The only rule students need to know about "mixed fractions" is how to interpret them: "9 1/2 weeks" means "(9+(1/2)) weeks"; "-8 3/4 inches" means "-(8+(3/4)) inches", and how to produce them: "+-(n/d)" becomes "+-(floor(n/d)+(mod(n,d)/d))". Thus, if you see a fraction "n/d", you type n/d into your calculator, followed by "+/-" if there is a "-" sign in front. If you get a mixed fraction "i n/d", you type the following sequence into your calculator: n/d+i, followed by "+/-" if there is a "-" sign in front. Everything else is a massive waste of time, until _after_ the student has learned enough algebra to start learning a little number theory. There's an appropriate time to learn about putting fractions into "common denominators", but it isn't until considerably later. At the appropriate time, what would have been months of torture, then becomes one or two lessons, and is then immediately obvious. Here's a bad analogy: How many high school (American) football players would there be if each one had to be able to kick a 20 yard field goal prior to playing his first game? While kicking field goals is an important & valuable capability for a football team, hardly anyone can do it, and eventually someone specializes in this task. At 04:28 PM 10/28/2011, Thane Plambeck wrote:

People write mixed fractions all the time: eg 9 1/2 weeks or whatever.

I've had a couple of my own kids run this gauntlet at school and I just told them to immediately convert them to what I've taken to calling "fractions for grown ups" as a way of disparaging them and motivating my kids to not attempt to manipulate them in math homework, but to say that no one on Earth actually uses them is overstating the case in my opinion.

On Fri, Oct 28, 2011 at 3:20 PM, Henry Baker <hbaker1@pipeline.com> wrote:

...

I've been going through the Khan Academy math exercises to see what math kids are learning.

www.khanacademy.org

While I am very impressed with the Khan Academy & its exercises, I am appalled by the time & effort in teaching fractions -- especially "mixed fractions".

I realize that this is not the Khan Academy's fault -- KA is merely providing exercises to teach for the tests that the kids will have to pass.

But who on Earth actually uses this stuff & why do we torture kids this way?

No wonder people hate math.

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I think that the ability to do rudimentary programming is far more valuable to every kid than the ability to handle "mixed fractions".

In fact, the ability to sum/difference numerical fractions at all is simply not terribly relevant. Ditto for greatest common divisor and least common multiple. (Truth time: when was the last time you used "least common multiple", except on a test?) Yes, there is a time for "number theory" & gcd's, but it should come considerably later, in conjunction with algebra & groups, rather than with basic arithmetic. Yes, there is a place for summing fractions: when simplifying algebraic expressions, but not in basic arithmetic.

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The hours in every kid's life are valuable, and the hours in every teacher's day are even more valuable. Why do we want to waste these hours teaching them skills that bore them out of their minds, and that they will never use?

If there is an educational crisis, it would appear to be caused by clueless adults.

-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/