2.1 What is mathematics all about? The assignment brief suggests two viewpoints: (1) Mathematics is a given body of knowledge and standard procedures that has to be covered or
(2) Mathematics is an interconnected body of ideas and reasoning processes

2.2 The first viewpoint considers mathematics as a discipline consisting of rigid compartments of knowledge with set techniques and routine algorithms. The second viewpoint suggests that mathematics is made up of interlinking ideas to be developed through experimenting and investigation.

2.3 From a teaching and learning point of view, one’s conception of the nature of mathematics is considered to have a profound impact on one’s teaching practice. According to Hersh (1986), the issue is not “What is the best way to teach but, What is mathematics really all about?” (Grouws, 1992, page 127).

2.4 The perception of the nature of mathematics not only influences how the subject is taught, but also has implications on how mathematics education for school is defined. Indeed, Ernest (1991) states that the view of the nature of mathematics together with the social and political contexts are seen as the key factors affecting curriculum planning (Ernest, 1991, page 125).

2. Literature Review

3.5 Lerman (1990) has identified two contrasting themes concerning the nature of mathematics, namely the absolutist and fallibilist views. According to him, they correspond to the two competing schools of thought in the philosophy of mathematics suggested by Lakatos (1978): Euclidean and Quasi-empirical. The former considers mathematics to be based on a body of unchallengeable truths whilst the latter sees mathematical knowledge a result of a discovery process involving conjectures, hypotheses and refutations.

3.6 Ernest (1996) explained that absolutism considers mathematics to be timeless and a priori knowledge. In his view, teachers who hold...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available arePlimpton 322 (Babylonian mathematics c. 1900 BC),[2] the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC)[3] and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-calledPythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greekμάθημα (mathema), meaning "subject of instruction".[4]Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning andmathematical rigor in proofs) and expanded the subject matter of mathematics.[5] Chinese...

...Level 1/Level 2 Certificate
Mathematics
Specification
Edexcel Level 1/Level 2 Certificate in Mathematics
(KMAO)
First examination June 2012
Edexcel, a Pearson company, is the UK’s largest awarding body, offering academic
and vocational qualifications and testing to more than 25,000 schools, colleges,
employers and other places of learning in the UK and in over 100 countries
worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of
vocational qualifications from entry level to BTEC Higher National Diplomas,
recognised by employers and higher education institutions worldwide.
We deliver 9.4 million exam scripts each year, with more than 90% of exam papers
marked onscreen annually. As part of Pearson, Edexcel continues to invest in
cutting-edge technology that has revolutionised the examinations and assessment
system. This includes the ability to provide detailed performance data to teachers
and students which help to raise attainment.
Acknowledgements
This specification has been produced by Edexcel on the basis of consultation with
teachers, examiners, consultants and other interested parties. Edexcel would like to
thank all those who contributed their time and expertise to its development.
References to third-party material made in this specification are made in good faith.
Edexcel does not endorse, approve or accept responsibility for the content of
materials, which may be subject to...

...mother of Europe's languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all."
- Will Durant, American Historian 1885-1981
Mathematics is an important field of study. Mathematics is essential as it helps in developing lots of realistic skills, in fact study of mathematics itself include the concepts related to the routine lives of human. It not only develops mathematical skills and concepts, it also helps in developing the attitudes, interest, and appreciation and provides opportunities to develop one’s own thinking. So, mathematics is undoubtedly a discipline which is imperative to know and study. Figure 1 clearly specifies all the skills that are developed by the mathematics. Mathematics starts from simple things and linear thinking that lead towards the more complex things and higher order thinking skills. Mathematics has taken centuries to develop in its present form and that’s why it will be really fruitful to know about its development.
Fig. 1, Importance of MathematicsC:\Users\naveen\Desktop\Untitled.png
Mathematics has played a very significant role in the progress and expansion of Indian culture for centuries. Mathematical ideas that originated in the Indian subcontinent have had a...

...Week 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To obtain the opportunity to take your final exam you should have delivered at least 6 activities.
Please keep this Agenda at hand so that you can deliver you assignments on time.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Bibliography
Posted on: Thursday, October 3, 2013
Hello guys,
The books we are going to use are:
Text book:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68391-3
Workbook:
Richards, Jack C. & Sandy, Chuck (2009). Passages 2 (2nd ed.). New York, N.Y. Cambridge University Press.
ISBN 978-0-521-68393-7
Make sure they are the 2nd. edition, because the 1st. edition is completely different.
In your course, in the Bibliography Section you have a link of a bookstore where you can buy the books. You can try other bookstores in your city, of course, but they don't usually have the book in stock.
Greetings,
Blanca Alanís
Posted by: BLANCA HILDA ALANIS PENA
Posted to: CEL.HI09107V.343.13320 Inglés VII
Grading in the courseWeek 5
Final Exam
Continuous schedule from Friday , November 1st. 9am until Saturday , November 2nd., 23:59pm.
Monday, November 4, 2013
20%
100%
To...

...concrete model.
Looking on the locality of the paper, I highly acknowledge the fact that the researchers described the current state of math education in the Philippines. They emphasized the fact that we are more focused on procedural knowledge rather than the more desired conceptual knowledge. That is our disadvantage because we usually train students to perform math without understanding or making connections on what they are doing. By mentioning this, the readers would really have an idea that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as implementing the same study but now comparing it to the results gathered from high and low performing students....

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know today.
From the notched bones of early man to the mathematical advances brought about by settled agriculture in Mesopotamia and Egypt and the revolutionary developments of ancient Greece and its Hellenistic empire, the story of mathematics is a long and impressive one.
Prehistoric Mathematics
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known...

...SYMMETRY
Symmetry is everywhere you look in nature .
Symmetry is when a figure has two sides that are mirror images of one another. It would then be possible to draw a line through a picture of the object and along either side the image would look exactly the same. This line would be called a line of symmetry.
There are two kinds of symmetry.
One is bilateral symmetry in which an object has two sides that are mirror images of each other.
The human body would be an excellent example of a living being that has bilateral symmetry.
The other kind of symmetry is radial symmetry. This is where there is a center point and numerous lines of symmetry could be drawn.
The most obvious geometric example would be a circle.
Geometry is the branch of mathematics that describes shapes.
Sphere:
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball.
The shape of the Earth is very close to that of an oblate spheroid, a sphere flattened along the axis from pole to pole such that there is a bulge around the equator.
Hexagons:
Hexagons are six-sided polygons, closed, 2-dimensional, many-sided figures with straight edges.
For a beehive, close packing is important to maximise the use of space. Hexagons fit most closely together without any gaps; so hexagonal wax cells are what bees create to store their eggs and larvae.
Cones:
A cone is a three-dimensional geometric shape that...