Math+as+an+AOK

Math Q: How did they discover the area, circumference and diameter? How many moons would fit inside the earth? What is the velocity of the moon? How many craters are there in the moon?

http://www.nasa.gov/worldbook/moon_worldbook.html

What is the escape velocity of the moon?

2.38 km/s

http://en.wikipedia.org/wiki/Moon

Does the distance between the moon and the earth change over time?

Yes, The distance of the moon from the earth increases by 38 mm per year.

http://en.wikipedia.org/wiki/Moon

What is the size of the moon compared to other moons? What is the diameter of the largest crater on the moon that can be seen on Earth by the naked eye?

Tycho

It is located in the southern lunar highlands.

http://en.wikipedia.org/wiki/Tycho_%28crater%29

How inclinable is the moon?

**Math as an Area of Knowing**

 * With the Moon as our starting point to link the Ways of Knowing (WOK's - Think PERL) and the Areas of Knowing (AOK's - Think IB Hexogram - Math / Natural Sciences / Human Sciences / Arts / History) we will a) make sense of some of the Math questions raised in our Moon Perception exercise and b) have fun interpreting some quotations about Math as an AOK.**


 * Copy the following onto your Math page and add your thinking:**


 * A. Record here 3 Math Questions raised in class that interest you. Then under each write your answer/s and reflect on your process for expanding your knowledge in that area.**


 * Q1.**


 * Q2.**


 * Q3.**


 * B. Read the following Math quotations (some you may have heard before) and below three of them, write your interpretation of what you believe the author is trying to say.**


 * "Mathematics is neither physical nor mental, it's social." Reuben Hersh, 1927-**


 * "The useful combinations (in mathematics) are precisely the most beautiful." Henri Poincare, 1854-1912**


 * "Mathematics is the abstract key with turns the lock of the physical universe." John Polkinghorne, 1930 -**


 * "Everything that can be counted does not count. Everything that counts cannot be counted." Albert Einstein, 1879-1955**


 * "The mark of a civilized man is the ability to look at a column of numbers and weep." Berterand Russell, 1872-1970**

This quote means that mathematicians can look at simple things and be able to turn it into something more logical and produce theories and formulas. Without simple things, mathematicians are not able to come up with complicated theorems.
 * "A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96**

In the earlier years, math was discovered little by little, as people discovered and invented numbers people, specifically mathematicians, see numbers more than what they are. They were able to come up with formulas and theories that eventually lead to more discoveries.
 * "Mathematics began when it was discovered that a barce of pheasants, and a couple of days have something in common: the number two." Bertrand Russell, 1872-1970**


 * To speak freely, I am convinced that it (mathematics) is a more powerful instrument of knowledge than any other..." Rene Descaret, 1596-1650**

This means that different people have different interpretations of numbers. Math is not all about the formulas, people solve things differently.
 * "Instead of having "answers" on a math test, they should just call them 'impressions", and if you got a different "impression", so what, cant' we all be brothers?| Jack Handy 1949-**

Math helps me misunderstand the world?

Math helps me misunderstand the world because in math, calculations, measurements, and accuracy are involved. If miscalculations occur, there would be misunderstanding and misinterpretations of data. Math might not be used as a way to communicate to everyone since not every one is good at math specifically the ones who doesn’t receive proper education. Math is also a more complicated way to, for example, give directions whereas if you describe the place it would be so much easier. In math, it would be difficult for you to understand what people are saying if you don't know what the formula is or if you haven't learned that certain topic. Math may be used in our everyday lives like simple arithmetic (Addition, Subtraction, Division, and Multiplication), but the things we learn nowadays like trigonometry, functions, calculus, etc aren't really needed and applicable to our day-to-day activities except for those who specialize in this field. It only causes confusion to some people, especially to those who are not completely interested in math. Math is like learning a new language but it is more than just memorizing formulas and equations but it focuses more on its application

** Option III ** – Define mathematics as an area of knowledge and write a 200 word essay: · describing the definitions you found in your search. · Explaining YOUR choice of definition (yes, it is o.k. to create your own new or hybrid definition) · Give examples (interesting ones) from your life that helps the reader understand your definition and perhaps convinces the reader that your thinking makes sense.

