So, I have been doing a bit of research on Common Core Math and how upset people are getting at the idea of changing the way that these kids are being taught basic mathematics. I will admit, I watched a couple of videos of people opposed to 'common core' ideas and was leaning to their viewpoint, until I realized that they were teaching kids to do math the way I have always done it: simplify the problem.
The example that is given, in the video I watched, is a slightly confusing way to obtain an answer for a basic math problem. They take a problem like 32-20=x and, without explaining the steps involved and what the steps involved are asking you to do, they come up with an answer like this:
And then, instead of telling you why, or making clear the principle behind the numbers, they simply tell you to take the middle row and add them up.
3 + 5=8 +10=18 +2=20
And, low and behold, there is your answer: 20.
This seems so complicated when explained, or not explained, the way they did. There is no wonder that parents, with nothing but viral videos to learn from, are so opposed to it. What they are really teaching these kids is that they need to identify that there is a difference between these numbers and they are finding simpler solutions to help them find why they are doing the steps they are doing.
We are subtracting 12 from 32, so we know that we need to find the difference between the two numbers.
Take the first step: 12+3=15 . ... .. why did we start here? Honestly this is meant to bring people to numbers that are easier to deal with, simplifying their thought process. Personally, I would have started with 12+8.
So 12+3=15, add 5 more to get to 20 (another easy number to work with, add 10 more to get to 30, and then add the remaining two. In my mind, I would have thought it out as 8+10+2, doing these steps in my head.
The reason for the grid is to give kids a way of organizing their thoughts and making it easier to write on paper.
If you don't think you do this, take the question 15*5=x. You could put it on a multiplication table, bring your numbers down, and get the right answer, but it didn't teach you why you were doing it. In my mind I would simplify this and say 5*5=25 , 10*5=50 , 25+50=75. A quick process in my head, but I surely don't build a multiplication table unless absolutely necessary.
Keep in mind this is the basic math stuffs, I have not looked into the more complex, nor have I looked into any other subjects.