NAEYC Affirm Analysis

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
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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
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"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

The Mathematics Of Mathematics Into Mathematics Education
Mathematics is a versatile and always changing subject as people research and theorize new ideas.
Calvin Clawson proclaimed that "the single most compelling reason to explore the world of
mathematics is that it is beautiful, and pondering its intriguing ideas is great fun" (2). To make this
subject easier to explore, teachers should be implementing the history of mathematics into
mathematics education. They should do so because of the numerous benefits that it would yield to
students and teachers. Po–Hung Liu stated that integrating history of mathematics into daily lessons
and such will help students and teachers by increasing the students' motivation to learn, help them to
develop positive feelings for math, help to develop students' ... Show more content on
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This issue is not contained exclusively in the United States' education system; it is a worldwide
problem that has effects on people all around the world. Implementing the history of mathematics
into all mathematics education will save millions of students from loathing mathematics without
really knowing what mathematics is truly about or where it came from.
Involving the history of mathematics in schools would prove to very beneficial, but there are not
many teachers today that are very well enlightened on the history of mathematics and how the
implementation of said topic can be beneficial. We cannot expect those teachers to be able to teach
our students about an area of mathematics that they have no to little knowledge in. A study by
Danielle Goodwin made a very interesting and relevant conclusion:
"There are significant relationships between what California high school public teachers know about
mathematics history and their beliefs about mathematics. Teachers with lower history scores are less
likely to believe that mathematics is a discipline for everyone and that mathematics shows cultural
differences. Teachers with low mathematics history scores are more likely to believe that
mathematics is a disjointed collection of facts, rules, and skills, and that everything important about
mathematics is already known" (87).
Having this kind of mindset as a teacher can be very detrimental to a student as it will discourage
them from further

Development of a Math Laboratory at the Professional...
RESEARCH PROJECT PROPOSAL TITLE OF THE PROJECT: DEVELOPMENT OF A MATH
LABORATORY AT THE PROFESSIONAL DEVELOPMENT SCHOOL Presented to the Faculty
Development Committee Dr. Sheila Mehigan Assistant Professor of Education March 11, 2002
RESEARCH PROJECT PROPOSAL TITLE OF THE PROJECT: DEVELOPMENT OF A MATH
LABORATORY AT THE PROFESSIONAL DEVELOPMENT SCHOOL {PDS} PROJECT
SUMMARY This project is being developed for the purpose of funding a math laboratory to be set
up during the 2002–2003 school year where preservice (college students) will work with at–risk K–
5 students at the Professional Development School (PDS) at Jackson Elementary School.
Professional Developments Schools (PDS) are public school settings in which a school district ...
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The simultaneous co–product of this investigation is the potential to help at–risk K–5 students
develop their mathematical communication skills and math efficacy (Nicholls, Cobb, Wood, &
Yackel, 1990) through activity–based experiences. Project Plan This research study will be
completed with two parallel studies. The first study will focus on the preservice teachers enrolled in
a K–8 math methods course at Elmhurst College, EDU330 –– Math for Elementary and Middle
School Students. The second study will focus on the K–5 elementary students at Jackson
Elementary School participating in the math lab sessions. Jackson Elementary School is partnering
with the Education Department at Elmhurst College to form a Professional Development School
(PDS) and thus a collaborative relationship as well as vacant instructional space that provides a
unique opportunity for this project. In sum, the research project has two guiding goals ––
mathematical efficacy and communication. The first goal is to discern the changes in math self–
efficacy in both the K–5 students and preservice teachers. The second goal is to examine if the K–5
students and preservice teachers participating in a math lab, which is centered on reflective activities
and mathematics communication skills, improve as math communicators. Preservice teacher growth
and development in mathematical teaching efficacy

The Importance Of Mathematics In Education
In this paper, I will be writing about the math curriculum, including geometry, taught in schools
across America in grades first through twelfth. In addition, I will also discuss what students in other
countries are taught in the areas of mathematics. Then, we will look at the level of mathematical
knowledge of students in the United States compares to those other countries. Finally, we will find
out if there is a way we can improve our educational system to better our future generations
understand of mathematics. First, we will briefly discuss the importance of learning mathematics at
an early age. One of the most important reasons it is important for children to learn mathematics is
that is teaches critical thinking skills. Sometimes what students learn in math is not so much
important is that it is teaching students how to think. Some math concepts are very involved and not
regularly used but if a student can understand those they will be prepared when faced with real
world problems. Understanding basic math is also an important of basic life. regardless of
occupation, people will need to use numbers in their finances and other areas. In addition, math is
used across many fields to solve problems. Basic calculus principles are the foundation to
engineering. In the United States, education standards are regulated by state governments. From
kindergarten to twelfth grade, the states decide what will be in their curriculum. Starting in 2010, a
set of math and english

Critical Assessment Of Teaching Elementary Students
Literature Review In today's education world, there is a glaring lack of effectiveness of teachers in
teaching elementary students to be successful when solving word problems. Evidence of a need for
improvement in this area is low standardized test scores on these types of problems as well as poor
student attitudes toward even attempting these types of problems (Benko, Loaiza, Long, Sacharski,
& Winkler, 1999). A recent study indicated that today's assessment of mathematics has progressively
become an assessment of student's ability to interpret and perform problems rather than an
assessment of computation skills (Pearce, Bruun, Skinner, & Lopez–Mohler, 2013). Furthermore,
the authors stated that in studying the 2009 state released test, ... Show more content on
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Research shows that although students can read the words in the problems, many struggle with
determining the root information and are incapable of developing an appropriate number sentence or
equation (Van Klinken, 2012). The same author goes on to report that research over a period of
decades demonstrated that students who are weaker at solving problems can be taught to be
successful. To address the problem–solving issues within classrooms, elementary teachers need to
be aware of what strategies or professional developments they can implement to increase student
knowledge, such as applying CGI lessons in with their teaching. Another thing to consider when
investigating the issue of success with word problems in a math classroom is the gender difference.
Whether male and female students learn material differently and solve problems differently would
be necessary to take into consideration when deciding how best to teach these math skills. A study
of gender differences investigated whether there were significant differences in the ways boys and
girls solved word problems. The study showed that there were no significant differences between
the number of correct responses between male and female

