Math

 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. Does the distance between the moon and earth change over time? Yes. The furthest distance is known as apogee, and the closest distance (on its monthly journey around the earth) is perigee. In addition, the moon is receding from the earth due to tidal friction, at a rate of about 0.85 inches per year Q2.How many moons would fit inside the Earth?

The Moon has approximately 1/4 Earth's diameter, 1/50 Earth's volume, and 1/80 Earth's mass. By volume, 50 moons fit in Earth.
Q3.How many craters are there in the moon? A crater is a large, bowl-shaped cavity in the ground or on the surface of a planet or the moon, typically one caused by an explosion or the impact of a meteorite or other celestial body. The number of craters on the moon is uncountable, because no matter how much you magnify the moon you will still see more craters, the smallest being so small that they are invisible to the unaided eye. The crater pattern is a fractal!


 * 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.**

= Being part of society and culture, it's both internal and external. Internal to society and culture as a whole, external to the individual, who has to learn it from books and in school. = = he means the most useful things in math are the most charming ones. = = Math is the solution for everything. =
 * "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**
 * "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-**

MATH, is it just a subject in school? Or is it more than that?

I’ve learned math since first grade, but off course as I grow up, math gets more complicated and seems more pointless. When I was younger, we’ve learned addition, subtraction, multiplication and division, and it was easy for me to relate it to some examples where we need to use these basic math operations, for example to know how to handle money, tell time, cook, share things, or know how many of any item will be left if some are used. But as we get older math gets more complicated and harder, as we start studying algebra, and here comes the student to a point where he becomes confused and wonders, “why are we studying? We’re never going to use it!” So when do we use math? Do we ever use in real life problems? Or is it just something that we need to study in order to pass the exam and then never utilize it? I would say math helps in so many aspects. If you would never use math after school, you may think taking math or calculus in school is totally useless. Actually, it improves our thinking skills and helps us to understand and clarify the true meaning of a lot of things. All kinds of natural science subjects and engineering are related to math, same with economics, finance and even philosophy. Our brains have the capability to think logically, but if we don't learn "the language of logic" which is math, then our brains wouldn’t have the habit of thinking logically. For example our bodies have the ability to perform ballet, but if we don't take ballet lessons we will either not know how to dance properly, or we'll learn a simple way of dancing and we wouldn’t be capable to dance to a more advanced level. Thinking logically is the same kind of thing, and in order to move beyond basic logical thinking to a more advanced level of thinking logically, we need to learn the steps. Every person in the world would benefit from having an ability to think more logically, whether or not he will ever become a mathematician. So if we think about it, and about the question “how does math help me understand the world?” I would definitely say that math helps me to shed light on and understand some of the questions that we always inquire to know the answers for.

– Define mathematics as an area of knowledge and write a 200 word essay:

Mathematics as defined in the dictionary is a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement”, and this means that it is a study of [|quantity], [|structure] , [|space] , and [|change]. Mathematics is also considered the language of logic, so therefore people who use it will always sound rational and reasonable. This definition says that math is a science, and if we define science, it says, “Science (from the Latin scientia, meaning "knowledge") is, in its broadest sense, any systematic knowledge-base or prescriptive practice that is capable of resulting in a correct prediction, or reliably-predictable type of outcome.” For example in math, we always calculate to find to the right answer at the end, but it’s all based on using the right formula, right method and so on .. If I were to define math, I would say that it’s a universal language because we don’t use Arabic, English or any other languages, we use numbers which makes it a logical lingo, in which we use to travel to another world where everything is lucid, yes I know that math can be kind of complicated, for example functions and logarithms, but still at the end we find an answer for each equation; where in real life, most of the times we can’t find answers to the questions that we inquire to an answer for everyday with our explorations. For example, a math problem that says, “ There are 6 pails, 3 of the pails are filled with water. Can you move only one pail and make a pattern of: full pail, empty pail, full pail, empty pail, full pail, empty pail?” The solution for the math problem is to pour all of the water from the 2nd pail into the fifth pail. Where a question that still remains unanswered is for example “what it truth” and I can give thousands of answers for this question and still not know which one is the right one. So in conclusion, math might seem like a complex subject, but in reality it is the only reasonable subject that we study.

How have technological innovations, such as developments in computing, affected the nature and practice of mathematics? MIRAL, HANOUF, DANA, RAZAN

Technology has affected the nature and practice of mathematics in such a way that it disables us to have the ability to do any sort of mental math, develop our radical thinking and exercise our brains. Developments such as calculators, computers and the applications used, do all the thinking for us where we just sit around, type what we want and wait for an answer. It has affected the practice of mathematics as we are not able to understand fully the methods and techniques used because we are all dependent on a calculator to do everything for us. It can be seen that students nowadays are more dependent on the calculator to do the calculations for them, instead of them broadening their abilities and developing their understanding. Technology also doesn't affect the nature and practice of mathematics in some ways, some would argue, because when we apply complex methods and formulas, we need to know most by heart and learn when to apply them and how. This part of math, technology cannot help us with, although it is used to obtain a final answer, but it's not used in the process of writing and solving the formula or equation. An example would be trying to see which formula, Un = U1 r^n-1 or Un = n/2 (U1 + (n-1) d) to use, to find the amount of terms in a sequence. You would have to use a calculator eventually to obtain the final answer, but technology would not be able to interfere with applying the method, rearranging the formula and simplifying it down. This all has to be done mentally. It depends which way you look at it. There is always two sides to a story, and usually one case would seem more reasonable than the other, although in this case it seems that both cases can work out perfectly, if applied to the correct situation.