I’ve been watching my 4th grade daughters homework since the school year started with the new Common Core Standards being taught. Camille brought home some math homework the other day that was really basic addition with some other division problems that I will talk about in another post. Since I have a math background and have written on her learning what a rectangle was in Kindergarten I thought that this would be an interesting post. Turning 55 this year it has been interesting to see how she is being taught in the subjects that I love. Here is the problem and solution as it was taught:
9 + 6 = x
9 + (1 + 5) = x
(9 + 1 ) + 5 = x
10 + 5 = 15
While that is correct, to me it is an interesting way to factor to the answer. Now if we replace the non 9 number, which in this case was 6 with y this is how it was done when I was her age. Take 1 off y and add it to the first digit to the left of the 9 and replace the 9 with the new y. I am using 49 instead of 9 to show it with a bigger number below, but with the single digit 9 there is no number in front of it so you assume to add the 1 + 0 where I am using 49 instead of 09.
49 + y = x
49 + 6 = x
6 – 1 = 5
4 + 1 = 5
x = 55
It’s still 3 steps but the answer is the numbers from the two other equations. Lets try it with 3 digits
189 + 8 = x
8 – 1 = 7
8 +1 = 9
x = 197
or when you are in the 3 digits or more in the 90’s, 900’s, etc.
199 + 9 = x
9 – 1 = 8
9 + 1 = 10
Here is the extra step with the carry over 1 in 3 digits or above where you need to take the 1 and add it to the number in front of the second 9.
1 + 1 = 2
x = 208
Carry over is taught in 3rd grade, so students should know how to do that when taught larger numbers. Of course all of this is a matter of opinion, whose teaching and who is the supposed expert at knowing what is the best method. I don’t think there is a best method, but it was curious to me coming from a math background through college Calculus of the changes from when I was younger. The other big difference from when I was younger is that we memorized addition and multiplication tables so we could rattle and answer off without using a piece of paper, whereas I have not seen one flash card or memorization technique from Camille. Not that I’m worried about her because she got a perfect score on in math on the FCAT in 3rd grade last year.
Just some fun math and interesting differences from 1967.
I really like TED Talks. I have a subscription, the app on my iPhone and an email subscription. Today is the 4th of July, the day we celebrate our countries birth and freedom from British rule. But, do we really believe in the ideals of freedom and treating all of our citizens as true Americans with the rights afforded by the Constitution? The following TED Talk made me think about that today. Are we a paranoid, politically correct country that believes in freedom if you are like us, not because you are an American?
Think about it, watch the video, what do think before and after watching it?
I was looking something up and I ran across a opinion piece in the NY times called “Is Algebra Necessary?” I was shocked to read the nonsense babbled by the author that we don’t need Algebra as a subject in our schools as a requirement. Really, Are you listening to yourself Mr. Hacker? That is an appropriate name for this gentleman because it really is a poor point of view on his part. This is especially true because Mr. Hacker is a Professor of Political Science which is the one Science that you don’t have to be right because you make it up as you go in politics. Maybe if you cared more about the skills that Algebra teaches the Political Sciences would be more reasonable and you would see more conflicts settled with common sense problem solving skills. Today’s politicians do no problem solving, they just take sides and place their feet in cement.
I have only one point to make about teaching Algebra as a required course in High School and College. It teaches problem solving skills that are useful in every part of life. It makes you think, it makes you take the time to try to figure something out. There are many studies that show taking more math actually helps in other subjects. One of which I wrote about some years ago “The secret to being good at Science: Take more Math classes”. It says it all. Anyone that thinks you can get by with just basic math in life needs to go back to school, sit in any class and tell me that you don’t see Algebra and its problem solving skills being used.