Pros And Cons Of Mathematics In Education
American 15–year–olds have inferior performance in international test scores, particularly in math,
than students in many other developed countries. As an American Mathematics teacher, it concerns
me that our neighbor, Canada ranked third in the world to the United States' 24th place in the
average scores of its students on the PISA 2015 reading literacy scale. Canada ranked tenth in the
world to the United States 40th place, below average, in the PISA 2015 reading literacy scale. For
clarification, mathematics literacy is defined as an individual's capacity to formulate, employ, and
interpret mathematics in a variety of contexts... It assists individuals to recognize the role that
mathematics plays in the world and to make the well–founded judgments and decisions needed by
constructive, engaged and reflective citizens (OECD 2016c, p. 5).
Canada has consistently been a high performing country on international assessments of student
performance than the U.S. Canada has many similarities to the U.S. in education with the major
difference of virtually no federal government presence in schooling. The ten provinces and three
territories run the school systems with local districts with elected boards. A 2015 survey reported
that Canada's teachers are among the world's top paid educators with their wages falling just under
those reported by teachers in Germany and the Netherlands, both nations ahead of the U.S in all
three PISA scores ( Kastberg, Ying Chan, & Murray, 2016). Based

Stem Education ( Science, Technology, Engineering And...
STEM Education (science, technology, engineering and mathematics) is one of the most profound
aspects of education today and it is moving the world forward in research. However, in the STEM
occupations, there is a gender gap and underrepresentation of women in the field. For this research,
the gender gap (with women) in STEM education/careers and how it can be reduced will be
examined. Furthermore, it has been hypothesized if teachers encourage and support girls who want
to go into STEM education, it will promote more women to go into STEM careers in the future.
Moreover, the following ten literature reviews will strive to support the hypotheses. In a journal
article, it discusses the progression of STEM, a study that was conducted that focused on the
conceptions of STEM from faculty members and how the faculty members perceived STEM. For
the methodology of the study, the researchers conducted a quantitative study by emailing the faculty
members two survey questions: "What is STEM? How does STEM influence and/or impact your
life" (Breiner, Harkness, Johnson, & Koehler, 2012, p. 4). For the analysis, each researcher
independently read the responses and coded them according to their own schematic (null
relationship, personal reasons, and societal issues) (Breiner et al., 2012, p.5). As a result, "in
response to research question #1, What is STEM? 72.5% (161 of 222) of the respondents described
STEM as it related to science, technology, engineering, or mathematics, yet the

A Study On The Classroom
Alina was observed during the morning in her third grade class. At the start of the observation, Alina
appeared focused and engaged as she worked independently on a math assignment. After a few
minutes, Mrs. Hippchen, Alina's third grade teacher, reviewed the math answers to the class. As
Mrs. Hippchen reviewed the answers and called upon students to provide answers, Alina appeared
focused as she listened and wrote on her math worksheet. She occasionally looked over at a peer's
paper during the activity. When Mrs. Hippchen asked the students to raise their hands if they
obtained the correct answer to a question, Alina raised her hand. At one point, Alina was called upon
to solve a math problem. She incorrectly answered the question, however, with her teacher's
feedback, she was able to correct her answer.
Mrs. Hippchen then instructed the class to clear their desks to start a new math activity. Alina
followed her teacher's direction. As Mrs. Hippchen reviewed a math homework assignment to the
class, Alina followed along appropriately. When the students were asked to draw a diagram to aid
them in solving a problem, Alina appeared engaged as she drew on her paper. After the homework
review, Mrs. Hippchen instructed the class to take out their math workbooks. Alina followed her
teacher's direction as she cleared her desk and pulled out her math workbook from her "cubby." As
Mrs. Hippchen taught the math lesson, Alina wrote in her workbook, listened to her teacher, and

Mathematics Education in America: A Troubled System in...
Mathematics Education in America: A Troubled System in Need of Change
On a trip to Fidler concrete in Goshen, Indiana, a man ordered forty feet of rebar for home use.
When he went to pick up the rebar, the adult employee in charge asked the man what size pieces he
would like. The man asked for six–foot sections. The employee furrowed his brow and said, "Now,
if it were five foot sections, that would be ten of them for forty feet, right?" The man replied, "No,
ten of the five footers would be fifty feet." The employee pondered that and said, "So in the six–
footers...Ah, I'll just give you twelve. That should be enough." This is a true story.
In this one experience, the employee showed a lack of ability ... Show more content on
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Furthermore, numerous studies like "A Nation at Risk" and the Third International Mathematics and
Science Study (TIMSS) have demonstrated decisively that math competency in the United States is
well below the world average. How the only remaining superpower on Earth can see these facts and
not act to improve the situation is incomprehensible.
In the middle of the twentieth century, courses in mathematics were not optional in this country. The
space race with the Soviet Union forced the United States to cultivate mathematicians and scientists
capable of working with complex mathematics, physics, and rocket science. Around the time
Sputnik was launched, student achievement in mathematics reached higher levels than ever before.
Since that time SAT I scores have shown a marked and consistent decline from 1963 to 1983, a clear
sign of decreasing mathematical competency. At the same time America, which used to be at the top
of the manufacturing pyramid, was being surpassed by Japan in automobiles, by South Korea in
steel, and by Germany in machine tools ("A Nation at Risk"). Without the push from the space race,
the need for scientists, engineers, and mathematicians was not emphasized by the government, and
therefore not emphasized by schools. America turned apathetic toward mathematics and a
mathematically illiterate public was the result.
In 1983 the United States Department of Education released "A

Dualness Of Mathematics
Thinking in interdisciplinary terms as I research, the topic of the effectiveness of online
mathematics education, has proved to be both challenging and enlightening. Defining a topic was
the first challenge I encountered. Initially, I planned to research the topic of online education
effectiveness in the general sense; unfortunately, what I found was that there was not a lot
information available that would enable me to find documentation from my two concentration areas
of mathematics and informatics. As Repko (2012) discusses in chapter three of our text, it is
necessary to "define the scope of the problem;" he further mentions it is often found that the scope
of the problem needs to be redefined throughout the STEPS of the ... Show more content on
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193–220).
Repko (2012) mentions identifying relevant disciplines as a key step of the IRP, I have found it to be
a necessary concept to the process thus far (p. 143–145). There is much to be said about this topic
from the perspective of education, psychology, sociology, and even science (technologies).
Understanding how these perspectives have tried to solve the problem is necessary to move forward
with new ideas from the perspectives of mathematics and informatics.
While we were not required to read from chapter six, "Conducting the Literature Review," I did find
it a useful read in preparing for finding relevant documents (STEP 6 of the IRP) for my research. In
particular, Repko (2012) discusses ways to assess a document for relevance to the topic, strategies,
as well as common mistakes; some of his questions such as identifying whether a document offers
new information, is a partial match to the topic, and searching the references of the work – were
very useful as I waded through the mound of documents found (p. 180–182).
With my literature search concluded, I have begun the process of evaluating the ideas of all the
researchers. Of the literature I have thus reviewed, I have found that several them discuss a system
of online content delivery, relating it to student progress. It has been interesting to consider each of
these perspectives and conduct an analysis to recognize both the strengths of the

