Algebra and Statistics

Algebra and Statistics

Please look at the article (you may vene want to read the whole thing)

http://www.newyorker.com/reporting/2008/03/03/080303fa_fact_holt

I am pasting:

In Dehaene’s view, we are all born with an evolutionarily ancient mathematical instinct. To become numerate, children must capitalize on this instinct, but they must also unlearn certain tendencies that were helpful to our primate ancestors but that clash with skills needed today. And some societies are evidently better than others at getting kids to do this. In both France and the United States, mathematics education is often felt to be in a state of crisis. The math skills of American children fare poorly in comparison with those of their peers in countries like Singapore, South Korea, and Japan. Fixing this state of affairs means grappling with the question that has taken up much of Dehaene’s career: What is it about the brain that makes numbers sometimes so easy and sometimes so hard?

Let us use the idea of the article in our class. Let us empower ourselves to re-own our original number sense that was stolen through too many abusing math teaching situations over many years.

I will also explain more in class but am inviting you to try it before.

For example listen fist to what one of the most insightful young mathematician Manjul Bhargava shares about the Fibonacci Sequence and numbers and music (you can google or just try:
http://www.npr.org/templates/story/story.php?storyId=4111253

The talk is very enlightening and connected actually to statistics.

In order to understand it (we will also explain in class) you need to understand how to choose subgroups from a bigger group (I call it mother group) and you can use google to confirm:

For example group of 4 people (say A B C D) Now, how do you choose 2 out of them?
Answer: AB AC AD BC BD DD (6 possibilties) I type in google 4 choose 2 and get 6. Isn't that fun?
Now it is time to play and feel the Math:

Say 6 choose 3 : Mother group: ABCDEF 3 subgroups: ABC ABD ABE ABF ACD ACE ACF ADE ADF AEF BCD BCE BCF BDE BDF BEF CDE CDF CEF DEF
I counted 20 all together: To check in google I typed 6 choose 3 and got 20 also. Also there is a logiccal formula that is very simple to remember through example and seeing the pattern:
5 choose 1 = 5 7 choose 1 = 7 etc...
5 choose 2 = 5*4/1*2 (=10) 5 choose 3 = 5*4*3/1*2*3 (=10) etc...
6 choose 2 = 6*5/1*2(=15) 6 choose 3 = 6*5*4/(1*2*3) (=20) etc..

Make up your own problems and just have fun playing. It has also applications to Statistics and the Fibonacci sequence (Lynn is going to talk about it)


If you allow time with this exercises you will not only learn and invent (create anew in your mind) math but you will learn important facts related to algebra and statistics.

Here is an exercise that can be good food for your brain and help you connect with Algebra and Statistics.

Look at (a+b)^2. It is (a+b)*(a+b). Now follow the patten of make words (you do not have to see it as multiplication but just as a word game)
The only rule of creating words is that you join letters from the first (a+b) to the second and keep order. Do it many times until it becomes like a rythm (natural). Also say the letters when you do it.

aa ab ba bb

after you feel good add the + sign a*a + a+b + b*a + b*b and finally combine to a^2 + 2*a*b + b^2

Now do it for (a+b)*(a+b)*(a+b)
aaa aab aba abb baa bab bba bbb
do many times until it is fluent. The combine. Your distilled final product will be a^3 + 3*a*2*b + 3*a*b^2 + b^3