Mathematics (from Greek "knowledge, study, learning") is the study of quantity, structure, space, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858-1932), David Hilbert (1862-1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions. Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.

Who invented the addition sign??
The plus or addition sign was invented by Michael Stiple in 1544.

MULTIPLICATION OF FRACTIONS
Multiply the top numbers (the numerators).Multiply the bottom numbers (the denominators). Simplify the fraction if needed.

The reciprocal of a fraction is obtained by interchanging the numerator and the denominator, i.e. by inverting the fraction. Ratio
It is a relationship between two quantities.
REDUCING RATIO IN LOWEST TERM
To reduce ratio in lowest term divide the given ratio by their GCF. Proportion
If the...

...often complain about Math and its application in life
• Mathematics is “..the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.”
Body
A. Early Math skills directly correlate to scholastic achievement
• Those who learned most math in Kindergarten had highest scores during further education
• UC Irvine Distinguished Professor of education Greg Duncan conducted a study wherein he discovered the value of Mathematics in the academic development of kindergarteners.
B. Mathematics in Everyday Life
• People compute when they make miscellaneous purchases.
• People create budgets, estimate costs etc.
• Math is often used by most high-profile professions, whether through simple or complex means.
• Skills we learn in Math, such as problem solving and objective analysis help us in analyzing real situations in life.
C. Mathematics for Progress
• A study was conducted by Allan Gottfried that discovered that the more The more math courses students take and excel in, the more likely they are to attain at least a bachelor’s degree.
• Experts say that algebra and other higher math classes lead to good jobs and financial comfort in the 21st century.
• Mathematics is integral in multiple fields and is the foundation for progress towards the future....

...my weak point is. I am not a writing women; I am in love with numbers. Mathematic is my favorite subject since I began to study. My mother is an accountant, and my father is a civil engineer. The first thing that I teach me was to count 1 to 10 with only one year and half. Math is my favorite subject, for three reasons, this subject-matter pushes me to think carefully, be organize when solving math exercises, and the most important numbers are easy to me. For these reasons I enjoy every single day in my job.
First of all, it helps me in my life because I learn to think and concentrate clearly. When I have a Math problem, I read it and try to think in a easy solution. This helps me understand the situation. When I have all the data, I write the formula. I always try not over thinking it, because this can affect the result. My mother told me that math is like a puzzle, like a game.
Second, I am extremely organized with numbers. I always follow all the rules and keep the solutions steps by step in my records. The result need to be clean, which means that anyone can understand the result without my presence. By the time that I have the solution, I feel free
and comfortable. I can only hear in my head, I win, I win!!!
The third and final reason is that numbers are easy for me. Equations, problems, geometry, addition, multiplication and rest are fun to me. I see this...

...Investigation: Intersecting Chords of a Circle
On completion of the investigation I had learned many new important qualities associated with the intersecting chords within a circle theorems. The three theorems studied in this investigation include: Two chords intersecting externally, two chords intersecting internally and the intersection of a chord and tangent. Each theorem can be used to determine different things (e.g. the tangent-chord theorem can be used to determine the approximate distance from the horizon a person is dependant on their height above the earth’s surface).
The most important thing that I learned is how the theorems are derived as well as how to apply these concepts to real life problems. In each case the theorem is derived using similar triangles. By using the similar triangles formed between chords, or tangents and chords, an equation can be formed in order to determine the relationship between certain lengths on the diagram. An example of this for each theorem is:
Example 1
Two Chords Intersecting Externally
By using similar triangles the connection between chord lengths can be seen.
Triangle ACE is similar to Triangle BDE (equal angles)
Example 2
Two Chords Intersecting Internally
By using similar triangles the connection between chord lengths can be seen.
Example 3
The Intersection of a Chord and Tangent
By using similar triangles the connection between chord...

...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
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...

...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...

...Maths and other subjects relation
Mathematics and its importance
Mathematics is a fundamental part of human thought and logic, and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other schoolsubjects such as science, social studies, and even music and art.
Firstly, we ask the question: why does mathematics hold such an important and unique place among other subjects? That is, what is the significance of mathematics in the overall school curriculum? As a point of departure we offer a few thoughts on why mathematics should be treated as an important subject in overall curriculum.
- Mathematics has a transversal nature. If we reflect on the history of curriculum in general, then mathematics (geometry and algebra) were two of the seven liberal arts in Greek as well as in medieval times. This historical role supports the notion that mathematics has provided the mental discipline required for other disciplines.
- Mathematical literacy is a crucial attribute of individuals living more effective lives as constructive, concerned and reflective citizens. Mathematical...

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The study entitled “TEACHERS’ ATTITUDE AND ITS RELATION ON THE MATHEMATICSSUBJECT AS PERCEIVED BY SELECTED SECOND YEAR STUDENTS OF DASMARIÑAS NATIONAL HIGH SCHOOL S.Y. 2010 – 2011” conducted by Aira Shane M. Balmes, Ruth A. Bobadilla and Mika B. Miralles aims to determine whether the perception of the students to the attitude of the teachers has a significant relationship to their academic performance.
The researchers used the Descriptive Research design to describe the characteristics of targeted individuals in an accurate and systematic way. Stratified sampling was also used in the study. This was used because the researchers grouped the respondents according to their sections.
The researchers conducted a survey to identify what are the opinions of the students about their Second Year Mathematics teacher. Questionnaires were used to determine the point of view of students about the attitude of their teachers. To get the desired number of respondents out of the entire population, the researchers used the SLOVEN formula.
Most of the respondents perceived that the following teacher’s attitude which are Enthusiastic, concerned, optimistic, expresses humor, self – confident, well versed on subject matter, challenging, disciplinarian, flexible, explains well, helpful, neat in appearance, punctual, do not play favoritism and strict were done frequently by their second year mathematics...