Teaching, Education, And Teaching Values In The Public School
Even as a young child, I enjoyed the school environment; the safe space in which students can
participate, experiment, and grow both as learners and as people. The messages both implicit and
explicit often aligned with my values of the importance of obtaining knowledge, rational and logical
thought, and hard work. As I have grown older and even through my program at the University of
Wisconsin–Madison, I am more aware of some of the inconsistencies inherent between these values
and our current public school system. As a "smart," white, male student I had a different experience
than many. One of the reasons I want to teach is to spread my largely positive and empowering
experience of schooling to as many students as possible. I could not count the number of times I
have heard "I'm not a math person," "I can't do math," "I never understood that," or similar
comments that reveal negative associations with math in our culture. I have observed and been
shocked at how socially acceptable this viewpoint has become. For example, it is almost unheard of
for someone were to make a similar statement about reading or writing due to feelings of
embarrassment or shame. I have always held the view that math and mathematical thinking are of
paramount importance in modern society. However, as Schoenfeld (2001) argues, this type of
quantitative literacy is often absent in the mathematics classroom despite how crucial it is to
everyday life. My goal is to bring this quantitative literacy into

John Forbes Nash Research Paper
John Forbes Nash, was born on June 13, 1928, in Bluefield, West Virginia, a former coal town deep
in the Appalachian mountains. His mother, Virginia, who was also very intelligent, was a former
teacher who had big dreams for her son, she taught him how to read, learn Latin at the age of
4(Nash, 2). When growing up children are usually really active in playing sports or just playing with
toys outside; however, Nash's parents noticed that he had a great interest in education at a very
young age. On which they started enthusiastically encouraging Nash's education by buying his
science books, coloring books, and being self taught by his mother while his father would work.
In high school Nash's parents, pursued opportunities to supplement his education by making him
take advanced mathematics courses at a local community college called Carnegie Institute of
Technology. Nash was later given a full scholarship for his outstanding performances in
mathematics, the George Westinghouse Scholarship, which led him to major in chemical
engineering. During his last semester before graduating, Nash came in contact with John Synge who
was the Head of the Mathematics Department. Synge and other Mathematics professors quickly
recognized Nash's remarkable mathematical talents and tried to persuade ... Show more content on
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In 2010, he received the Double Helix Medal, it's given to individual who have positively impacted
human health by raising awareness and funds for biomedical research something Nash loved to do.
In 2015, Nash was presented with the Abel Prize award it's an international award given by the
Government of Norway for being the most outstanding mathematician of the year. A Beautiful Mind
is a 2001 American biographical drama film based on the life of John Nash

My Philosophy of a Constructivist Mathematics Education
At what point does a student, in all intents and purposes, experience something mathematical? Does
it symbolise a student that can remember a formula, write down symbols, see a pattern or solve a
problem? I believe in enriching and empowering students' mathematical experiences that
fundamentally stems from a Piagetian genetic epistemological constructivist model that allow
students to scaffold their learning through cognitive processes that are facilitated by teaching in a
resource rich and collaborative environment (Thompson, 1994, p.69).
The student
Constructivist learning in mathematics should endeavour to encourage students to "construct their
own mathematical knowledge through social interaction and meaningful activities ... Show more
A skilled teacher will also construct an appropriate classroom environment where students openly
discuss, reflect on and make sense of tasks set before them (Clements et al, 1990). Through
pedagogical constructivism (Noddings, 1990, p.14) I believe that in order to teach well, "we need to
know what our students are thinking, how they produce the chain of little marks we see on their
papers, and what they can do (or want to do) with the material we present to them (Noddings, 1990,
p.15)." Through pedagogical constructivism, teacher should warrant the use of more effective
diagnostic tools, such as understanding ways of thinking, methodical errors and misconceptions
(Noddings, 1990, p.15). This is achieved by using an array of effective teaching strategies.
Justified Learning & teaching strategies to develop understanding
It is important to note that a student's view of a subject is founded upon the experiences in which
he/she is immersed in and this subsequently forms their expectations of mathematics (Knowles,
2009, p.29). The strategies that teachera employ should be both challenging but achievable and
furthermore within Vygotsky's zone of proximal development (ZPD).
"Realting is the most powerful contextual teaching strategy and is at the heart of constructivism
(Crawford et al, 1999, p. 34)." This is where students draw on their own life experiences and use
their prior knowledge to address a problem or question at hand. It is

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;

The Math Skills Of Asian Children
Abstract Nowadays, many people know about the superiority of the math skills of Asian children.
According to the 2012 Program for International Student Assessment (PISA), top five countries that
do well in mathematics are China, Singapore, Chinese Taipei, Hong Kong, and Korea. All of them
are Asian countries (Weisenthal, 2013). [Context] Asian people are statistically better in
mathematics, especially in terms of mathematics calculation. However, researchers in non–Asian
countries tend to get more achievements in research mathematics. [Subject] Researches in pure
mathematics and applied mathematics are significant as mathematics can be applied in various
areas, such as economics and physics. If Asian researchers' ability in mathematical ... Show more
Nowadays, researches have showed that Asian students are better at mathematics, while most non–
Asian students are better at research mathematics. Although Asian people tend to perform well in
math contests, they tend to be inferior in the area of research mathematics comparing with their
international counterparts. This report will analyze it on many aspects and pay attention to its
significance. Besides, this report will also make suggestions, in order to improve the performance in
the field of mathematics for Asian students and make more contribution to the development of our
countries' science. 2. Comparison of math skills between Asian countries and non–Asian countries.
In Programme For International Student Assessment, a program held by OECD, Shanghai middle
school students ranks first in mathematics level test, outstripping those from other 75 countries,
which is greatly admired by the British people and shocks the western world. By comparison, the
rank of American is 36. Now and then, people in America calls on "saving our students, please".
Afterwards, 60 math teachers in Shanghai middle schools were invited to England to introduce their
experiences in math teaching. Ranks Countries and Regions Scores 1 China( Shanghai) 613 2
Singapore 573 3 HK 561 4 Taiwan 560 5 Korea 554 6 Macao 538 7 Japan 536 ... ... ... 13 Canada
518 ... ... ... 26 United Kingdom 494 ... ... ... 36 America 481 1. A chart of

