Wednesday, October 10, 2012

Math Fact Fluency vs. Math Proficiency

I came across a video about Emma J King.  Emma is a physicist (physicists do a lot of complicated math) who is somewhat dyslexic and struggles with arithmetic (basic math).  She is not fluent with her math facts!  Complex math is made up of a lot of formulas with a lot of variables.  Her brain seems to be wired for complex math, but disadvantaged when recalling math facts and seeing some of the relationships between simple numbers.  The two skill sets are quite different.

I've heard, but been unable to verify, that Albert Einstein had a similar issue.  If you've taught very long at all, you've had students who didn't get math very well at all, who knew their facts well, and other students who did well with more complicated math, but did not know the facts.

So educationrealist, who teaches a high school math support class, wonders if we are spending too much time teaching for math fact fluency.  (I'm thinking this is because her students mainly fall in those two groups.)  Maybe math fact fluency is not critical to math proficiency?

We need to remember that we are talking about a minority of math students.  Also, that fluency frees up working memory, which is good for all students.  Perhaps the real question is how much time should be spent to achieve math fact fluency, versus other math proficiencies.  Obviously, as little as possible!  All the more reason for efficient and effective practice.  Students who struggle with math fact fluency will benefit the most from mnemonic devices, or mental "hooks" that will help them remember.  The data we are getting here at Math Facts Pro shows that learning increases steadily with practice up to about 400 correct facts/week.  So if students practice 50 facts in class, and 50 at home, at least 4 times a week, they are learning the most effectively.  The same frequency also happens to be the best at preventing forgetting.  However, these are averages.  We do not have enough data yet to say what is optimal for those struggle to learn the facts, or those for whom it is easy.  My hunch would be to have the struggler practice in smaller amounts, more frequently, and have those who excel practice less, as long as they are getting what they need.

Obviously, there isn't going to be a concrete answer to how much practice is too much.  (our data shows tha the more you practice, the more you learn, it just isn't as efficient)  But remembering that each child is has different natural abilities, that math fact fluency is very helpful, but students can be successful without it, can help give teachers, parents, and students perspective, and compassion.  Watch the video on Emma, it's pretty cool.  And stay smart with math facts fluency practice.

1 comment:

  1. Don't know how I missed this the first time. As I said in that post:

    "Assertion: Students who are categorically failing in math are almost certainly not doing so because of math fluency. They may or may not be fluent, but fluency is not the condition holding them back.

    Tentative hypothesis: The rationale for math fluency (quoted above) does hold for many students who are moving through the math curriculum without ever achieving genuine proficiency, who would certainly be able to learn and hold onto more information if they weren’t spending so much of their time trying to remember what 6 x 3 is, particularly in algebra. "

    In other words, fluency is good for the big bulk in the middle who *could* achieve fluency but *aren't*. Fluency is rarely the reason students aren't achieving in math. That's my assertion and hypothesis, anyway.

    I don't ever discuss my gender on my blog one way or the other, to keep my anonymity. Most think I'm a guy, but every so often someone calls me a she. Go figure.