kitchen table math, the sequel: Why do we insist on teaching fractions like we teach poetry?

## Wednesday, April 28, 2010

### Why do we insist on teaching fractions like we teach poetry?

...asks professor Hung-Hsi Wu of Berkeley at last week's NCTM (National Council of Teachers of Mathematics) Conference. Once you learn algebra, precision is most desirable, mathematics can not be taught in an ambiguous manner. He brings Mark Twain, Shakespeare and Keats into an informative and, for me, entertaining conference session.  (At one point, he turned the definition of multiplication of fractions into free form verse!) From his presentation:
Consider Hamlet's comment on Denmark after his father's death:
'Tis an unweeded garden
That grows to seed; things rank and gross in nature
Possess it merely.
Compare it with the definition of 3/4 :
Take a pizza (or a fraction bar) and divided it into 4 equal parts. Take 3 parts.
My favorite quote from his presentation came after working to understand the product formula (is there an official name for this?): a/b x c/d = ac/bd. He said something along the lines of:

"You've worked so hard to understand, don't you need a treat? Here's the standard algorithm. You can almost use it mindlessly."

At which point people in the audience started snickering & guffawing. Wu continued:

"We drive mindlessly. Do we consider the internal combustion engine when we do so?"

He insists that computation is a part of mathematics:
Analogies and metaphors have a place in mathematics. They can be very helpful in the understanding of precise concepts and reasoning. However, it is a mistake to allow them to replace precise concepts and reasoning.
Let us hope that fractions will be taught with less poetry, but with more emphasis on
precise definitions, and
precise reasoning
Want to enjoy the whole presentation in your own home? Point your browser to: http://math.berkeley.edu/~wu/NCTM2010.pdf

Katharine Beals said...

As RMD has suggested here , perhaps we should insist on teaching poetry in the same way that "we" (as in we at kitchentablemath) insist on teaching math.

RMD said...

Katherine . . . thanks for highlighting my comment .. .I really enjoy your blog

I have one more thought on teaching math . . .

Why do we make students "recreate" so much of it? It took civilization thousands of years to develop it . . . why don't we just catch everyone up on the latest and greatest?

Greta said...

Thanks for posting. I really enjoyed reading Prof. Wu's paper.