Algebra 1: Math Curriculum Paper Written by Middle School...
I am a mathematics teacher, with a middle school education degree (grades 5–9) with an emphasis
in mathematics and social studies, teaching at an area high school. I have decided to focus on
Algebra I for this curriculum paper, because it requires more abstract thought and problem solving. I
will address the following areas: curriculum standards (national, state, local (district)), textbook
adoption, community, and design of my classroom. This paper will relate the standards at these three
levels, discuss procedures for adopting textbooks, focus on the community background and describe
my classroom procedures. The first area that I would like to address is curriculum standards.
According to the National Council of Teachers of ... Show more content on Helpwriting.net ...
The Program of Studies lists five critical areas that must be met in the Algebra I class. The first of
the five is linear equations, inequalities, and functions and this area relates to 2.7, 2.8, 2.9 2.10, 2.11,
and 2.12 of the Academic Expectations. Nonlinear functions: quadratics, exponential and absolute
value are related to 2.7, 2.8, 2.9, 2.11, and 2.12. The third area, proportional reasoning connects to
2.7, 2.8, 2.9, 2.11, 2.12, while the fourth area sequences relates to 2.7, 2.8, 2.9, 2.11, and 2.12. The
last of the areas is probability and it relates to 2.7, 2.8, 2.11, 2.12 and 2.13. Now that we know
which Kentucky Academic Expectation numbers relate to the Program of Studies critical areas, we
need to know what each number covers. The Kentucky's Academic Expectations 1.5 to 1.9,
Mathematical Communication and Reasoning; 1.16, Technology; 2.7, Number Concepts; 2.8
Mathematical Procedures; 2.9, Space and Dimensionally; 2.10, Measurement; 2.11, Change; 2.12,
Mathematical Structure; 2.13, Probability and Statistics; Goal 5, Think and Solve Problems; and
Goal 6, Connect and Integrate Knowledge. Every high school course should incorporate problem
solving, mathematical communication, and connections and mathematical reasoning. The Core
Content for mathematics assessment specifics what content will be assessed from the Kentucky
Academic Expectations and Program of Studies. The four areas are the same

Assessing Conceptual Understanding of Rational Numbers Essay
Assessing Conceptual Understanding of Rational Numbers and Constructing a Model of the
Interrelated Skills and Concepts
Students continue to struggle to understand rational numbers. We need a system for identifying
students' strengths and weaknesses dealing with rational numbers in order to jump the hurdles that
impede instruction. We need a model for describing learning behavior related to rational numbers –
prerequisite skills and development of rational number sense – that is dynamic and allows for
continuous growth and change. It would inform us of the important background knowledge that
students bring with them and the prior experiences that influence their level of understanding. It
would further enable us to assess students' ... Show more content on Helpwriting.net ...
What is being suggested is to bring it all together in a practical way. Briefly highlighting various
assessments and reports that have identified and highlighted the importance of conceptual
understanding enables one to trace back to the "hatching" of the idea. In addition, outlining the
course that got us to where we are today, trying to determine what it means to understand something
and how understanding can be assessed assists us in continuing that course of action in the right
direction.
In 1980, recommendations were made by the National Council of Teachers of Mathematics for
reforming mathematics instruction in An Agenda for Action. These recommendations were based on
results of the second National Assessment of Educational Progress (NAEP) and on data collected by
the National Science Foundation (NSF) largely from a study called "Priorities in School
Mathematics" (PRISM). Specifically in the area of fractions, NAEP contended that students'
inability to compute with fractions was the result of dependence on rote memorization of algorithms
and a focus strictly on routine problems. Among eight recommendations, An Agenda for Action
called for problem solving to be the focus of school mathematics in the 80's and basic skills in
mathematics to be more than computational fluency. The fourth NAEP showed improvement, but
indicated that mathematics instruction still lacked depth,

Maryam Mirzakhani And Maria Agnesi
Woman in mathematics are so common now days that we have forgot who the first ladies were and
what they did. These woman did a brave thing, by making people look differently at the math field.
These ladies make a big difference on the world and how woman are looked at in the math world.
Maryam Mirzakhani and Maria Agnesi are only two of the many ladies that inspired all of the
woman to enter the math field. Maryam Mirzakhani, was the first lady to win the Nobel Prize for
Mathematics, this is the highest honor a mathematician can reach. The first Nobel Prize for
Mathematics was awarded in 1936, is worth 15,000 Canadian Dollars. This prize you don't just win
over night, it take a lot of time. Maryam waited 50 years to win this Nobel Prize for Mathematics, it
took all her dedication and time to reserve this award. She is also a professor at Stanford University
in California. Maryam played a big part of inspiring woman to challenge themselves. ... Show more
Hypatia studied with her father at Neoplatonist school. Then later, she became the salaried director
of this school in 400. In "1646–1684" (About.com) Elena Cornaro Piscopia was the second woman
in Mathematic. "Her father also taught all his children personally and then she began to study with
tutors in Latin, Greek, music, theology, and mathematics" (About.com). After Elena was finish with
her schooling, "she became a lecturer in mathematics at the University, where she served until her
early death in 1684" (About.com). These woman where the start of woman in

The National Council Of Teachers Of Mathematics ( Nctm )...
Summary: This article focuses on the positions of both the National Council of Teachers of
Mathematics (NCTM) and the National Association for the Education of Young Children (NAEYC)
stating that having high quality, challenging and accessible math education is essential for 3–6 years
olds, creating a promising future for students. Within their daily classroom setting, there needs to be
a research based curriculum that includes policies, organized support and appropriate resources.
Essential Questions:
Should teachers start incorporating math into all other subjects? Or should math be a stand alone
subject?
Yes should be incorporated into all subjects. Of the 10 things key professionals should incorporate
into high quality math education, number 7 is prominent. It states, "integrate mathematics with other
actives and other actives with mathematics" (Boyd 2008). When children at the early elementary
level are processing knowledge they don 't have each subject sectioned off. When a teacher is
teaching a lesson on math, a child doesn't process that as we are doing math. There brains aren't
quite developed as a "cubbybox", Therefore, if a teacher is incorporating math into all their lessons,
there are many applicable ways students can use math without even knowing. For example, when a
teacher assigns a project or investigation, students must use math to collect date, record information
and any mathematical question.
Should parents be encouraged to teach their children some

