troy can solve math problems and Tim made a skateboard from the heater. A singing center
would be more helpful towards children's literacy and pragmatics skills through sing nursery
rhymes.
Discussion
In order to help children's cognitive development, the application of Piaget and Vygotsky theories
are highly positive and critical. As Woolfolk and Margetts (2010) mentioned, teachers can extend
children's knowlegde by using children's disequilibration as the motivation. The use of cultural tools
in classroom can also benefit children, because they

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