Math+as+AOK

==** Math as an Area of Knowing ** ==

**Video: [|Phases of the moon] **

**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. How many moons would fit inside the Earth? ** Approximately 30.

**Q2. How much light does the moon produce? ** None, it reflects light form the sun it does not produce light.

**Q3. What is the diameter of the largest crater on the moon that can be from Earth with the naked eye? ** The largest "topographic feature" of the moon that can be seen is known as theSouth Pole- Aitken Basin, it is a giant and has a diameter 2, 240 km. It is the crater on the moon, and the largest in the Solar System.

**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-** This means that knowing math and formulating things from your own knowledge does not mean anything if we do not share math, it should be respected as a language because if we did not use and and talk about, and learn from others there would be nothing more to math then pure numbers. **"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** I believe what this author means is that often when one see's something beautiful or touching it is natural to feel an emotion and usually to express one. Personally to Berterand Russell, it is evident that to himself he seems a civilized man, and man that would be considered orderly and well preserved, yet he feels so strongly of numbers, and it is to him as dance is to me. I think he feels that if he were not as well composed as he was he would weep as a column of numbers. Yet it also has a nonchalant feeling to it, as if he it is so normal for him to weep at the sight of numbers. **"A mathematician is a machine for turning coffee into theorems." Paul Erdos, 1913-96**

**"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**

**"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-** Jack Handy is trying to prove that in so many other subject the freedom of being right or wrong based on ones own interpretations is accepted, yet in math it is not. He attempts to prove that math should be accepted as a free subject, one that is open for interpretation and one that is not closed off the common cliche's of rights and wrongs directly from the rule books. He indirectly states that if we are able to have different "impressions" in english and history, and art, why not in math. I believe that "impressions" are usually what lead many great mathematicians to discover some amazing things.

How does math help me MISUNDERSTAND the world?

==== A common misunderstanding may be described as the simple inability to grasp a concept due to factors that just have not ”clicked” and as one is aware, concepts along with misunderstandings are extremely common in life. Yet the question is how does math contribute to these misunderstandings? As identified in class, math is known as a universal language, one that incorporates the placement, calculation, and formulation of numbers and theorems to arrive at a final answer, an answer that must be undisputable. Whereas, in reality the skills one acquire for math vary drastically to the skills one need for the ‘real world’. In math all of the problems are straight forward, and can usually can be solved using common methods such a2 + b2 = c2. However, in reality nothing is cut and dry, when one is searching for a place to live for example, there is no given method, no rulebook, only passed traditions. Details are also much more necessary in reality then in math, the operations and tasks performed to reach a goal may be varied, detailed and open for question. Yet math is a subject focused on the “correct” method and “correct” answer. Take a proof for instance, the object Is to work with the given information and prove how your method will allow you to achieve the correct answer, in math there is only one right way where mistakes cause you to restart. Whereas in math, there are many ways of reaching a goal, and our mistakes are what leads us on the different paths. ==== ==== From my perspective, math grants one limited knowledge and skills, yes we will always need it, but will our proficiency in ONLY mathematics be sufficient enough to guide us through life? “Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.” ====

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OPTION II

“Mathematics starts with counting. It is not reasonable, however, to suggest that early counting was mathematics. Only when some record of the counting was kept and, therefore, some representation of numbers occurred can mathematics be said to have started.”

· what you think this means to you in terms of math

· what, if anything, does this say about learning or knowledge in general · whether you agree with it or not. Give real life examples.

Dear Text Book Company,

I am writing in clarification as to what the very first lines of your St. Andrews math piece imply. As a student studying mathematics as an Area of Knowledge it is fairly simple for me to deduce that what these lines mean are, that the form of mathematics using numbers, sequences, theorems, formulas and ways of calculation was not actually used to identify early counting. Mathematics only began once numbers or other ways on counting were recorded, but oral counting was not recognized as mathematics. Another noticeable fact mentioned is the concept of ‘learning mathematics begins by learning to count’, yet mathematics did not necessarily originate when counting originated. These few lines taught me quite a bit about knowledge and learning, that as we realize now, many of the subjects and ideas we are taught in school or home are always just concepts, and if we understand them we are satisfied. But now I realize that all of the assumptions we make about these concepts and their history could be complete nonsense, unless we uncover the history. I do agree with this concept to some extent, seen as the dictionary definition for mathematics is “ the abstract science of number, quantity, and space.” This adds meaning to the above statement that only once counting was being recorded did it classify as mathematics counting is essentially recording numbers. Yet it also contradicts the above statement because of the use abstract, should we not be able to make calculations and count without having to record anything? For example we can see a chair, but sometimes we often touch it to prove that it is really there, which is why I trust the judgment and see the sense in the statement. Everything relates to how we know that we know.

Is there a clear-cut distinction between being good or bad at mathematics?

From a teachers perspective: There is no clear-cut distinction, meaning there is no specific line that separates a person from being good at math or bad at math. Yet many math teachers have come to recognize that some students just have a higher order of thinking, that some students are just able to work better with numbers then others, and apply numbers, patterns, formulas etc to real life situations easier then others. From a students perspective: There is also no specific distinction between being good and bad at math, yet it is easier for a student to classify themselves as good or bad based on extenuating circumstances. Such as the topic being studied, the teacher, and their strengths and weaknesses. Other factors that could affect the distinction between being good and bad at math are: Elementary teachers: Our elementary teachers actually have a great affect on our future learning and which of our skills are developed properly or not. For example in 3rd grade I had a school teacher who was going through a lot emotionally, she was absent a lot of the time, and was very distracted when it came to teaching us subjects that she not inherently good at. Our substitute teachers were also very weak seen as they were not real teachers, so as I went through 3rd grade my language skills were fine, but my math suffered due to my unreliable teacher and her knowledge of the content. It is also possible that because I was so young, and the basis of my math knowledge was no developed ideas were not structuring in my brain as they should be. Whereas my brother, who had a teacher who drilled them on their times tables, and really knew her content well, now grasps math concepts extremely quickly. I however have deferred to my language skills. All of us should be born with the ability to recognize numbers and patterns, it depends greatly on our development of those skills, whether we are good or bad at math.