Math Education Education

From a report on problems teaching teachers to teach math:

... It found the programs, within colleges and universities, spend too little time on elementary math topics.
Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication.

I wonder just how many courses on multiplication are appropriate. Perhaps multiplication should be offered as a major. I can see a potential senior thesis already: "The Impact of Multiplying by Three on the Integers Between Five and Nine: A Multicultural Approach."

Fennell, who instructs teacher candidates in math at McDaniel College in Westminster, Md., said a common area of weakness among his students is fractions — the same subject the national math panel described as a weak area for kids. "Part of the reason the kids don't know it is because the teachers aren't transmitting that," he said.
To boost teachers' understanding of math, the math departments at universities ought to place more emphasis on training educators, Fennell added.

Yes, because having math PhDs teach fractions is an excellent utilization of their time. Why are math departments busy teaching complex analysis and differential equations to engineers when there are "educators" out there who don't know what a common denominator is? First things first!

Ann adds:

How bad is math education? How about this: When our 2nd grader started to do entry-level fractions, the school sent home an explanation for parents in the class newsletter. You see, apparently, parents don't know that the numerator is the one on the top, and the denominator is the one on the bottom, and the school had to give them a heads-up so they could help their 7 year olds do their homework.

And, if you watch this video, you can see that maybe a PhD in arithmetic wouldn't be such a bad idea. These days they are making the algorithms they are using to teach kids how to multiply and divide so complicated and difficult, that you do need a higher level of education just to follow along:

Steve says: Seven months ago, I posted this comment under this youtube video:

"Ambivalent. Fundamentals are good, but I never use the standard algorithm in my head. For 26x31 I do 26x30 (780), then add in 26 to get 806. I use a calculator for 3 digits, or use two digits and multiply by 100 when an approx. is ok. Clearly, the altases are used with stats such as population, income, area, etc. With calculators around, it is often more important to know *when* to multiply. I agree group work is over-emphasized. Try that on the SAT or on the job. "

Ann says: I don't know. I've always been pathetic at keeping more than a couple numbers in my head at a time (from phone numbers to math), and usually need to reach for a pencil. In that case, getting the algorithim right makes a big difference. The methods taught on the video and in the textbooks are hunt-and-peck methods with so many extra steps that errors are bound to occur. That's part of the problem. Instead of a condensed system, there are so many steps, that the mistakes almost must happen.