Mathematics is the use of numbers and symbols to study measurement, properties, and relationships of quantities. In Mathematics, answers to questions are more definite. It is a very rigorous study, and requires accuracy in computations and measurements. Mathematics can lead to endless possibilities (Infinity), and can be applied to our daily lives. For instance, when deposit your savings in the bank, you can compute for the compound interest or annual interest to see how much you pay the bank and have a better idea on how to save more money. Another simple example is when you bake and you follow a recipe, if you are inaccurate with your measurements, you would likely end up with a disastrous meal, whereas if you follow the recipe and use the measurements correctly, you would end up filling good with the meal you made. Mathematics has made a tremendous change ever since the invention of numbers. It has made our life a lot easier and more convenient.

http://education.yahoo.com/reference/dictionary/entry/mathematics

Mathematics and knowledge claims

Can a mathematical statement be true before it has been proven?

Yes

Based on our perspective, We believe that a mathematical statement can be accepted as true before it has been proven. Consider the three types of triangles that we know such as isosceles, equilateral, and obtuse. As we all know, isosceles triangles have two equal sides, equilateral triangles have the entire length sides equal, and obtuse triangles doesn’t have any equal sides. If we have given numbers, we can prove if the statement is true or not. But we would say that some mathematical statements just like this example could be true without being proven because of the knowledge that we know about it and another reason could be maybe someone else discovered it a long time ago.

Some mathematical statements can be proven and at the same time can be accepted as true without being proved. For instance, we all know that complementary angles form a right angle and it add up to 90. So if we are given two angles, let’s say, we have 60 degrees and 30 degrees, we can do the math to prove that it is complementary but even if you didn’t prove it, you will still know that if it is complementary or not because of the shape of the angle.

In some cases, We think that we mostly depend on our own perception rather than being reasonable that’s why we consider our knowledge as the truth.

No

No, I do not think a math statement can be ture without proving, the whole basis of math is on proving, showing that one statement leads to another, and math unlike the other sciences cannot be experimented on, and therefore the only was to know if a statement or true or not, is by supporting your statement with sufficient proof.

For example we all know fire is hot, but how did we know that? We touched it and got burnt, there was proof to support that when a body of lower temperature comes in contact with a body of higher temprature, the heat starts to flow form the body of higher temperature to that of the lower temperature. But this is an experimental setup, math is does not support this kind of experimental knowledge, therefore moving to a non-experimental example would be any math sum, trigonometry for example, one would not know that a particular statement is true or false, the only way of finding out is by equating the right hand side (RHS) to the left hand side (LHS) and by doing so we are providing proof.

Another question that occurs is, then would all the statements not proved be false? For example we have not proved what is infinity, or what is a number divided by zero, why is it called undefined? Is it because we cannot prove what is a number divided by zero it is called undefined.

Mathematics and knowledge claims

Can a mathematical statement be true before it has been proven?

-It is possible, depending on the situation

-Example: If we’re given a simple equation: 3+x=5, even before proving that this statement is true it is already true because we know that 3 plus some number is equal to five. But we use proofs to validate the statement. If we solve for x now, we transpose 3 to the other side. Then we get x=2. And then we substitute 2 to x, then the statement will be 3+2=5, then we are now certain that this statement is true.

Another example is if we have this series: 2, 4, 6, and 8. We know that this series is even and it is true because we know the definition of even, that it must be divisible by 2. If we then prove it to verify our answer, we solve for the common difference of this arithmetic series (U2-U1) 4-2=2. Then we just proved that our answer is valid. That 2+2=4 then 2 added to the previous number gives us the next number. The series given is true even before we proved that it is.

-What are proofs for? To prove that the mathematical statement is true or to validate and back up our answer.