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Math Tables By Third Grade


Q. Kids today just don't seem to know the math facts, at least not as thoroughly as we did. The teachers seem much more interested in group projects in which the kids discuss math concepts and story problems. They don't seem to want to make the kids knuckle under to good, old-fashioned computation and drills. But nobody likes rote learning, like endless worksheets. What's the answer?


Rote learning! All it means is that you know math facts by heart. Memorization isn't torture. It isn't poisoning the kids. But a lot of Whole Math educators have been brainwashed into that false belief. Miraculously, somehow, without memorizing the multiplication tables or getting a lot of practice doing division problems with pencil and paper, kids are going to able to grasp the concepts in complex story problems and understand the math that it takes to solve the problems presented . . . out of thin air, and certainly not because they were instructed!

Where are Whole Math educators getting that idea, that math prowess happens by a happy accident of fate? It appears too many teachers are being misinstructed in schools of education, by professors who themselves have been misinstructed. After all, "progressive education" has now been championed in the colleges of education for decades. If you're for memorizing math facts and practicing math problems to the point of automaticity, you aren't "progressive." You're "backward." It's been that way for decades. So now we are not just dealing with one miseducated generation: it's closer to three.

For example, teaching math without teaching students the addition/subtraction and multiplication/division tables in second or (at the latest) third grade, is a bit like teaching English, including vocabulary and use of the dictionary, without having taught the students to memorize the alphabet.

Quite often, it doesn't even occur to the teachers to ask questions that require mental math computation with no paper, pencil, calculator or computer assistance. Many or most of them would not know how to answer these questions themselves.

The convoluted, counter-productive reasoning has wreaked all sorts of havoc in math classes over the years. One longtime math teacher wrote, "We teach simple equations without letting students know that you can move items in the right order from one side to the other side of the equal sign by just reversing the operation on the second side. Instead, we insist on slowing them down and complicating things by teaching them extra, time-consuming steps that just complicate things."


Another example: "When I teach simple equations in second and third grade, I often insert a question mark instead of a number. That never bothers these bright rascals. With simple numbers -- say under 10 -- they can tell me immediately the value of the question mark. And then I may say: 'Hey folks, do you mind? -- I hate question marks. What if I erase the question mark and replace it by something else, like a capital 'A'? Now what is 'A? They always think that is a stupid question and 'A' has the same answer as the question mark. And then I might even slip in an 'A' and a 'B.' Well by that time, I have sneaked in a bit of basic 'algebra'  with one or more 'unknowns' and with one or more equations. Then I tell them at the end of the session, that they have just learned some basic 'algebra', and they go home and brag to their parents what that crazy visiting teacher made them learn today. I also tell them that we adults use the word 'algebra' just to scare the pants off youngsters like them."

He added, "You bet they remember these simple discussion when they finally get introduced to algebra, formally, some time in middle schools -- usually in the 7th or 8th grade."

Another point to ponder: "I believe our types of textbooks and our kind of teaching are inexcusable. Instead of using the KISS principle (Keep It Simple, Stupid), we use the principle of LSHCWCMT (Let's See How Complicated We Can Make Things). It also enables the math experts to show how much smarter they are and how much more they know than our kids."

Homework: Review the solid, back-to-the-basics math curriculum sold by Saxon Publishers,


By Susan Darst Williams Math 07 2008




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