We have been using Math Mammoth for math for the past three years. I do not love it, but it is thorough, so I feel that we are covering our bases. It was Common Core aligned before Common Core was implemented. This program is popular with homeschoolers who do not end up shelling up big bucks for textbooks, yet get a complete curriculum.
So how does so called "Common Core math" look like? It looks like offering many different ways and tricks to solve a problem. For example, the third grade addition and subtraction review lists different mental math tricks: counting backwards, completing the next ten, etc. All these are good strategies, what's not to love, right?
Well, since I had two very different kids go through the same curriculum, I can say what I see as the issue. My oldest, who is quite good at getting work done, reads the suggestions, implements then for that page, and then moves on. He might use them in the future, he might not. He might think about them again, he might not. Either way, he can solve those problems when they come up in real-life situations and get correct answers, which means that whichever strategy he chooses to employ works just fine, even if it's not the most efficient one.
My younger one is rigid in his approach. I know that he has better number sense than my older one, but he does not believe in himself. Having all these different approaches to try and remember and use only paralyzes him. He tries to add to the next convenient number, same as they do in this example, but to him, there is no next convenient number, so he randomly guesses: should I add three more? or four more? If I add three, that's fifteen, and if I add four, that's sixteen. And then I have to add some more... meanwhile, he totally lost track of which problem he was trying to solve in the first place. Instead of feeling that he has one solid way to solve the problems, maybe a but clunky and inefficient at time, but the one that will solve them correctly every single time, he feels that there is some unknown magic in picking out a good strategy and then arriving at the right answer.
I wonder how many other kids are there in the classroom like him, who are able to think in one way which works for them, and who are bewildered by all the choice and options. Speaking of choices, in the above example, I was solving coffee change problem differently from the author. I still got the same answer. I would take away four dollars, and get 14$ and then take away 30 cents and get $13.70.
By the way, maybe by doing many. many problems "the old way" and really feeling that you know what goes on is a start to be motivated to find shortcuts and easier solutions? I doubt that many students dutifully subtracted 1999 from 2000 and never wondered what on earth is going on. I think many of them simply wrote "1" in the answer line, only to have teacher grade it as incomplete and be told to show their work, while they mentally figured out the "new math" trick.
I was in Russian school learning my math. Russian math is not known for its flexibility or user-friendliness, but the idea behind it all was that first you drill and practice till you are fluent, and then you can spend time thinking and understanding. I remember being in 6th grade and spending time on the bus thinking about positive and negative numbers, how they add up and cancel each other out. I am pretty sure we were doing much higher math at the time, but since I felt so safe and confident in those properties, I could just mentally play with them.
Then came 10 yo's long division. Now I am confident in my ability to carry it out, but it always leaves me with that teeny wobbly bit because in Russia we were taught to set it up a bit differently than in the states.
In Spain, Italy, France, Portugal, Romania, Turkey, Greece, Belgium, and Russia, the divisor is to the right of the dividend, and separated by a vertical bar. The division also occurs in the column, but the quotient (result) is written below the divider, and separated by the horizontal line.
127|4 −124|31,75 30 −28 20 −20 0I hope that you feel just that tenny bit of anxiety looking at this set-up, and you understand that teeny bit that I feel when faced with American way.
When Math Mammoth introduced it, it was fine, and he practiced, and he got it. Then, this year, they decided to reinforce that division is just multiple subtraction. The way it was set up, it took me a few minutes to figure out what they were driving at! And let me assure you, nobody divides like that, not for any good reason that I can think of.
To check my hypothesis, I tried doing this problem mentally, and I showed it to my husband. Both of us estimated, but neither felt that the suggested approach is the one that we would use if we encounter such a problem (and total lack of paper and pencil to solve it!)
So, yes, Common Core math could be good and could be useful, but I do not think that expecting every student to learn and use every single technique is realistic. Moreover, it is discouraging to students who do not "get it", and confuses the students who like knowing that they already have a tool to tackle the problem.