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.