Featured
Article
Math
Magic
Article By: Lisa VanDamme
VanDamme
Academy
Most
math curricula are an absolute pedagogical mess.
I
have long known that math programs treat children
like human calculators, programming them with
processes they use to input numbers and churn
out results. But this became poignantly clear
to me when I tried to teach my daughter long
division this summer.
Confronted
with a problem such as 2,832 divided by 8, I
began my "explanation," hearkening back to the
process that had been drilled into me in third
grade. "8 goes into 28 how many times? 3. So
you write a 3 above the 8. 8 times 3 is 24.
Subtract 24 from 28 and you get 4. Then bring
down the 3. 8 goes into 43 how many times?..."
and so on. At the conclusion of my presentation,
she said something simple but telling: "That
is going to be a lot for me to remember."
Indeed,
it is a lot for her to remember, because she
is remembering, and not understanding.
If you want to grasp the poverty of your own
education in math, I offer you the following
challenge: explain long division. Explain it
to a child, to an adult, to yourselfbut really
explain it. Use words to describe not the process,
but the reason for the process: why each number
goes where it does; why you subtract, or divide,
or bring down; why the process works. It won't
be easy. I maintain that if you had been educated
properly in math, it would be.
One of the defining principles of the VanDamme
method is a concerted effort to ensure that
every item of knowledge possessed by the child
is true knowledge, to ensure that he understands
it thoroughly, independently, conceptually.
To realize this goal in math will require a
total overhaul of the standard curriculum. It
will require that someone strip the program
down to essentials, arrange the material with
total faithfulness to hierarchy, and design
assessments that are true tests of the child's
understanding. Meanwhile, we can take moderate
steps in that direction, by requiring, for example,
that the children give complete, verbal explanations
for all that they do in math.
Mr.
Steele, a math teacher for a group of 7 & 8yearolds
at VanDamme Academy, demands of his students
that they not just blurt out answers, or crank
through mechanical processes. He makes them
explain the processes using the proper terminology
and demonstrating that they understand what
they are doing and why.
If, for example, he is teaching subtraction
with borrowing, and puts a problem on the board
such as 2700  350, someone in the class will
invariably ask, "Can I just tell you the answer?"
Mr. Steele's answers are charmingand pedagogically
correct.
Sometimes
he says, "I don't want you to do 'magic math.'
I don't want you stare up at the sky, come up
with a number, and blurt it out to the class.
That doesn't help us understand, and that doesn't
show me that you understand. I want you to explain
how you arrived at your answer."
At
other times, he says, "Let's play a game called
'Mr. Steele bumped his head and can't remember
math.' Don't just give me the answer, teach
me the process by which you arrived at your
answer." The students proceed with explanations
that demand, among other things, that they use
concepts of place value (if they begin the problem
above by saying, "0  0 is 0," he says, "That's
true," and waits for them to tell him that you
put a 0 in the ones' place), and that they explain
what they are doing when they borrow (if they
say, "Cross out the 5 and put a 4, and put a
10 in the tens' place," he will ask, "What does
that 10 represent? 10 what? 10 monkeys?" which
will make them giggle and offer the correction,
"10 tens silly!").
These
children are not treated like human calculators,
they are treated like thinking beings. And when
they truly grasp the concepts they are using,
when they can explain them fully and articulately,
when they retain them because they are not memorizing,
but understandingthat is real math magic.
This
article is brought to you by:
Lisa VanDamme
VanDamme Academy
