Tuesday, August 31, 2010

"delaying" math

This past spring a fellow homeschool mama shared this article below. Sensing what it was about I didn't even bother to read it—it was preaching to the choir (me). Homeschooling has been as much of a learning process for me as it has been for my children. Some people refer to this as unschooling ourselves as parents. Meaning: As an adult who went to school (as opposed to homeschooling) I was naturally drawn to being "schooly" in teaching my kids.

Fortunately for all of us, this didn't last long. I quickly realized that my kids will learn when they're ready, and not before. I'm not going to fight with them and make them do school work when they're not ready. Learning academics isn't a race, and they shouldn't feel pressured or frustrated with themselves for not meeting an artificial deadline. Adults don't go around testing each others math or reading levels. As adults we hope to succeed in life doing what we love, utilizing the gifts we are born with. If I told you I was terrible at remembering history—no matter how many times my history buff husband tells me—would you think less of me? No, you would say that's okay, because I'm using the gifts I was given, and history isn't one of them ;-)

By being outside, playing, crafting, and reading books, Zoe and Ashley learn a lot with minimal effort on my part. I create an atmosphere for them to learn in, and give them the tools they need. Although we read books from the Ambleside Online book list, we don't follow the schedule. Zoe and Ashley only watch about 45 minutes of TV a day, and they enjoy playing educational games on Time4Learning for about the same amount of time per day—Not part of the Charlotte Mason protocol, but that's okay with me.

I've said this before, but there are other human qualities which I believe are perhaps even more important than GPA and SAT scores. People often compliment me on my children's manners, and say how polite they are. The reason for this is so simple that you may not even believe it, but it's true. My husband and I are our children's role models. They spend all of their time at home with us (we both work from home). Zoe and Ashley treat each other and everyone the way they see Andy and I treating each other and everyone. How easy is that? ;-) Andy and I say "please" and "thank you," so the girls say "please" and "thank you." We show love, kindness and gratitude, so they show love, kindness and gratitude.

But I may be digressing slightly here. Back to the article that I knew to be true. Just as I take a lot, but not everything from the Charlotte Mason philosophy, I take a lot from this article, though I may not follow everything it suggests. I don't think Zoe in particular will be in 6th or 8th grade before learning math, but I do agree that in most cases it is best to delay math to some extent. As you can tell by the photo above of Zoe reading, surrounded by library books, completely absorbed, she has a passion for reading and writing. Great. Love that. Math however... How can I explain? It's like not part of her mentality yet. She would rather be wrapped up in stories, playing or creating something.

I had theorized, even before reading this article, that if I would only wait until Zoe was ready to do math, that it would come as a snap to her. I decided to test my theory, and sure enough I was right. Like the math problems our neighbor who is two years older has done with Zoe, the math we did today was effortless. Zoe is beginning third grade this year, but she was technically "behind" in math. We sat down together in our favorite coffee shop this morning and breezed through a second grade math workbook. If every day we do the same amount as today, we could be done with second grade math in a week. How about that? She could be all "caught up" before we're even half way into September. Very interesting, isn't it? :-)

♥, Kelly

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And if you would like to read the article I keep referring to, here it is:

When Less is More: The Case for Teaching Less Math in Schools
In an experiment, children who were taught less learned more. Published on March 18, 2010 by Peter Gray

