I have two boys, ages 8 and 6 1/2. Last year we used Saxon 1, the year before we used Math-U-See, and the year before that we used A Beka math. Some time ago I read your statement regarding not doing formal math with children before they were 10 years old. Based on my personal experience (although I went through college calculus, math was always, and still is, a major struggle) and based on my experience with the math curricula I listed above, my gut told me you were right. But for some reason, I’m still unsure. I’m all prepared to jump into Saxon 2 with my two boys this September, but I am also dreading it. Especially with my 8-year-old. He just doesn’t get it — the addition and subtraction stuff, that is. The shapes, patterns, measurement, etc., he picks up right away. But no matter how many manipulatives we use, he really struggles with making the jump from concrete (manipulatives) to abstract (worksheets). Besides that, he is very easily distracted during worksheet time and can take up to 5 or even 10 minutes just to write his name on the top of the sheet. My husband and I are convicted that our boys must learn that although there is great joy in learning, it is not always fun. We want them to know that worthwhile things are worth working hard for. We don’t want school to always be fun at the expense of their learning the value of hard work. However, I recognize what you are saying about the developmental aspects of this math issue. Meg
In our book Teaching the Trivium we deal more specifically with the issue of how to teach math informally in the years before age 10. I want to touch on a few issues you have raised.
Remember when your oldest was learning to walk? At six months you might have held onto his hands and stood him up on the floor to test the strength of his legs. Maybe you even helped him “walk” a few steps. You put him through the motions, but he wasn’t really walking. But you didn’t get all worried because he couldn’t take off walking all by himself. You knew he wasn’t developmentally ready to walk yet. You simply waited until he was ready. I’ve heard that some children walk as early as nine months, but most will walk at about a year, while a few will be fully sixteen months before they take their first step. The age that a child learns to walk really has no bearing on his intelligence–a child who walks at 16 months can be just as smart as a child who walks at 9 months. It’s a physical developmental issue. It’s the same with learning to read. A few will learn to read at age four and a few at age ten, while most will learn sometime between the ages of six and eight. The child who learns to read at age nine may be “smarter” than the child who learns to read at age four. It’s a developmental issue. Unfortunately, some of us don’t handle it as calmly when our child learns to read at age nine as when our child learns to walk at 16 months. Sometimes we worry unnecessarily. We may even try to force the child to read before he is able. Rather than gently introducing the letters and their sounds little by little as the child is ready, we are intent on our goal of the child learning to read in first grade.
Learning math is a developmental issue also. Some children seem to understand the mathematical concepts at an early age, some at a very late age, while it seems that, for most children, the light bulb goes on around age 10. We have discussed this issue quite a bit at other times, so I won’t go into it here. I want only to address the issue which you raised about teaching children to work hard. If we press children to perform before they are developmentally able, then we will discourage them and cause them to fail, which in turn sets them up for further discouragement. No amount of hard work on the part of a 4 month old child will result in the ability to walk. No amount of hard work on the part of a wee five year old who is not developmentally able to blend (putting the sounds of letters together to read a word) will result in reading. Similarly, sitting at the kitchen table with the same 1st grade math workbook page before him for 45 minutes will not help a developmentally unready six year old learn to subtract. Perhaps you can get him to memorize the procedures of subtraction and walk him through the page, but the light bulb is still not on. Why not wait till age 10 and all those procedures of addition, subtraction, multiplication, and division become clear to the child and he understands it in a flash.
Yes, we want our children to learn the value of hard work. But there is a difference between hard work and exasperation. Colossians 3:21 Fathers, do not provoke your children, lest they become discouraged. Exasperation is placing a greater burden upon someone than they are developmentally able to bear.
I saw this readiness principle borne out clearly in our oldest: she effortlessly learned the names and sounds of all the letters at 20 months (yes, really!) but just couldn’t put them together until that light bulb came on at 6.5 years. Then she went from zero to C.S.Lewis and Tolkien in less than a year.
Now we have a 4yo who is beginning to read with very little effort on my part.
I had 2 siblings that walked at 7mos, while most of my 7 children have walked between 12 and 15 mos. My parents worry, but we’ve learned not to stress over it. They go when they’re ready – we just provide a learning environment and plenty of encouragement!