Math Tables By Third
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?
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!
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.
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
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, www.saxonpub.com