This morning started in a jumble of errant alarm clocks
and rushed schedules, and as I wait for the day to right
itself (and for my delayed coffee to take effect) I have
Math Thoughts cluttering my brain.
I think math education is suffering, at the moment, from
the same growing pains literacy was afflicted with
during the last two decades. When my sisters were in
elementary school, there was a move to eliminate
phonics. Phonics was bad! No Phonics. Whole Word
Reading was the way to go. Don't break words into
bits, make those kiddos recoginize the entire word!
Needless to say, this worked for some children, but
not for others, and the parents who had grown up with
the realm of phonics were left wondering who was
steering the reading train. Eventually, everything
merged back into a balance of some phonics, some
whole word.
Math, I was going to talk about math. Here's how my
allegory fits in. There has been a push to change
math curriculum to teach math with greater depth.
"Manipulables" are the "in" thing. Teach children math
with things they can hold, touch, feel. Create deep
understanding, and then introduce the notation.
No more will children learn cheats like "Invert and multiply
ours is not to wonder why" for dividing by fractions.
Instead, we'll expand the problem and deal with the
parts, so there is full understanding. In theory.
But, along with throwing out the mindless cheats,
we will also set aside algorithms. That multiplication
we all learned as children, with carrying and indentations,
forbidden. Now we will think in clusters and parts.
Oh, and parents will be left behind, to wonder at what
is going on and why what they learned is so bad.
This is where I see the similarity between literacy
reformation and the current math. The wholesale
disregarding of "traditional" or "quick" methods, not to
mention the abandonment of parents in the learning
equation.
So. To be completely clear, I LOVE the idea of deeper
understanding of math. I glory in a good math game.
I am happy thinking of as many different ways to
explain or calculate an equation as possible. The ideas
behind the current math is sound and glorious to me,
but I see it failing.
I see teachers spending days and weeks setting up
concepts, but then not being able to link the idea to the
more direct method. Here's an example using fractions
from my daughter's class. Egg cartons are used to show
how you can divide a whole (the carton) into twelfths,
sixths, fourths, thirds, and halves. Fabulous. Wonderful.
BUT, after all that prep, there isn't enough follow through
to show how you find common denominators for any
fraction. The foundation is laid, a spark has been lit,
but the faster method of finding a equivalent fraction
for any denominator is lacking. Yes, the child can now
envision how 3/12 = 1/4, but they can't reduce 5/25
to 1/5 because that's not in an egg carton.
And this is the crux if my complaint, time is spent
building this deep base of understanding, but the actual
implimentation that they will carry forward with them
is missing. My youngest daughter may understand
fractions and the idea of equivelant fractions better than
I did when I was 9, but she can't quickly manipulate them.
When it comes to adding un-like fractions or mixed
fractions, what will she do? The mechanics of fractions
has been left behind for the theory of what they are.
This brings me back to my allegory about literacy.
I think we need to do more work blending methods.
Deep understanding is a wonderful ideal, but we
still need to push the algorithms and the mechanics.
We need drills and repetitive worksheets so the nuts
and bolts become second nature. After the idea has
been explained, we need time for the faster equations
to be absorbed.
Oh, and parents, take them along on the journey!
When my older daughter went through her elementary
math, I spent lots of time watching You-Tube tutorials
so I could follow along with the methods being taught
to her (hello clusters!). When I would try and talk
to her teachers about what they were doing, I'd get
"blah, blah, deeper learning, blah, algorithms are
evil, blah." but no actual instruction. I am very happy to
say that with the younger girl's math, I've gotten
parent hand outs. "THIS IS WHAT WE'RE DOING".
What? Parent inclusion? Subtitles for me? Yay!
Why is this hard for math programs? If you include me
in the calculation, I will toe the line and act as your
reinforcement. If you make this a pitched battle of
new versus old, and make parents and their methods
out to be the enemy, you've alienated your home forces.
If I ruled the math education world, I would add back in
some of what they've tossed out. I would make parent
education packets available for every unit. Oh, and
while I'm at it, I'd reduce class size. Smaller really is
better, and each of those brains really do absorb math
differently. But that, is a different rant, for a different
day. The coffee has been consumed, and I have chores to do.