The Mathematics Of Math Education
When in math class many students say, "What is the point of math I am never going to use it." That
statement is not true, math is used on a daily basis in our everyday life. "Mathematics is the queen
of science, and arithmetic the queen of mathematics" (Carl Friedrich Gauss). Not only is math a
tremendous part of everyday life but it is also a substantial part of education. Education is
something that many people are passionate about, but many people overlook how much influence
math has on other subjects. Understanding the importance of math in education will help students`
succeed. Mathematics can teach students' information valuable to their future. Math is valuable to
succeeding academically, learning skills, and the development of young children's minds. Math has
been a substantial part of education for a long time. "...According to author David Klein in his paper
A Brief History of of American K–12 Mathematics Education in the 20th Century. During this time,
students were taught basic math skills that had immediate practical applications. After World War II,
policymakers began to advocate for a stronger math curriculum, a movement that increased with the
space race of the 1950s..." (Wile). Math helps students achieve successfully in other subjects such as
reading because in reading you are learning to understand the author`s purpose and vocabulary and
etc. Reading is similar to math because in math there are word problems and in word problems you
have to determine what

Designing Evidence Based Games On Mathematical Thinking Essay
DESIGNING EVIDENCE BASED GAMES TO ASSESS MATHEMATICAL THINKING Saurabh
Khanna Centre for Education Innovation and Action Research, Tata Institute of Social Sciences,
Mumbai The goals of modern mathematics education are progressively being based on foundations
of innovative learning and problem solving skills, the foremost one being mathematical thinking.
Mathematical thinking runs throughout any mathematical activity as a process, and hence cannot be
effectively gauged by prevalent assessments which are outcome based and sporadic. Continuous
assessment interlaced with learning is seamlessly built into the fabric of learning games. There is
also a need to define and standardize measurable evidence in order to quantify abstract
mathematical skills. An evidence based game design framework is proposed to assess mathematical
thinking in students. THE CONTEXT The emergence of 21st century learning and skills has been a
direct consequence of the dawn of a technology driven century where the half life of current
knowledge shrinks by the second. The domain of mathematics has consequently seen a newfound
impetus on learning and innovation skills as defined by The Partnership for 21st Century Skills
(P21). The primary goals of designing learning environments have taken a turn towards
'mathematisation of the child's thinking' (NCF, 2005), rather than just building on core mathematics
concepts. But despite concretizing these modern goals in national policy and curriculum design

Stem Education : Science, Technology, Engineering, And...
Most schools now are pushing for students to have a STEM education only believing that it prepares
them for the world that's becoming highly competitive and complex. When coming across STEM
education what your thoughts? Why do people like STEM and what's the objective of STEM?
STEM is based on four curriculums – science, technology, engineering, and mathematics. STEM
integrates the four into an organized learning template based on real–world applications. It's
showing students how to apply the scientific method in our everyday lives. When schools are
pushing for STEM cuts are being made towards arts and humanities. The future of students is being
chosen for them, they no longer have that freedom to choose. We should not standardize our
education because it just messes up the system. STEM should not be the only best way for an
education to run, the best way for an education is incorporate arts, humanities, and the college
experience a student should have. STEM's main goal is to push students to focus towards a career
that is STEM based. Students should not be pushed towards a STEM career and have no opportunity
to choose for themselves. Authorities want to spend their money, getting students into STEM
because they believe that students would find better job opportunities. Society has gotten so
competitive where the focus is on how to students can get out school fast and start making money.
Many people believe that a STEM education can help solving complex problems.

The Effect of Student Attitudes and Beliefs on Mathematics...
IMPACT OF SMASSE INSET ON STUDENTS' ATTITUDE AND PERFORMANCE IN
MATHEMATICS IN SECONDARY SCHOOLS
IN KOSOFE DISTRICT
BY
BERNARD – SAMUEL – CLEMENT
MATRIC NO: PT/10/22738
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
NIGERIA CERTIFICATE OF EDUCATION
(N.C.E)
DEPARTMENT OF COMPUTER/MATHEMATICS
IN
ADENIRAN OGUNSANYA COLLEGE OF EDUCATION
IJANIKI, OGUDU CAMPUS
JUNE 2013
DEDICATION
To my God the beginner and the author of my life who made it possible for me to start and finished
well. I say thank you for your guidance. Also to my beloved wife, Oluwabunmi, and our great kids,
Aliyat, Bernard Junior (BJ), thanks for all your support, love and encouragement
ACKNOWLEGEMENT
Many people ... Show more content on Helpwriting.net ...
v
LIST OF ABBREVIATIONS / ACRONYMS vi
TABLE OF CONTENTS vii
LIST OF TABLES x
CHAPTER ONE. 1

1.0 INTRODUCTION TO THE STUDY 1
1.1 Background to the study 1
1.2 Statement of the problem. 4
1.3 Purpose of the study 7
1.4 Objectives of the study 7
1.5 Research Questions 7
1.6 Research hypotheses 8
1.7 Assumptions of the study 8
1.8 Significance of the study 9
1.9 Scope and Limitations of the study 11
1.10 Theoretical framework 11
1.11 Operational definition of terms 14
1.12 Summary 16
CHAPTER TWO 17
2.0 LITERATURE REVIEW 17
2.1 Introduction 17
2.2 General Review of literature 17 2.2.1 The learning gap and the need to
improve............................................17
2.3 Review of literature related to Attitudes ...21 2.3.1 Mathematics Teaching in
Nigeria....................................................23 2.3.2 Analysis of attitudes towards mathematics of
standard six pupils...............24
2.4 The process of planned change: A theory of innovation 26
2.5 Review of literature related to SMASSE INSET

