More from Math Coach . . . Know the Warning Signs of Inferior Education

Back to reading more from Math Coach, A Parent's Guide to Helping Children Succeed in Math, by Wayne Wickelgren.

Wickelgren, bemoaning the new math curriculum which had been introduced just before his daughter entered sixth grade, said he was able to identify the problem quickly because he knew the warning signs of inferior math education "...despite the claims of the teachers that this new program would be superior to the previous one."

At first, according to Wickelgren, he tried "to counter the new math agenda."

When that failed, he "implemented a plan to teach (his daughter) the math she would suddenly not be taught in school."

Wickelgren went on to say that their "stopgap measures prevented any long-term damage."

Here is one last paragraph written by Wickelgren on the subject of inferior math education and preventing its damage:

"Oddly, the methods that so frustrated (his daughter) and left (his son) far behind are part of the latest fashion in math education, one based on the 1989 Standards of the National Council of Teachers of Mathematics (NCTM) -- which I call Standards math. Virtually all parents of children going to school in the present era will encounter teachers and other educators influenced by Standards math. Thus, it is critical to understand these methods and how they might shortchange your child's math education."

Three things that I want parents to notice:

1. Wickelgren was able to quickly identify the problem because he knew what "Standards math" involved. This is where most of us as parents unintentionally drop the ball (I was one many years ago myself.) and this is when most of our children "get off the track." And sadly, we might not even know they are off the track because we are lulled by the teachers' promises of a better way coming.

2. He tried to counter the new math. (more on this later) I think this is what most of us do, if we are knowledgeable enough to be able to identify the problem at the start.

3. He identified what was not being taught and intervened. He implemented a plan which taught his daughter what she would fail to learn.


My first encounter with "new math" (but I didn't know it):

Our own son, coming through high school in the late 80's and early 90's, was very smart in math, and was on a fast track. He started geometry, and quickly told me "Mom, I'm not enjoying math at all."

I looked through his geometry textbook. Geometry had been about my favorite math, and I was incredulous at what I saw, or more specifically, what I didn't see. This math did not even resemble what I expected! Students were given problems to solve but had not been taught theorems nor anything about using theorems in the proofs. Folks, that's what plane geometry is -- using/listing theorems needed to solve the problem and then (proofs) why that theorem helps get the answer. The theorems and proofs take you step by step through the problem until you get the desired solution.

I tried to explain theorems and proofs to our son and how they worked, (I guess I was at step 2 above -- trying to counter what he was learning -- but I made the mistake of using the school's textbook and I just couldn't help him. I knew our son was terribly off track. It was week two and damage had already been done. His self confidence was zero.

So I had identified a problem, although I knew nothing of "new math". And after trying to help, I had been pretty quick to identify what was NOT being taught (step 3), but my mistake was trying to counter what was being done by using his textbook as it was being taught. It just didn't work at that point because there were gaps and I couldn't fill in the gaps using that "new math" system.

And so from my experience, I will agree with Wickelgren that trying to counter what a child is learning probably won't work by following what's in the "new math" book. I needed to start all over again and teach him plane geometry the "traditional" way.

(Let me call your attention to this: It is typical of "new math" curriculum to require students to solve problems before they are exposed to the information and concepts they will need -- to give them the chance to "discover" and to build their own methods and plans. All it did was upset and confuse my smart son.)

I called the teacher, who was very nice and assured me that our son was not alone, that it was typical for students to be confused at this point. She also asked that I give them a few more days to get through the chapter and then it would get better. It did get better, thank goodness, and we had our old son back! Remember, he was a good math student. I wonder now what happened to students for whom math didn't come easily.

I'm convinced in hindsight, that this was one of the very first "fuzzy math" textbooks. However, I had never heard of that, and it never entered my mind that anyone would be so foolish as to skew the math I had loved so much into a twisted bunch of disconnected ideas.

It is my desire to help parents quickly identify bad math teaching and implement a plan to correct it and fill in the gaps. No matter how old your child is, it's not too late. It's doable.

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?

"NOT THE NONVERBAL UNDERSTANDING OF THESE CONCEPTS."

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

I'm loving this book!!

Intervention, Part 2

Should you decide to "intervene" on behalf of your student, do not be surprised to find that some people in your school may not be happy about it.

Schools often design their own plans for intervention. There may be a distinct intervention "order" which you and your student should/must follow: You start at point A (probably your student's math teacher); if that isn't helpful, proceed to point B (another math teacher), etc.; then on up the ladder to perhaps the head of the math department. This is how the school has decided you must do it.

I know many teachers who gladly help students before school, after school. To them, the goal is student understanding and they are willing to help.

And don't misunderstand; I commend schools for becoming involved in the tutoring process to help students.

