Tuesday, June 17, 2008

Helping Children Succeed

I'm reading
Math Coach, A Parent's Guide to Helping Children Succeed in Math, by Wayne A. Wickelgren, Ph.D.

This is a wonderful book, directed at parents, on how to help children who need more instruction, who need to get caught up, or who need to be challenged.

He says it's not too late, even if they are in 5th or 6th, to catch them up by helping them at home in time for Algebra in 8th grade.

Here are some quotes that are especially appropriate for our intermediate grades:

"Most children can learn math much faster than the school system prescribes. That means that even if your child is currently behind, there is plenty of wiggle room for catching up, especially if you start early. Math education proceeds slowly in school before eighth or ninth grade, so those are the
ideal years to improve your child's mastery of math or speed him or her ahead through the curriculum (though starting later is okay too)."

" . . .{by taking prescribed steps}, your efforts will change your child forever. Investing time in your child's education -- whether it's tutoring, consulting with educators, or helping your child set goals -- will show your child that you think education is important. Even when your child complains about doing extra schoolwork, rest assured that he or she is lerning, however, unconsciously, to value learning. It is a value your child will carry throughout life and, in all likelihood, into the next generation."

". . . even if your child is behind in math now, you can get him or her back on track with only moderate effort. If your child is not behind, you can propel him or her substantially ahead in math."

"It is the math prior to algebra that is taught especially slowly in the U.S. Thus, the
pre-algebra years are the ones in which you can most easily speed your child ahead, or help him or her catch up in math, giving the child a chance to learn as much math as possible."

Wickelgren has some fascinating studies that show how soon children can grasp concepts of adding and subtracting from a group. And there is great information here on when children can begin sounding out words, although that is a different subject.

He discusses age-related limits to math learning (I was surprised to find that there are very few.) and biological barriers which are connected to processing math, and (one that I've always heard thrown out here) maturational limits.

Here's a great quote from Wickelgren, related to that last statement:

"Of course your child may have temporary trouble understanding certain math concepts, but the reason for that is unlikely to be a maturation issue.
It could be lack of verbal skills."

". . .
it is the verbal encoding of addition and subtraction that is often lacking in young children and not the nonverbal understanding of these concepts."

Did you get that?


Children can understand math if we find another way of showing students what the digits and symbols actually mean.

I'm loving this book!!


Catherine Johnson said...

Wayne Wickelgren got me started on my quest!

I had no idea what constructivist math was until I read that book---

Paul B said...

I'm a career shifting math teacher. One of the things that shocked me upon returning to the mathematical world from engineering was the almost total absence of written mathematical content being put in front of kids through middle school now. The curriculum in my district reinforces this by insisting on lots of written (composition) reflections on mathematical concepts.

It's as if the curriculum design deliberately takes kids away from the language of mathematical notation, preferring instead english language descriptive material. Because I work a lot with ELLs this is a double whammy on them. They're already learning a foreign language (math) via a foreign language (english) but we never model or let them see the math.

What I do, when the Land Rovers aren't cruising my corner of the savannah, is insist on solutions in mathematical notation, rigorous algebraic manipulation of everything. Make the math tell a story not the English. Ells find this far easier than trying to translate into composition.

The irony is that their algebraic solutions are perfectly acceptable explanations when it comes to standardized state testing but in the classroom teachers are made to insist on composition.

Concerned Teacher said...

paul b, I think that "verbal" can mean more than one thing here.

Thank you for your comment. I understand your use of "verbal" and agree with what you are saying. There is far too much use of written explanations and processes. I remember several years ago getting caught up in having students write an explanation of all the steps needed to solve a problem. Wisely, I stopped that time-consuming nonsense.

However, I believe some of what Wickelgren means by "verbal" skills is the understand of what words mean when they are combined. There are children who have no idea what they are to do just litening to verbal instructions, but when they see the manipulation of the numbers and symbols, they quickly get it.

Simple words such as prepositions can be confusing to some children (below, beside, inside, outside, on) and we don't yet know why these simple words "throw" children; and combinations of words as "three fourths of what was left" can mean trouble for some. What if a student sees the word "left" and thinks of "left" as opposed to "right"?

Verbal skills in math mean the student must process words and think of mathematical operations.

That said, I do think it's important for students to be able to put into words what a story problem is telling them. This is where the student weak in verbal skills will struggle the most. So it's important to link verbal with nonverbal as much as possible. However, this must be under the guidance of a skilled teacher who can spot where "meaning" fails a student and who can present in another way.

Verbal and nonverbal are connected in our lives all day long. And it is the student who struggles to "get" this connection that I love to teach and help. They want to understand so badly and are so appreciative when you help them over that hump.