I remember way back in the day, when I was a teen, my Dad helping me with my math homework. I hated to ask him for help because it invariably worked him up into a frenzy of frustration. He would want me to do the math the way HE was taught and I was adamant that I had to do it the way the teacher showed us in class. He could not figure out why they had to reinvent how we did geometry or algebra. You got the correct answer his way...what's the difference? I refused to do it, explaining I would get in trouble, be the only one doing it that way, that his way was stupid. He would spend an hour attempting to understand my convoluted and, most likely, wrong explanations of how we were taught to do it in class. What should have taken twenty minutes ended up taking an hour and a half with both of us practically in tears. Now fast forward twenty five years.
I live in dread of my second and third graders math homework. Seriously. They are doing multiplication and division and addition and subtraction of two and three (or more) digit numbers.Sounds easy, right? Sadly, there are evenings when I cannot, for the life of me, figure out how they are supposed to do their work. I am not even kidding you with this. One night Sam had to use a certain strategy, I can't remember the name of it now, to solve two digit addition and subtraction. I followed the directions step by step but could not get the correct answer. I KNEW the correct answer because I solved it the good old fashioned way by carrying but I could NOT get it using the strategy he was supposed to use. How could I help him if I couldn't even do it? How frustrating to have the answer but not know how to get there.
Dad...I owe you a big apology. I never got what you were getting so upset about. I mean, it was MY homework. Boy, do I get it now. The math program the school uses wants the kids to know the theory behind the calculations. So instead of just having the kids memorize their times tables in second grade they learn all about arrays and do multiplication stories and draw out big long explanations of how they get to an answer. While I think this is admirable and important and has it's place, I think we are getting caught up in something most kids are not developmentally ready for at 7 and 8 years old. I learned my times tables in the third grade and I have such a distinct memory of that AHA! moment in grade five when I finally got what I was doing when I multiplied. Even though I didn't understand it in third grade or fourth grade, I still got 100's on my tests. I still could do the homework. When I was ready to understand, it all clicked and I went on to do just fine, all the way through Calculus II (with the exception of geometry).
Poor Sam can't even make an array because all his little dots or x's get all mashed up together and his 6 by 7 array gets out of control and isn't a 6 by 7 array in the end so he gets the problem wrong. Even though he can tell you 6 times 7 is 42 without missing a beat. I do the times table flash cards and they know their math facts but there is no getting around the fact that they must still demonstrate the knowledge behind the facts. And they still need to fill in their homework no matter how crazy it looks to me. I do my best. The other night I spent about fifteen minutes figuring out how Sam was supposed to complete his math homework. He had six problems of multi digit numbers he was multiplying together. I had to do the work "my way" so I knew the answer and then figure out how to fill in the worksheet so Sam could get the answer their way. I don't know that their way is easier or better than the way I was taught. Of course, my way is easier for me because it's the way I learned to do it. The way Sam is being taught looks like more work and is very confusing. But maybe I'm biased. You tell me.
This here is the worksheet with all six problems. Does it even look like anything remotely similar to anything we learned in math? Not me anyways.
This is the little formula cheat sheet I came up with to help Sam solve the math problems. Honestly it took me far too long to figure this out. But I was DAMN proud of myself afterwards. Sam, poor little lamb, was not as happy with my little formulas. "But Mumma...there are no A's and B's and C's....." He finally understood what the letters meant when we wrote them above the numbers in the latticces.
A close up of one problem. I look at this and think how easy it is to make a mistake. Put a number in the wrong box. Carry a number into the wrong column, multiply a number with the wrong number. To me, lining them up one above the other and multiplying first by the number in the one's place and then by the number in the tens place and then adding them up is just easier. Less fraught with potential mis-steps. But again, I could be this crochety old fashioned stick in the mud too. What do I know? All I can say is...I quiver with fear thinking of decimals and geometery and algebra. I can't even add, subtract and multiply and divide correctly according to this math program. How am I going to survive middle and high school math?