Investigation Of Turkish Students ' Mathematics...
Investigation of Turkish Students' Mathematics Performance based on PISA 2012 Objective The
purpose of this study was to investigate the relationship between selected student– and school–level
variables and mathematics performance of Turkish students using PISA 2012 dataset. Two research
questions were investigated: (1) How much do schools vary in their mean mathematics achievement
in Turkey? (2) Which student– and school–level variables are associated with students' mathematics
performance in Turkey based on PISA 2012 results? Theoretical Framework PISA is a 3–year cycle
of international assessment, which has been organized by Organization for Economic Co–operation
and Development (OECD) since 2000. The primary aim of the PISA assessments is to determine the
extent to which young people, who are 15–years old, have acquired the wider knowledge and skills
that they will need in their real–life challenges with considering a literacy perspective in reading,
mathematics, and science. According to PISA 2012 overall results, Turkey ranked 44th, 42nd, and
43rd positions across the 65 countries in mathematics, reading and science, respectively (OECD,
2014b). In this present study, some student– and school variables were chosen to determine if there
is any effect on students' mathematics performance in Turkey. Gender is the first variable coming to
mind when someone starts an educational research because there are not any certain statements;
therefore, the influences of gender on the

Taking a Look at Math Anxiety
Math anxiety maybe unknown to many people and yet many more suffer from it. Math anxiety is
defined as the feeling of tension and anxiety that interfere with the manipulation of numbers and the
solving of mathematical problems in a wide variety of ordinary life and academic situations
(Curtain–Phillips). Other studies suggest that math anxiety not only causes one to feel anxious in a
mathematical situation but also causes a person to completely avoid a situation because of the ones
insecurities of the subject ("Math anxiety,"). What can be done about it? What do I need to know?
What is relevant? These feelings and tendencies all stem from somewhere, therefore knowing where
it originates and what the facts are will ultimately help one to cope and in some cases prevent math
anxiety.
Anxiety in the subject of math is said to be caused largely by failure in the years prior to the
realization of math anxiety. It has been said that due to the methodology of teaching math learners
grow to be more anxious and less confident in their math skills. Methods such as imposed authority,
public exposure and time deadlines tend to have a negative effect to today's generation of learners
(Curtain–Phillips). Also because of math's serious nature, many argue that humor is necessary to
lighten the atmosphere. Young children are entertained by cartoons and jokes and therefore experts
promote their use for discussions or to introduce a concept. Furthermore teachers are being made to

The Most Memorable Challenge In My Educational Career
The Most Memorable Challenge in my Educational Career The great English writer Samuel Johnson
once said, "Great works are performed not by strength but by perseverance". One time in my life
that I remember this being especially true was in my second–grade class taught by Mrs. Whitmore. I
had excelled in reading and writing, and my math skills had been respectable up until that point. It
was time to take on the what was soon to be dreaded multiplication tables. I can flashback to taking
those timed tests with ease; the colorful posters filling the walls, the hushed murmur coming from
all the students as the test was being passed out. I would come to find out these tests would be my
arch nemesis of my whole second–grade experience. I failed over and over again, I got unbelievably
frustrated, and most of all, my little second–grade self's brain was filled with self–doubt and
wondered if I was "stupid" or not. The failure and multiplication tables, and my eventual success
showed me that failure does not always mean incompetence, but a lot of the time it is because of a
mental limitation I put on myself. The first time I failed the multiplication table test will forever be
engrained in my memory. I remember being fairly confident about the test going into it, but I was in
for one of the worst testing experiences of my life. There I was, a little second–grade Tanner, with
the loud buzz of the pencil sharpener in my ears as Mrs. Whitmore walked down the aisles of desks
passing

The Fear Of Math Anxiety
Math Anxiety Anxiety is the most common problems faced by the high school students. High school
students may feel an oppressive sense of sadness, fatigue guild, and hopelessness. Depression is a
common high school students' experience that in one seven may face. Brought on by a combination
of high school students' vulnerable age and the stress and demands of high school life, depression
and related conditions can strike for the first time of the high school students, or come back to haunt
those had first battled in elementary school (Bhattacharjee, 2011). Math anxiety or fear of
mathematics is actually quite common. It is a fear that causes lack confidence, a fear that it is too
hard to control, and a fear that is one won't be able to do the mathematics problems. For the most
part, mathematics anxiety is the fear about doing the mathematics problem right, our minds draw a
blank when we are solving mathematical problems and students think they will fail, they are think
that they don't know what to answer about the problems, they think that they don't have an idea on
solving mathematical problems, more frustrated and insecure minds become the greater chance for
drawing blanks (Russel, 2011). ... Show more content on Helpwriting.net ...
In this study Mathematics anxiety determined the level in terms of cognitive factors, psychological
factors, physical factors and environmental factors. In the study,there are no significant studies
mainly focusing mathematics anxiety, despite the fact that Mathematics anxiety has been identified
in the literature as a problem on the mathematical performance. So these factors find out which
affects the math anxiety of the students (Journal of Education and Vocational Research., Volume 4,
No.3,pp 77–85, Mar 2013 (ISSN

Mathematics Education And The Myth Of Mathematical Education
Mathematics is a word that stirs up many mixed emotions within the general population. Three in
every ten Americans report that they are not good at math, and for the most part their feelings
towards math stay along the same guidelines. Mathematical education in a way can be compared to
teaching a child to play the piano. At first they just watch someone play a tune, and are expected to
copy it without knowing what the keys mean and without much practice. Some succeed and learn
the names of the keys and how they go together while the others are stuck trying to memorize
simple rhythms. Children having a lack in their mathematical ability can also stem from their
learning environment because "sometimes the math teacher contributes to this myth. If the teacher
claims to have had an entirely happy history of learning mathematics, she may contribute to the idea
that some people––specifically she––are gifted in mathematics, and others––the students––are not.
A good teacher, to allay this myth, brings in the scratch sheet of paper he used in working out the
problem, to share with the class the many false starts he had to make before solving it" (Tobias, pg
53). Many people believe the misconception that the ability to do mathematics is genetic; either
someone has it or they do not. This is simply not true, but a purely mental concept. An experiment
conducted by researchers at Stanford and Columbia found that when they told the students that
mathematical ability is a myth showed