But let's consider that your student's math teacher is not competent in teaching new concepts or in identifying gaps in reasoning. What happens if your student goes to this teacher for tutoring (because that is where you must start)? This teacher will use the same approach used in class. What didn't work in class will be tried during the tutoring and your student will probably not get much benefit.

And how does that make your student feel? I'll tell you (but you know). He feels no better, maybe worse! Now he sees that even with extra help, he still doesn't get it!! He may start saying that he is "dumb".

So you desperately attempt to find alternative support and help. Woe be to you, if the school Math Department finds that you have, on your own, asked another teacher to help your child. You could be soundly scolded for not taking advantage of the proper recommended "line" of help.

I know because I was once an "alternative" choice by parents. They had tried the school's plan for after school tutoring by the student's math teacher. The student continued to fail tests, and the parents were desperate for some help. (He had gone from A's to F's in less than a year.) They pleaded with me to help. When I agreed, the parents asked for an extra book for me, but were chastised sharply for not following the "school's plan".

"You should have gone to . . .", the parents were told, and the plan of choice was explained.

This was so baffling to the parents. They just wanted help for their student.

Wouldn't you think that schools would appreciate a parent's desire to get help for a child? Well, schools may tell you that they appreciate it, but you may find out that they are grateful only if the school's "plan" is followed.

(By the way, I did tutor the above-mentioned student, though only for a couple of weeks, and I was able to help him. He passed his first test of the entire year (and this was April) after only two tutoring sessions.) The most important thing, however, according to his parents, was his self image. He knew he "got it", he understood it, and his confidence soared. This student wasn't used to failure. He needed to feel successful again.

All kids want to feel successful. Success give confidence. If your student needs intervention, take the steps. Go to battle, if necessary, for your kids.

Intervention

Perhaps you have identified a few concepts that your student hasn't nailed down (maybe it's learning simple facts, or perhaps it's more complex like long division or multiplying fractions) and you have decided it's time for you to step up and try to do something. Where do you go? What do you do? Is it something you can do yourself? What if the school tells you that in a few months they will cycle back through and that perhaps your child will get it then. They tell you not to worry. Should you even try?

Yes, please try. You must intervene and the longer you wait, the harder it will be. There are so many web sites to help now, and so many families who have gone before you. Help is all around and I urge you to start with sites and blogs, such as Kitchen Table Math so you can have support and help. Locate a few websites, if you need a little review, or even hard copies of helpful books, such as Math on Call, which will give you procedures and confidence.

Be willing to try. Then, tell your child that you know it's been hard but that "we" are going to do something now to help.

Decide on an amount of time. If it's a tutor, the time will be decided by the tutor, or by your budget. (See below on suggestions for tutors.) If it's your time, set aside a certain amount each day. Explain to your child the time requirements so that it will be clear. Stick to it.

Decide on a short range goal, one concept, that you can work on, and go for just that. Do everything to ensure that your child experiences immediate success of some sort, even if it's something small, the very first day. Success builds confidence. I assure you your child wants to feel and be successful. So make sure that your student sees that he/she has made progress that first session.

Be willing to make this a long-term commitment, if it is needed. I mean for a year, or two, maybe more. Catherine Johnson, from Kitchen Table Math worked with her child, using an entirely different textbook in the afternoons, in addition to the school assignment. If you're looking for how much she did a week in the other textbook, I'm sure she'll help and encourage you.

Your child is looking to you for help. You can do it. At least try. Many have and you will be able to. Whether you do it yourself, or whether you support a tutor. Do it.

Many times I intervened, short term, for our own children when they needed a little help. I always looked over all of their work. I did that early on in primary grades and they got used to it and accepted it. If I saw trouble, I made up some problems right then and there on the spot and watched them work. I could tell by watching where they got off the track. Once the problem areas were identified and addressed, we worked a little more, maybe several nights. I usually had one rule: show me that you can do 5 problems correctly without any mistakes, and we will stop. What does that do? It makes them focus on all the little things you've identified and it makes them work carefully. A few days was usually all it took.

Now for tutoring: Any time I've agreed to tutor a student, I explain to the parents that I want more than one session a week. I will agree to tutor only do it if I can have a minimum of 2 times a week, but 3 is even better. Why? Well, usually, I find that some of the trouble is procedural and simple carelessness. And what good can I do if a student has one hour with me to work on correct procedures and then the rest of the week he reverts back to incorrect methods? It is said that a person has to do something about 34 times for it to become a habit. So practice becomes very important, but it takes not just practice, but the correct kind of practice, and consistency. The work must be done properly every time. So keep this in mind, whether you are the tutor, or you are considering hiring someone. I usually find that after about 6 weeks, students may not even need me anymore because they have corrected the bad habits and see the value of working with care.