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10 Sep 2005 - 01:12

math fluency

I spoke too soon, and I shouldn't be picking on teachers anyway, even when I've never met them and they're featured in news stories that make them sound dumb. (OK, probably especially not when they're quoted in news stories that make them sound dumb.)

Fourth-graders at Columbia Elementary School in Burbank increased their math scores by nearly 20 percentage points.

Fourth-grade teacher Erin Bennett said much of the growth is because of a new strategy called math fluency. Teachers give a short math assignment every night, and then go over it in class the next day. The assignments revisit the same concepts over and over again, to help children really get it.



I was wondering whether 'math fluency' could possibly mean actual math fluency, and it appears that it does. Here's what looks like a terrific short summary of math fluency and the 4 stages of learning over at Illinois Loop:

The second stage of learning is the fluency stage where the learner acquires the information at an automatic level.

[snip]

Research shows that to be fluent children should be able to accurately solve math facts at a rate of one per every 2 seconds. Naturally, if the child has poor fine motor skills or is younger, that has to be taken into account on any written timed test. One of the biggest teaching mistakes in math is when teachers don't stick with this part of instruction with children who have more difficulty. I'll give my son as an example. Not only was Justin one of the slowest learners of addition math facts I had ever worked with, but once he finally knew them he had absolutely no fluency. It could take him hours to complete 50 addition math fact problems. (I waited him out once.) Fortunately, his teacher wouldn't let him move on until he was fluent with them and I started to work with him on fluency every evening for ten minutes. Now many an educator would have said, "He has an attention deficit disorder and just doesn't have the attention span to do a timed math test." I was not willing to put this limitation on my son in second/third grade. To work on fluency, every night I set aside a time and gave him a sheet with all his addition math facts. I then set the timer and his goal was to complete one more problem than he had answered the night before. I think when he started he could answer 4 or 5 problems in the ten minutes. He literally progressed problem by problem. If he didn't beat his goal, we would practice saying the answers and then set the timer again. Fortunately once he could do the addition, the other facts came much easier. By fifth grade Justin was the fastest student to complete the once-a-year check-up math timed tests, and not only will he be studying algebra in eighth grade, but he can take any timed math achievement test and score around the 90th percentile. If we hadn't focused on the fluency, none of this would have been possible.

This directly contradicts the stated policy of TRAILBLAZERS, which is that math facts 'aren't gatekeepers.'

Good.


And notice: this mother brought her son to fluency in 10 minutes a night.

This is something I've been thinking about. So far, it seems to me that you don't have to put vast hours of time into homework, classwork, Saturday work, summer vacation work, and on and on and on in order to learn math.

It seems, based in what I've seen, that shorter bursts of effort repeated every day are incredibly effective. It's the consistency and the repetition that are the magic, at least some of the time (I've seen this with math facts specifically).

I'm hoping to find some research on this, but I'm not optimistic that 'efficiency' of learning has been an important focus of investigation. Most of us think of studying as work, and of work as good. I certainly do. The question of 'how little you can get away with' is uncomfortably close to the question of 'Will it be on the test?'

So I'm guessing we don't know too much about this. But we'll see.


update

Another very nice statement of the cognitive science supporting math fluency:

Grover Whitehurst, the Director of the Institute for Educational Sciences (IES), noted this research during the launch of the federal Math Summit in 2003: “Cognitive psychologists have discovered that humans have fixed limits on the attention and memory that can be used to solve problems. One way around these limits is to have certain components of a task become so routine and over-learned that they become automatic.” Whitehurst, 2003)


update

The Grover Whitehurst quote comes from a 'promotional white paper,' the kind of marketing document publishers and vendors are producing in response to NCLB's requirement (if that's the correct word) for research-based textbooks & teaching methods (and possibly before). In this case, the product being sold is a software program designed to help students achieve fluency with math facts.

I find these promotional materials incredibly helpful, so long as you bear in mind that they are not literature reviews; i.e., you're not going to hear the contravening evidence.

Just wanted you to know--

Here is the whole paper, which is almost certianly worth skimming. Research Foundation & Evidence of Effectiveness for FASTT Math (pdf file)


fuzzy math in WA state



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It seems, based in what I've seen, that shorter bursts of effort repeated every day are incredibly effective. It's the consistency and the repetition that are the magic, at least some of the time (I've seen this with math facts specifically).

That's good news!

I'm gonna go make Ben do 10 minutes of fast facts before bedtime.

-- CarolynJohnston - 10 Sep 2005


I don't think he needs to do that many.

All but one of the kids I've worked with (a tiny bunch) did great with 5-minute sheets.

The one child who didn't do well probably needed a much shorter sheet.

I might start with one-minute sheets--

I'm going to switch to one-minute sheets for my Singapore Math class.

-- CatherineJohnson - 10 Sep 2005

WebLogForm
Title: math fluency
TopicType: WebLog
SubjectArea: CognitiveScience
LogDate: 200509092111