Gifted Issues Discussion homepage Forums Parenting and Advocacy Minute Math in 7th grade

What a lovely, sensible post, tortuga.

A deeper understanding of mathematics allows one to mathematically reason much more quickly. This is true at all levels.

People who think fast and talk fast probably are judged to be more intelligent -- think of the phrases "fast on his feet" or "quick study". The association of speed and intelligence has some justification. As people age, their fluid intelligence declines, and they think more slowly. I've noticed this in my parents, alas. To what extent speed can be developed by drilling is a different question.

This is true. But its converse -- "Reasoning more quickly in mathematics allows for a deeper understanding" -- is false. These timed tests assume the latter because the former is true and more importantly because timed testing is an easily quantifiable, low-cost measure of 'progress' in an education system that currently rewards schools for performance on short-term metrics. So perhaps a basic failure in logic (assuming a converse to be true) is to blame, which is ironic since logic gets such short shrift in the math curriculum!

But with math minute you are not reasoning quickly. You are recalling facts quickly.

Reasoning and recalling a fact from memory are two different things

Well, yes and no. Why is the 10 times table easier to memorise than the others? Because you don't really memorise it - you understand the numbers well enough that you can work it out very fast. Hands up all those who still don't feel as though they truly recall times table facts from memory, but rather, work them out every time fast enough that it looks to everyone else as though they're recalling them from memory? (My hand is raised, even though as I said elsewhere I think of myself as a slow processor.) [ETA: on second thoughts, this is less true than it used to be before I helped DS learn his tables, actually! I am now wasting several more synapses on this task than I used to ;-) ]

Reasoning and remembering are really intimately entwined. When you solve a novel problem, you never approach it completely from first principles: part of what you're doing is allowing your memory to bubble up possible approaches that have helped with similar problems in the past. To over-simplify, there are two ways to be bad at problem solving in maths:

1) too much reliance on memory: being unable to solve any problem that isn't extremely similar to something you've solved in the past

2) too little reliance on memory: being overwhelmed by the need to work out anew a strategy for doing every tiny piece of arithmetic that comes up in the course of doing the problem.

Times tables and other number facts are about as far on the memory end as it's possible to go, but even there, I bet if we had the neuroscience to be sure, we'd see that logical reasoning plays a role even there for many people. And a key thing for mathy children who hate memorising is: this is fine. If you can get the answers fast enough and easily enough that it looks as though you have them memorised and working them out doesn't slow you down, that's OK. And practising strategies so that you get that fast is worthwhile in that it deepens your understanding of how numbers work, in a way that "dumb" memorising isn't.

Yesterday ds looked at this sample ACT question and was not told how to solve it.

The lead of a screw is the distance that the screw advances in a straight line when the screw is turned 1 complete turn. The screw is 2 1/2 inches long and has a lead of 1/8 inch. How many complete turns would get it all the way into a piece of wood.

Once he'd read the problem it took him about two seconds to figure it out and solve it. He did it in his head and he was correct.

This morning I randomly asked him, while he was on minecraft, to tell me what 8 times 7 is and it took him about 2 seconds to answer.

I don't know what this means other than when he's relaxed and confident he can think deeply in math.
As for the timed recall, I imagine if he hadn't been distracted by minecraft and I had told him to hurry up, or told him he was being timed, it may have taken him longer.

Conversely, I am very fast in recalling times tables. I could have said the answer in a fraction of a second. But it would have taken me longer to think about the problem above and solve it.

And I want to add, I'm so grateful for all the responses this thread received. This particular subject I feel passionate about because I've known for years that ds is gifted in math but his confidence has slowly been eroded over the years through timed tests and the assumption that fast means good and slow means bad.

I've been working with him, a little bit every day, about ten minutes at most, because his math avoidance is so prevalent and strong.

Two days ago he gave me a hug and thanked me for working with him. And the best thing ever was the moment when he told me he loved math.

You sure he wasn't still thinking about Minecraft for 1.95 of those seconds, lol? Mine would have been...Then he'd have asked what the question was again.

Yes!! lol! I'm sure he was.

I would say that if someone tried to measure future advanced mathematical ability by testing speedy arithmetic in kids, then there would be unacceptably too much "noise" compared to the "signal" they are trying to measure. But nevertheless there is a signal there whereby some people have certain characteristics that enable them to have advanced mathematical ability in the future, and those same characteristics enable them to be speedy at arithmetic as kids.