Common Core Epic Fail! #geekhumor #math #mathematics
Also see appended edited comment below.
One father, who has an advanced engineering degree, couldn't figure out the approach used to calculate a math problem presented on his son's elementary homework assignment: “Jack used the number line below to solve 427 – 316. Find his error. Then write a letter to Jack telling him what he did right, and what he should do to fix his mistake.”
“Dear Jack, Don’t feel bad. I have a Bachelor of Science Degree in Electronics Engineering, which included extensive study in differential equations and other higher math applications. Even I cannot explain the Common Core mathematics approach, nor get the answer correct. In the real world, simplification is valued over complication. Therefore, 427 - 316 = 111. The answer is solved in under 5 seconds — 111. The process used is ridiculous and would result in termination if used. Sincerely, Frustrated Parent.”
Edited: I posted this as a silly joke I've seen floating around Facebook, but it's turned out to be an annoying political kind of serious debate issue, it seems. So I'll qualify this with a serious comment as well. Btw, it may just be an urban legend -- and it might not have anything to do with actual 'Common Core' curriculum problems.
First, I think teaching difference (or sum) of numbers as distance is useful, and in general anytime
you can visualize something abstract in a concrete geometric way, you can get a better intuitive understanding of what the math is actual doing. This particular one isn't to scale. Btw, the error is obvious to me instantly: he forgot to count off the 1 ten and skipped it, and just subtracted the hundreds and the six ones, and so was off by 10 in the end, so he got 121 instead of the correct 111.
I've taught negative numbers to 2nd graders by introducing them to vectors. One girl showed me a proof of how 3-5 was impossible: she put three of her pencils on her desk, and said, "I can take away one; I can take away 2; and I can take away all 3; but I can't take away 5 pencils when I start with 3 pencils. It's downright impossible." (Boy I wish I had a video of this to post to youtube -- she was awesome. )
So I responded that was a wonderful proof; but that the reason you don't hear older kids say "take away" and say "minus" instead, is that subtraction isn't really taking away -- rather, it's moving left on the number line. So I showed them that if you add, you can put arrows head to tail of the two numbers you are adding, and at the end is the sum. And subtracting, you are adding a "minus number" that points the other way. So I had her, and all of them try it again, on the number line on their desks. They complained, "but the number line stops at zero!" And I said, "in kindergarten, then don't even have a zero -- their number lines start with 1. Well, this is the real answer -- we extend the number line left, just as we do to the right, and now we have answers to all these kinds of problems."
And so that same girl did a new proof: "Ok, I draw an arrow to the right 3 spaces; and then at the pointy end of that arrow I draw an arrow pointing left 5 spaces for 'minus 5' and then at the end it's 'negative 2'. That's the answer." And I said, "you got it!"
Hence, if the illustration is clear and understandable, I think the geometric version gives an intuitive sense of what you're doing. 'Upgrading' that little girl's (and her classmates') algorithm for subtracting was crucial to her intuitive understanding. That's what this pic is also trying to do, but it's just a bit confusing, that's all. The point of the visualization is to give you an understanding how the mat works: you don't want to solve problems that way. In general, I think that if you can demonstrate a visual proof of an arithmetic or algebraic equation, you can get kids to 'grok' what's going on much better. Btw, I also introduced them to multiplication as adding in two directions, making a rectangle, and then counting up the squares in the rectangle. Worked great. But again, that's a visual tool to sharpen intuitions; you wouldn't ever rely on solving problems that way, either.