In 1929, the superintendent of schools in Ithaca, New York, sent out a challenge to his colleagues in other cities. "What," he asked, "can we drop from the elementary school curriculum?" He complained that over the years new subjects were continuously being added and nothing was being subtracted, with the result that the school day was packed with too many subjects and there was little time to reflect seriously on anything. This was back in the days when people believed that children shouldn't have to spend all of their time at school work--that they needed some time to play, to do chores at home, and to be with their families--so there was reason back then to believe that whenever something new is added to the curriculum something else should be dropped.
One of the recipients of this challenge was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who responded with this outrageous proposal: We should drop arithmetic! Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: "For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child's reasoning facilities." All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children's minds, from common sense, with the result that they could do the calculations as taught to them, but didn't understand what they were doing and couldn't apply the calculations to real life problems. He believed that if arithmetic were not taught until later on--preferably not until seventh grade--the kids would learn it with far less effort and greater understanding.[1]
Think of it. Today whenever we hear that children aren't learning much of what is taught in school the hue and cry from the educational establishment is that we must therefore teach more of it! If two hundred hours of instruction on subject X does no good, well, let's try four hundred hours. If children aren't learning what is taught to them in first grade, then let's start teaching it in kindergarten. And if they aren't learning it in kindergarten, that could only mean that we need to start them in pre-kindergarten! But Benezet had the opposite opinion. If kids aren't learning much math in the early grades despite considerable time and effort devoted to it, then why waste time and effort on it?
Benezet followed his outrageous suggestion with an outrageous experiment. He asked the principals and teachers in some of the schools located in the poorest parts of Manchester to drop the third R from the early grades. They would not teach arithmetic--no adding, subtracting, multiplying or dividing. He chose schools in the poorest neighborhoods because he knew that if he tried this in the wealthier neighborhoods, where parents were high school or college graduates, the parents would rebel. As a compromise, to appease the principals who were not willing to go as far as he wished, Benezet decided on a plan in which arithmetic would be introduced in sixth grade.
As part of the plan, he asked the teachers of the earlier grades to devote some of the time that they would normally spend on arithmetic to the new third R--recitation. By "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked to talk about topics that interested them--experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would improve their abilities to reason and communicate logically. He also asked the teachers to give their pupils some practice in measuring and counting things, to assure that they would have some practical experience with numbers.
In order to evaluate the experiment, Benezet arranged for a graduate student from Boston University to come up and test the Manchester children at various times in the sixth grade. The results were remarkable. At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement. Of course, at the beginning of sixth grade, those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms. But by the end of sixth grade those in the experimental classes had completely caught up on this and were still way ahead of the others on story problems.
In sum, Benezet showed that kids who received just one year of arithmetic, in sixth grade, performed at least as well on standard calculations and much better on story problems than kids who had received several years of arithmetic training. This was all the more remarkable because of the fact that those who received just one year of training were from the poorest neighborhoods--the neighborhoods that had previously produced the poorest test results. Why have almost no educators heard of this experiment? Why isn't Benezet now considered to be one of the geniuses of public education? I wonder. [Note: Benezet's work was brought to my attention in a comment that Tammy added to my Feb. 24 post. Thanks, Tammy.]
For decades since Benezet's time, educators have debated about the best ways to teach mathematics in schools. There was the new math, the new new math, and so on. Nothing has worked. There are lots of reasons for this, one of which is that the people who teach in elementary schools are not mathematicians. Most of them are math phobic, just like most people in the larger culture. They, after all, are themselves products of the school system, and one thing the school system does well is to generate a lasting fear and loathing of mathematics in most people who pass through it. No matter what textbooks or worksheets or lesson plans the higher-ups devise for them, the teachers teach math by rote, in the only way they can, and they just pray that no smart-alec student asks them a question such as "Why do we do it that way?" or "What good is this?" The students, of course, pick up on their teachers' fear, and they learn not to ask or even to think about such questions. They learn to be dumb. They learn, as Benezet would have put it, that a math-schooled mind is a chloroformed mind.
In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle.[2] They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn't figure out that multiplication is used to find the area was evidence to Kenschaft that they didn't really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.
The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, "It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal ‘home schooling' of children." [Note: A reference to Kenschaft's article was provided to me by Sue VanHattum, who writes a great blog called "Math Mamma Writes."]
At the present time it seems clear that we are doing more damage than good by teaching math in elementary schools. Therefore, I'm with Benezet. We should stop teaching it. In my next post--about two weeks from now--I'm going to talk about how kids who don't go to traditional schools learn math with no or very little formal instruction. If you have a story to tell me about such learning, which might contribute to that post, please tell it in the comments section below or email it to me atgrayp@bc.edu within the next week.[3] I've already collected quite a few such stories, but the more I receive the more I'll have to say.

click for the link to this article


  1. I love watching my children learn in a comfortable environment. My son has always loved numbers but at 13/14 has decided he wants to work in a math book and will be taking a homeschooling algebra this fall offered by our local community college. This totally came from him. I have been amazed at how quickly he has flown through the pre-algebra. He didn't need years and years of learning the same concepts. When he was ready, he learned it. My daughter isn't really interested in math yet, except when it come to money! However, she spends so much time reading and researching. She spends lots of time on things that really interest her. I love it! We also get complements often of how polite and well mannered they both are. It has been easy. Like you said, treat each other and the kids with respect and they follow.

  2. This is a wonderful article. I wish more parents would read it and listen. My son loves math and was very anxious to start at a younger age. But not reading. I have never wanted to push him to read because I thought that it would push the desire to read right out of him. Now he is 8 years old and in third grade with Time4Learning. Suddenly he wants to read. He is reading everything, street signs, signs in store windows, cereal boxes. He truely wants to read. I am so glad I did not try to force him to read when he was younger. We love Time4Learning. I love that we have been able to work around reading until now when he is ready for it.

  3. Thank you for this. We are new to homeschooling and my husband and I are having "math" discussions.

    I look forward to reading more.