MATHCOUNTS lets smart middle schoolers compete to solve complex math problems, writes Jay Mathews in the Washington Post. It’s spread to 6,000 schools and 500,000 students.

“It’s very different from math class,” said Sarah Olson, a seventh-grader at Pyle Middle School in Montgomery County. “You can come up with your own ways of solving the problems.”

Alisha Seam, an eighth-grader at Longfellow Middle School in Fairfax County, took fourth place in the Virginia state competition this year. To her, even the hours of practice are fun. “You don’t just look at math as a bunch of numbers and figures,” she said. “We practiced five to seven hours a week.”

Experts say that competition and creativity add an element of joy to math and other subjects that can change students’ attitudes about what they are learning. “Motivating students to do more challenging math by showing it is more interesting and fun is a great idea,” said Matthew Gandal, executive vice president of Achieve Inc., a nonprofit educational organization.

The national competition was won by mathlete Gregory Gauthier, who answered: “How many five-digit positive integers have the sum of all five digits equal to 8 and the product of all five digits equal to 8?” (Answer: 10 integers) He attends Monroe Middle School in Wheaton, Illinois. Illinois, my home state, won the team competition, beating out California.

I’ve read a lot of negative comments here and in similar places about what has been termed “fuzzy math.” How is it that “fuzzy math” come in for criticism when MathCounts gets praised. There are a lot of similarities in the way MathCount approaches things and the way most of the newer math texts approach things. Is it political?

js

If you want to understand more about these issues you should go to http://www.mathematicallycorrect.org. You will find there that the NCTM standards often derided as the heart of “fuzzy math” commit sins not so much of commission but of omission. That is, the approaches embodied in these standards are fine things _in the context_ of a curriculum that provides the necessary foundations of mathematical knowledge and practice of skills; the trouble is that the standards themselves don’t make that sufficiently explicit. As a result, in the reviews published at Mathematically Correct, the textbooks written in the spirit of the NCTM standards receive grades ranging all the way from F to A. I’m very familiar with one of the books to which they gave an “A” – the 7th grade “Passport to Algebra and Geometry” from McDougal Littell- because it’s used at my daughter’s school. It’s a very solid book. So the approach advocated by NCTM can indeed be done well. The trouble is that it too often isn’t. This is neither a black-and-white issue, nor should it be a political one.

Hmm, according the MathCounts.org, one of their competitions is going to be on ESPN2. How long before there’s a Colorado style recruiting scandal associated with this? Hey, a former 8th grade Algebra geek can dream can’t he?

The difference are that the kids who do very well at Mathcounts knows the basics of math – they know how to add fractions, do long division, calculate the area of a triangle. Now they’re ready to take the math a step beyond to see how to apply it to problem-solving.

The great thing about math competitions, unlike math assignments, is that you don’t know which bit of math is going to be useful before you do the problem. When you get a math assignment, you’ll note that it’s in the section about percentages, so you know you’ll be doing a percentage problem. That’s a fine way to learn the basics, but real life, and competitions, require one to put all of it together.

Also notice that these kids practice a bunch of problems. The “fuzzy math” most people complain about tend not to have much in the way of drilling and practicing.

22211, 22121, 21221, 12221, 22112, 21212, 12212,21122, 12122, and 11222.

“Mathlete”

Now THAT’S cool!

Steve,

That’s a pretty fair assessment. Not all standards-based curriculum are created equal, just as all ‘traditional’ programs are not equal. This is a major factor in why some studies suggest children learn more with standards-based curriculum than traditional programs (and other studies suggest just the opposite).

Generalizing about ‘traditional’ or ‘fuzzy math’ only polarizes and obfuscates the advantages and problems with specific approaches. Unfortunately, that happens all the time in the interests of political agendas.

Mathcounts is great. ESPN2 did broadcast an hour of the competition last week and i believe they are airing it again a few times this month.

Rats. “Just John” beat me to it.

Here’s another way to come up with the number of integers, knowing that the answer has to contain 3-2’s and 2-1’s.

Think about a series of five slots where you have to place 2-1’s. (The remaining three slots will be filled by the 2’s.) To place the first 1, you have five options. Once the first 1 has been placed, you have four options to place the second 1.

That would seem to suggest 4×5 = 20 solutions. However, since the 2-1’s are identical, there are really half as many unique solutions as there are apparent solutions. Therefore, 20 divided by 2 equals 10.

—Tom Nally, New Orleans

Also, some of these new math programs want the students to solve problems without using previously mastered basic skills (or before they have them). I have seen cases where they ask the student to solve what are simple 2 equation and 2 unknown problems without explicitly writing down the equations and using something like guess and check. It is almost as if they think that any kind of previous knowledge and skill (drill and kill) will somehow prevent the student from “creative problem solving”. As I have said before, you have to know what is inside the box before you can think outside the box.

There was a picture in our state’s major paper about the loss of gifted programs for kids (a separate issue) that showed a photo of a program called “Spontaneous Problem Solving” where kids had to build structures using shaving cream and straws – no knowledge of engineering, structures, or architecture required. My thought is that they will only learn that shaving cream smells awful.

My concern is that terms like “fuzzy math” and “drill and kill” polarize and trivialize the educational debate. I prefer details. I would start with the problems that the students have to be able to solve year-by-year before they are allowed to continue on to the next grade. If you can’t agree on what is taught, then it doesn’t matter much about how it’s taught.

I’d note MathCounts is by no means a new program. I competed at both the Chapter and State levels back in 1991.

I went to Nationals back in 1986 and 1987! I believe 1987 was the 5th year.

Tom Nally,

Hmmm. I did it the way I handle difficult anagrams. (The “Jumbles” feature in the local paper, if you must know — I have to do them pre-coffee every morning just to assure myself that my brain is still there.)

Anyway. There have to be three 2’s and two 1’s; that’s obvious. So you set up three-digit cells for the beginning of the number. 222, 221, 212, 211, 112, 122, 121. Those are all that’s possible. Some have two possible terminations and some have one.

That technique works very well for anagrams. Take a handful of letters of your choice and “segregate” them; then mess with the rest and see what comes up. Obviously a big vocabulary and a sense of what letter combinations you’d expect to see don’t hurt. Though the cunning little devils use the latter against you; half the six-letter Jumbles containing the letters “ing” are

notgerunds. You are now warned 😉Anyway, I seriously miss math competitions. I was on a NY suburban math team when it — no, didn’t

winthe state competition, but came in second to NYC Team A, which naturally always won. (NYC had five teams then. Not sure what they have now — this was more than 20 years ago.)But second was unheard of. For us, anyway. It was sweet.