There are definitely kids who pick up math fast.

There just are.

I have no idea whether they pick up fuzzy math faster, too, but I wouldn't be surprised.

One of the things I've always heard (which I tend to believe) is that the kids who are managing to succeed in math in this country are the ones who can survive bad teachers & bad books.

-- CatherineJohnson - 30 Sep 2005

AND AND AND--he's talking about which children should have supplemental mathematics curricula at home, at Kumon, or with a tutor.

What he's saying is that, if it looks like you've got a mathematically talented kid on your hands, you should almost certainly supplement outside the classroom, period.

-- CatherineJohnson - 30 Sep 2005

His advice is that 80% of all children can study and master algebra in the 8th grade--and that they should do so.

-- CatherineJohnson - 30 Sep 2005

"Your child's talents may or may not be in reading and writing. So do all you can to motivate your child to read and write and provide the best teaching possible, but as only one part of a well-rounded life. When you've done that, you've done your best and should accept your child's progress in English Language Arts at school."

You guys!

Read the Whole Thing!

His standard for 'your child's talents may not lie in mathematics' is:

your child may not be destined to become a professional mathematician

Note that he includes, among the lesser, applied uses of math that a child who's not so talented might reasonably pursue:

engineering

also:

finance

The equivalent statement would be, 'Your child may not be destined to become a major American author.'

Most children are not destined to earn Ph.D.'s in mathematics, and most children are not destined to become major American authors.

That is what he's addressing.

-- CatherineJohnson - 30 Sep 2005

Steve & Barry I obviously have not done justice to the book.

This is a guy who accelerated his son 5 years ahead in math.

The book also includes a thorough critique of fuzzy math, and advises parents how to get around it--up to and including starting your own school.

-- CatherineJohnson - 30 Sep 2005

Steve's point is well taken. I know someone whose daughter is very bright but at the end of 4th grade, where the teacher religously stuck with EVeryday Mathematics, the girl concluded she wasn't very good in math. She was confused about what method to use to multiply, since EM gives kids so many wonderful "student-invented" algorithms.

-- BarryGarelick - 30 Sep 2005

Two comments:

"Your child has a very high ability in math--that is, appears to be among the best 10 percent of students in his or her class"

What if the curriculum is really bad and 15 percent of the other kids are getting help outside of class.

"Your child's talents may or may not be in math. So do all you can to motivate your child to learn math and provide the best teaching possible, but as only one part of a well-rounded life. When you've done that, you've done your best and should accept your child's progress in math at school."

If this is a comment for high school kids and parents, then fine. On second thought, no, it really isn't fine. If it is for K-8 kids and parents, then it really bothers me. Why does it bother me? Well, here we are at KTM talking about how pathetically poor K-8 math is. It is so bad that many kids (and their parents) end up thinking that they are "just not good in math". If (innate) ability is judged by how well or quickly someone learns the material, how much is innate ability, how much is help outside of the school, and how much is a good curriculum and good teachers? Given the easy level of K-8 math, why would anyone be concerned about natural ability at that age?

How does this sound:

"Your child's talents may or may not be in reading and writing. So do all you can to motivate your child to read and write and provide the best teaching possible, but as only one part of a well-rounded life. When you've done that, you've done your best and should accept your child's progress in English Language Arts at school."

It's OK if little Johnnie has trouble reading the paper and can't seem to put two thoughts together, there are really other things in life that are important. This is fine only if you have eliminated all other variables.

-- SteveH - 30 Sep 2005

Wickelgren on talent & when to supplement

Differentiating children by their abilities and skills is a controversial subject, but math aptitude can vary greatly among children, just as children differ in their ability to run, jump, give speeches, draw, sing, comfort others, tell jokes, or lead a group. And though it's generally impolite to speak of such differences, it is important to recognize that they exist--and for parents to have a sense of where their children rank among others.

Having a sense of your child's math ability can help you set realistic goals for your child in math. It can help you decide whether your child is progressing in math as fast as he or she can or whether you need to push a little harder or do something different--such as provide supplementary math education. For example, you probably want to supplement our child's math education if

• Your child has a very high ability in math--that is, appears to be among the best 10 percent of students in his or her class

• Your child is at least average in math and has career ambitions in math or a math related field

• Your child scores in the range of college-bound kids, but his or her school math training is inadequate for admission to the college-prep math track or for scoring at the child's ability on the math portion of the Scholastic Aptitude Test (SAT)

• Your child is of normal intelligence, but isn't mastering the basics of arithmetic in school--a necessity for independent living

One way to assess your child's math ability is to have him or her take an IQ test, but a simpler and probably more accurate method is to observe his or her learning rate relative to that of other children. If your child catches on to math concepts quickly compared to others the same age, he or she is probably a fast learner. Similarly if lots of other kids seem to catch on to math concepts more quickly than your child does, he or she may be of only average ability.

My daughter Ingrid says she was well aware of the differences in math ability between herself and her brother Abe, from the time I began teaching them at home at ages eight (Ingrid) and six (Abe). Ingrid remembers times when I would pose a problem to the two of them, and Abe would soon begin scribbling on his paper to come up with the correct answer. Ingrid, meanwhile, would look puzzled, wondering how Abe had figured it out so quickly. She knew she wasn't stupid, but it was obvious to her that her younger brother had a gift for numbers she could not claim.

Still, Ingrid took algebra in the seventh grade (when she was just eleven) without much difficulty. She learned plenty of math to complete a fast-paced college physics sequence and the curriculum required for a biology major. She is now a successful writer specializing in scientific and medical topics.

Meanwhile, Abe wanted to become a professional basketball player as a child and for years worked incredibly hard at improving his basketball skills. After first grade he played in a league every winter and went to as many as three basketball camps in the summer. Year round, he practiced basketball for an hour a day or more. As a result he was named the starting point guard for his seventh-grade team. But after that, his tiny stature and limited natural ability made him less attractive to coaches than kids who were bigger and learned new skills much faster. While his accomplishments in basketball diminished--he did not make the high school basketball team--his success in math continued unabated. He excelled in his advanced classes and remained five years ahead of grade-level in math.

It was clear from watching this drama unfold that Abe's natural talents lay more in math (and other school subjects) than in playing basketball. Similarly, it should quickly become apparent to you from your child's experiences whether your child is very talented at math or has lesser abilities in this area. But remember: Even if your child's natural talents in math do not suggest he or she should become a mathematician, your child could still use his or her math skills to become very successful-perhaps as an engineer [ed: yikes] or a financial manager. My son did, after all, develop a helluva basketball game, making him a top player in the adult recreational leagues he later joined.

[snip]

Your child's talents may or may not be in math. So do all you can to motivate your child to learn math and provide the best teaching possible, but as only one part of a well-rounded life. When you've done that, you've done your best and should accept your child's progress in math at school.

Despite what my dad told me, it is not true that you can do anything if you work hard enough. But if you temper your ambition with realism, you can derive enormous satisfaction from the truly spectacular results of hard work coupled with excellent instruction.