The Importance Of Using Manipulatives In The Math Classroom
The Importance of Using Manipulatives in the Math Classroom Can you recall a time in elementary
school when your teacher brought out blocks of all shapes and colors to use in the daily lesson plan?
How he/she allowed you to play and become familiar with the blocks? By exploring the blocks you
were able to visually and physically understand that although a blue and red block are in essences
the same shape, they are different or can be distinguished by color. Not only were your instructors
striving to keep you engaged, they were also utilizing a very important method used in all grade
levels today: Manipulatives. "Manipulatives are physical objects that are used as teaching tools to
engage students in the hands–on learning of mathematics" (Using Manipulatives, 2017, p. 1). From
examining what manipulatives are, the benefits they have on children, and the wide variety of topics
you can teach using this method it is clear that manipulatives are an important tool to use when
teaching mathematics in the classroom. Manipulatives are fundamental and easily available. An
educator is capable of using any object their mind can think of. Wither he/she finds an object at a
discount store, creates them on their own or uses an item that is relatable to their students, they will
all demonstrate the overall idea. "The use of manipulatives enables students to explore concepts at
the first, or concrete, level of understanding" (Using Manipulatives,

The Positive Importance Of Mathematics In Education
Mathematics is considered a science that manipulates symbols according to given rules or
instructions which can also be considered the science of numbers. My belief is that being literate in
mathematics is crucial in this world because I consider math to be the base to explain various
quantitative disciplines in fields such as finance, physics, biology, economics and chemistry.
Moreover, I have always had a positive attitude while solving mathematical problems because there
are so many different ways we can solve a problem such as constructing a graph, an equation, or
preparing statistics. As a child PBL was implemented gradually and I believe it should slowly be
introduced through the years to make teaching and learning more memorable for the students. Some
students believe they were born being incompetent in math; however, I believe that no one was born
being bad at math, they just believe so and as teachers we must motivate those who are in denial to
improve their mathematical skills in order to prevent poor academic performance and develop their
cognitive skills. Being a senior in UTRGV and studying math for more than sixteen years reflects
my positive attitude in regard to this subject. Mathematics has influenced my life positively by
allowing me to study a STEM field degree that will open various opportunities for me. Experiences:
As an elementary student, I would use math every day to solve problems in science, math, or even
while buying a snack during lunch. The

The Importance Of Early Mathematics Education
Early childhood mathematics education is essential in the development and enhancement of the
arithmetic mind of the child. The early age ranges between two to six years with environmental
centers of learning involving kindergartens and preschool care entities. The entirety of mathematics
study includes learning all the basic concept of addition, subtraction, number sense, matching,
problem solving, patterns, sorting, colors, shape, measurements, and more at primary level. Math is
everywhere for the children to learn and it starts at home. Before even enrollment to a kindergarten,
children explore math dimensions in their ecosystem (Bredekamp, 20160.) They make frantic
efforts to navigate space, form unique patterns and try to balance various objects like blocks. All
these dimensions are helping the young kids comprehend and make sense of environment outside
school. These math concepts are essential when transiting to kindergarten from preschool centers.
Parents and educators are critical in ensuring high–quality education to the children. Enhancing the
interest of the subject is vital in guaranteeing complete consumption of the content by having hands
on learning experiences. (Claessens, 2013). The material curriculum and practices of teaching
should account for all the developmental areas. These guidelines are essential in the complete
mastery of early mathematics education. Diverse environment utilization as learning platform makes
learning more enjoyable and fun.
In my

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

Questions On Teaching And Learning
The area of curriculum in which I am interested is primary school mathematics in New Zealand.
Learning and teaching mathematics is an important area of focus and challenge for teachers and
researchers. Children difficulties with like and dislike for mathematics seem to increase as they
progress to higher grades and, as testing become more significant in terms of its intermediate and
lower term consequences. The NZC (MoE, 2007a) provides a distinct statement of the knowledge,
competencies, and values deemed to be important for citizens in the 21st century. Students are
viewed as "lifelong learners who are confident and creative, connected, and actively involved"
(MoE, 2007a, p. 4). The teaching and learning of mathematics was presented in an individual
curriculum document comprising five strands: number, algebra, measure, geometry, and statistics
(MoE, 1992). In 2007, the learning area was renamed Mathematics and Statistics. Mathematics and
statistics are interrelated disciplines but they require different ways of thinking and problem solving.
"Mathematics is the exploration and use of patterns and relationships in quantities, space, and time.
Statistics is the exploration and use of patterns and relationships in data" (MoE, 2007a, p. 26). The
Mathematics and Statistics learning area (MoE, 2007a) emphasises the need for students to be
equipped with effective mathematical abilities, skills, and dispositions. Learning mathematics
should prepare students: to investigate,

Example Of Article Critique Paper
Article Critique
The objective of this article critique is to review and evaluate several empirical studies which have
examined mathematics perception cross–culturally. The main study that focuses on examining
mathematics perception cross–culturally is a study that was done in 2004 by Dr. Yea–Ling Tsao. In
this study, researchers proved that Taiwanese students consistently score higher in cross–national
studies of achievement than American students. Several other studies were done that also support
this theory. Therefore, the main purpose of this article critique is to evaluate Tsao's study in order to
properly assess both the validity of Tsao's design and the inferences drawn from the study. This
critique will also show that, while ... Show more content on Helpwriting.net ...
The researcher's main concern was to investigate differences in math perception between those
students scoring highly versus those students scoring poorly on national exams. The researcher
thought that the solution would be due to cross–cultural differences in achievement.
For this particular study, a survey including 39 closed questions (developed by Alan Schoenfeld in
1989) was used. All items on the survey were in the form of a seven point rating scale, with 1 being
"strongly agree" and 7 being "strongly disagree". The questionnaire was determined to be extremely
consistent with an alpha of 0.8468. The survey contained questions associated to student's
perception of what mathematics is and how to do well in it, what mathematics solutions should be,
how math problems can be solved, how mathematics is learned, and student motivation. For the first
33 questions, the students were asked to rate them on the seven point scale described above. The last
six questions on the survey dealt with grades, gender, and perception of the children's parent's
attitudes towards mathematics. The researcher also used a two–tail t–test to compare the
mathematical perceptions of Chinese and American students. The average of each cateogry in the
survey was also compared. As stated above, there were six main categories being compared: what

