Here is a cut and paste from www.triviumpursuit.com
Have any of you taken this approach to teaching math to your students? We are following this advice and it sure makes for happy, peaceful school days. I have talked to several homeschooling parents and they say that their math lessons ruin their otherwise enjoyable school days. Since I am new to these boards I would like to know if there are others who have taken this approach, and if so, were you pleased with the results?
By Harvey and Laurie Bluedorn
Early Language Skills First
So our focus before age ten is building language skills â€“ speaking, reading and writing â€“ especially vocabulary. This is the primary index of intelligence throughout life. Do things in a concrete way. At age ten, when the brain physically changes, and begins to make the complex connections, you begin the more complex and abstract learning. With this emphasis in the early years, we lay a proper foundation for a full academic load later.
Early Informal Math
We have often been asked about our suggestion that math before age ten is best taught "informally." This seems most uncustomary to many. At the end of this article we have placed our article History and Research on the Teaching of Math. This information also appears in the Appendix of our booklet series. We very much want to learn if there is any contrary research or historical evidence. Everything which we encounter on the question continues to confirm this common sense view on the matter. We continually receive positive and enthusiastic feedback from families which have followed these suggestions â€“ though many at first followed somewhat apprehensively. We are still waiting for our first negative feedback. Weâ€™re somewhat surprised. We at least expected there would be some families which were generally lax or unschooling in their approach, and would try to blame their math troubles on our recommendations. But we recommend no lax learning. Lax learning lacks learning.
What We Recommend for Math (and Grammar Too)
Itâ€™s the Method, ______
What we and others recommend regarding math is basically what was practiced with outstanding success until the twentieth century, when formal math before age ten was largely introduced into the world. Cultural math failure coincides with the innovation of early formal "workbook" math. We argue that itâ€™s the method. We believe in math before age ten. But we believe the evidence is against workbook math before age ten. The developmental evidence appears very supportive of that view. The same is true with grammar â€“ not language, but grammar. It is best to learn to speak and read and write a language before age ten. But grammar â€“ identifying Gerunds and Participles â€“ is best left until age ten. (Approximately age ten.)
The File Drawer Analogy
Math and Grammar can be "learned" â€“ and "learned" â€“ well before this time, but itâ€™s not the kind of learning we want. We compare it to putting information in the wrong file cabinet â€“ you have trouble later finding it and using it. At age ten, the information is literally stored in a different part of the brain than before age ten. (Again, approximately age ten.) Learning math in an abstract workbook fashion before age ten literally causes the brain to be structured differently. If the child depends upon his early math learning drawer, and does not develop a new file draw for later math learning, he runs into a brick wall when he encounters algebra. (We like to mix our metaphors.) Now, if he learns abstract workbook math before age ten, then he will either develop a second math memory after age ten (and, hopefully, not have a cross-indexing problem), or else he will begin to fail in upper math. But if he learns math in a concrete â€“ not abstract â€“ way before age ten, and he begins to learn abstract workbook math at age ten, then the brain will develop properly, the right connections will be made, and â€“ assuming normal abilities and developments elsewhere â€“ he will advance in math at a regular pace without unusual difficulties. The same is true with grammar.
The Computer Analogy
Or, to put it in computer terms, some word processors can handle some simple calculations. You can type in the data, and it will work with numbers on a simple level. But if you want to do complex calculations, you have to load a much more complex program on the hard drive. Until about age ten, children only have word processors. About age ten, the more complex spread sheet program begins to be loaded up on the hard drive. If you enter all of your math information in the word processor, then it is likely that when the child switches to the spread sheet program, the data will not be compatible. Formatting errors will abound. Youâ€™ll have to re-enter the data. Why not do something more profitable until the spread sheet program is up and running?
Time Better Spent
We are satisfied that the time spent studying math â€“ which the young child is not yet developmentally equipped for â€“ could better be spent developing verbal skills â€“ which the child is a sponge for at these early ages. Deal with numbers in a concrete and verbal way until age ten. Use actual objects when you can, and when you canâ€™t, then use words and names for actual objects. Our culture is so full of numbers and measurements, that we let them pass without notice. Teach the names for numerical values with dominoes. Teach counting with cards or Rummikub. Teach addition with checkers or chess. Teach base ten and place value with money or Cuisenaire rods, or other manipulative math programs. Teach measuring systems with tape measures, measuring cups, weight scales, odometers. Teach fractions with pies and cakes and cooking. Teach area by garden plotting and room arranging. One mom who had struggled with waiting in math wrote us that her son wrote down on a Sunday school form that math was his favorite subject. Since they didnâ€™t do math, she was surprised and puzzled. When she asked her son why he wrote down math, he said, "What do you mean, Mom? We talk about numbers all the time." When she sat down with her son and looked through a math program, she discovered that he already knew it all. This may be a little more intuitive and less structured than we have in mind, but it demonstrates well how these things are taught as part of life.
The Ideal and the Real
In our opinion, the ideal would be to learn to speak and write several languages and to become familiar with a wide scope of literature before age ten, which lays a wide and solid foundation for formal math and grammar beginning around age ten. Everything seems to point to this as the best course to take. But we have never said "don't ever teach math before age ten." The whole idea is as ridiculous as it sounds. You cannot avoid exposing your child to arithmetic concepts. They will discover it on their own at a very early age. Teach them what they are ready to learn. But teach them in a concrete way, not in an abstract way. Thatâ€™s what informal math is. It is not leaving the child to discover what he wants. Also, we have never said, "don't ever teach formal math before age ten." We have always said that that was a judgement call to be made by the parent, and if you should have a precocious little tyke who wants to learn math and works well with workbooks, then you would probably be mistaken if you were to hold him back. But if you force him beyond his developmental capabilities, then you are more prone to cause developmental abnormalities. In other words
And O ye fathers, do not aggravate [/exasperate] your children, rather, nurture them to full maturity in the correction and counsel of the Lord. â€” Ephesians 6:4, Very literal translation.
O ye fathers, do not overstimulate [/provoke too far] your children, in order that they should not be broken in spirit [/disheartened]. â€” Colossians 3:21 Very literal translation.