Friday, March 14, 2008

U.S. Math Education is "Broken and Must Be Fixed"

From the National Mathematics Advisory Panel Final Report, released yesterday:

International and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a level expected of an international leader. Particularly disturbing is the consistency of findings that American students achieve in mathematics at a mediocre level by comparison to peers worldwide.

During most of the 20th century, the United States possessed peerless mathematical prowess—not just as measured by the depth and number of the mathematical specialists who practiced here but also by the scale and quality of its engineering, science, and financial leadership, and even by the extent of mathematical education in its broad population. But without substantial and sustained changes to its educational system, the United States will relinquish its leadership in the 21st century.

This Panel, diverse in experience, expertise, and philosophy, agrees broadly that the delivery system in mathematics education—the system that translates mathematical knowledge into value and ability for the next generation—is broken and must be fixed.

Washington Post--A presidential panel declared math education in the United States "broken" yesterday and called on schools to focus on ensuring that children master fundamental skills that provide the underpinnings for success in higher math and, ultimately, in high-tech jobs.

NY Times--The report cited a number of troubling international comparisons, including a 2007 assessment finding that 15-year-olds in the United States ranked 25th among their peers in 30 developed nations in math literacy and problem solving.

Comment: Can we get rid of "Everyday Math" now and go back to the old math? After all, what was wrong with a system of math education that gave the U.S. its "peerless mathematical prowess?" It seems like that was a much better outcome than 25th place out of 30 among our peers (the panel was being kind to call that result "mediocre") .


At 3/14/2008 7:58 PM, Anonymous Anonymous said...

You ask a simple question -
After all, what was wrong with a system of math education that gave the U.S. its "peerless mathematical prowess?"

The simple answer is that the people in education cannot teach the "old math" so they invented the "new math." education suffers from people who do not know the subject they teach.

At 3/15/2008 11:49 AM, Blogger bobble said...

anon said: 'The simple answer is that the people in education cannot teach the "old math" so they invented the "new math." education suffers from people who do not know the subject they teach.'

not true.

my wife is a teacher. she is required to teach the math progam selected by the state board of education. these jokers are same ones that screwed up the reading program. please don't blame the teachers.

At 3/15/2008 5:45 PM, Blogger Doug said...

I want to thank you for this post. I had a concern about a year ago when my son was in 4th grade about his math homework. I could not do it. Now I have over 20 hours of college math, but I could not do "New Math." So I went to his teacher to get educated. I could not believe what they were teaching. Unfortunately, I let it go. After watching these videos I realized I made a mistake. Now I have an appointment with the curriculum director and plans to teach my son math the "old" way all summer.

At 3/15/2008 9:02 PM, Blogger concerned said...

However well-intentioned the math ed wanderings of the last 20 may have been, the result was clearly not beneficial to our children. I am very thankful that the panel has brought forth a clear focus in its list of Major Topics. Let's use them and move forward in teaching our children the mathematics they need to know to reach their full potential!

At 11/24/2008 10:30 AM, Anonymous jgo said...

I'd say it's been at least 50 years they've bollixed up the teaching and learning of math. (Heck, they can't even talk straight-forwardly about it, instead, insisting on such awkward terms as "schooling".) One problem is the phony insistence on "rigor", when the concepts weren't developed that way.

One must also distinguish between people who can do math, and people who know math, and people who can teach math. They require different skills, and you'd hope to find people who know, understand and can teach.

I know people who know and can do math, but are ineffective at teaching it. The primary problem is that they believe there is only one path of thought to understanding, but different students require different paths and means. Some are more verbally oriented (rather than those odd math symbols and Greek letters), others visual (think graphs, math concepts that are clearly illustrated in nature), so you need to figure that out and work with it. Some do better with a math history approach, seeing how the ideas developed.

You need to know what the student knows and is comfortable with, what they kind of know or have an inkling of -- to have a spring-board or base on which to build. A carefully crafted sequence of concepts with sets of exercises that incrementally pile concept on concept with enough repetition to secure each one in the student's memory is helpful to most. When introducing a new concept avoid unnecessarily adding to the difficulty; don't dump in several bits of new terminology or new notation at once. Avoid non-mnemonic terminology. If you run into something the student is having difficulty remembering, try using different words (before getting back to the ones you want them to know for later application), or drop back to repeat material you thought they knew but asking them at each tiny step whether they already knew it or not, to seek out the gaps.

And, you have to avoid approaches which build resistance. Some students need to be put on the spot or they'll never make the attempt to learn, while that can be disastrous for others. Some need to approach it as guided but personally motivated exploration, just as they would learning about dinosaurs, rocks or Pokemon. (I'm reminded of resistance to certain kinds of "rote learning drudgery", while they eagerly memorize football or baseball or Pokemon or bird or tree or dinosaur statistics and tables of facts.)

One strength that is also a weakness is that math allows a number of notations for the same things. Different notations work best with different students, allowing them to remember, understand, and apply the concepts and techniques more quickly.

Remember the magic number 7 (+ or - 2) -- the number of things most people can hold in mind at the same time. Don't exceed it or it will have turned into a game of whack-a-mole for the student as some ideas escape as new ones are added. This applies to each proof and exercise as well as to the curriculum. The only way to deal with it in the long-term is to subsume information into chunks, and those into mega-chunks... and then those mega-chunks learned so well that the details of each micro-chunk is still accessible while dealing with the most complex of concepts built on those mega-chunks.

P.S. Tom Lehrer's insight about octal being the same as decimal if you don't have any thumbs is most amusing, though it's been ineffective for me as a teaching technique... so far.


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