Basic Math Facts On Math
Michalczuk‟s (2007) understood basic math facts to be an important skill for students to succeed in
math. Michalczuk (2007) generalized students who could answer single–digit, 0 – 9, multiplication
problems (2 times 3, or 5 times 7, etc.) "Within three seconds will do well at math and those that
answer in less than one second will do excellent at math" (p. 1). Perso (2007) has defined the
"looking back–to–basics" as a need to teach and focus on the basic arithmetic skills needed as a skill
for higher level mathematics learning.
In addition, Hersh (2009) stated that skills in general are more important than ever because they
allow students to further their learning as well as make judgments about the meaning, adequacy, and
accuracy of the overall content. Clavel (2003) stated if students wanted to engage and be successful
in higher–order mathematical thinking skills, mastery of the multiplication table was critical. Henry
and Brown (2008) reported "students who learn to use derived–fact strategies in concert with
memorization are more likely to develop mathematical proficiency than those students who have
memorized the facts without supplementary strategies" (p. 172).
Wallace and Gurganus (2005) identified students who mastered the multiplication facts, not only
acquired a more positive attitude to mathematics learning, but they also developed an overall
positive mathematics experience. Basic math fact fluency provided the necessary foundation to
succeed in higher level

An Analysis of the Essay Math and After Math by Lensey...
Before Reading
Math and After Math
Essay by Lensey Namioka
What are you really GOOD at?
RI 1 Cite textual evidence to support analysis of what the text says explicitly as well as inferences
drawn from the text. RI 2 Determine a central idea of a text and analyze how it emerges and is
shaped and refined by specific details. RI 3 Analyze how the author unfolds a series of ideas or
events. RI 4 Determine the meaning of words as they are used in a text. L 5 Demonstrate
understanding of word relationships.
Knowing what you're good at can take you a long way toward finding work and activities that you
enjoy. In "Math and After Math," Lensey Namioka describes how she first embarked on one career
path and then later discovered her true talent. ... Show more content on Helpwriting.net ...
4. The detective's analytic approach to solving problems led him to the killer. 5. Your hypothesis
will not stand up to further testing.
Complete the activities in your Reader/Writer Notebook.
Author Online
Go to thinkcentral.com. thinkcen
KEYWORD: HML HML9–481
481
After Math lensey namioka
"Seven!" shouted the teacher. Or did he shout "Four"? I shrank down in my seat. Math class was an
absolute nightmare. The teacher scared me so much that my hands got sweaty, and my fingers
slipped on the abacus1 beads. I was in the second grade when I discovered that I suffered from
abacus anxiety. The trouble was that I was going to a school where the teacher spoke a different
dialect. I grew up with Mandarin, the dialect spoken by the majority of the Chinese. When the
eastern part of China was occupied by the Japanese, our family moved inland, to a region where I
could barely understand the local dialect. Writing was pretty much the same in any dialect, so in
language and history classes I didn't have trouble with what was on the blackboard. My problems
started in the math class, where we had to learn the abacus. Before the days of the calculator, the

abacus was the main tool for adding and multiplying. It still is, in many parts of China (as well as in
countries like Japan and Russia). The abacus teacher would shout out the numbers he wanted us to
add or multiply. My ears didn't always understand what he said, so seven, for

Advantages And Disadvantages Of The STEM Strand
Science, Technology, Engineering, and Mathematics or STEM Strand is an academic discipline that
focuses on math and science subjects. STEM strand education creates critical thinkers, increases
science and math literacy, and prepares the next generation of innovators. Innovation leads to new
products and processes that sustain our economy. This innovation in science and mathematics
literacy depends on a solid knowledge base in the STEM areas (Why STEM education so
important?, 2016). It is clear that most jobs in the future will require basic understanding of math
and science. Although we are talking about STEM strand advantages, we cannot neglect the fact that
it also has its disadvantages. Taking the STEM strand may result to some of the students' ... Show
more content on Helpwriting.net ...
First, it helps us to gain more knowledge. Second, it improves our skills. STEM means creating
learning environments that allow students to be more active. Whenever that happens, students are
engaged in their own learning. There's no manipulation in getting students active, either, it just
happens. The outcome is that students better remember what they've learned when they are engaged
in the process, and not passive by–standers (Ken Royal,. 2013). While the core of a STEM
education is a technical curriculum, students will be forced to flex their problem–solving muscles as
related to everyday tasks. STEM program will provide students hands–on challenges, like product
conceptualization and creation, which promote creativity and social skills. Many of the nation's top
engineering colleges require STEM students to take classes in public speaking and humanities, as
well (Rhodes S., 2017). Third, it will help us to decide on what course are we going to take in the
near future. With these statements, we would like to inform you the advantages of taking STEM
strand that will lead us to have a better technology in the near future. STEM strand prepares students
for college and the workforce. STEM education focuses on helping students develop critical
thinking and innovation skills, which is what they will need to succeed after high school. STEM
programs are

Mathematics Is A Essential Component Of The Education System
Mathematics is a vital component of the education system. Children should not only learn to read
fluently and comprehend books. Children should be taught to manipulate mathematical facts in a
fluent manner as well as think critically about mathematics. For students to be able to compete in
today's and tomorrow's economy, they need to be able to adapt the knowledge they are acquiring.
They need to learn new concepts and skills to apply mathematical reasoning to problems (National
Research Council, 2001). As students gain an understanding of mathematics, they engage in
problem–solving situations enhance their rational thinking skills. Teachers ought to provide learning
opportunities that allow students to explore, identify, and create viable ... Show more content on
Helpwriting.net ...
In addition, I insist that students become describers of concepts and their thinking. Therefore, I
implement an array of writing activities for students to explain the process they use to solve
problems. According to Cuoco, Goldenberg, & Mark, (1996), students should be able to manipulate
patterns and provide a sound explanation of the mathematical steps that they apply as they become
independent learners. The practices presented above can help my students develop as rational
thinkers.
Improving learning demands changes in my teaching practices. Teachers should be on an
interminable mission to learn and create new strategies to facilitate instruction. During this course, I
learned new strategies that can help me improve mathematical concepts in the classroom. One
strategy that I implemented recently was the missing factor puzzles. The puzzles are engaging my
students with fun challenges that they enjoy. Factor puzzles increase students' mathematical fluency
and flexibility with multiplication (Laureate Education, 2013). Currently, I am exposing students to
the puzzles as a way to build mathematical fluency. In my classroom, I have assigned a few minutes
of math time to build mathematical fluency. It is during this time that students are presented with the
puzzle and then discuss the solutions with partners. Another strategy that is current

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