From
Trivium Pursuit: Delayed Formal Math Approach:
Depending upon the child, upon the method, and upon the subject matter covered, there exists the potential for developmental harm from the formal teaching of arithmetic before age ten. Small children cannot understand many arithmetic concepts at an early age. We can teach them to perform the process, but we cannot make them understand the concepts. The child “learns” to hate “learning.” The child’s understanding develops along the wrong lines. He may actually develop mental “blocks” to arithmetic – actual physiological blocks in the brain.
I find this idea of delaying formal math interesting, especially since it is based on
a historical perspective and education research. My own take is that
math is a language and therefore its vocabulary should be taught every single day, just like we use letters and simple words every single day with our very young children. Further, I think
math should be a game, always. When it is considered a game, it's less likely to cause the physiological brain blocks referenced in the quote above.
With math-as-games, I think it's okay to challenge children before age ten.
We are using
Singapore math 1A/1B this year, but more often Gilgamesh's math learning is coming from his own independent play with
manipulatives,
refrigerator magnets, and technology (
flash card app on my phone,
more.starfall.com exercises).
He's getting a
much broader base in math than I ever had, especially for his age, because we aren't obsessing over a "spiral method" or a "linear method." To label it, I guess it would be a Pyramid Method: broad foundation leading up to finer math later on. He's played with:
- cardinal and ordinal numbers
- sets
- addition
- subtraction
- multiplication
- division
- charting
- graphing
- tallying
- skip counting
- time-telling
- money-counting
- scales
- measurement
- estimation
- geometric building
- fitting shapes into each other (tangrams, pattern blocks)
- spotting and creating patterns
- symmetry
- sorting
- three-dimensional and two-dimensional shapes
- geometry terms
- story problems
- dot-to-dot
...and probably some things I'm not even aware of, as he's sponging up anything he sees, hears, or reads even when I'm not around to make sure he does.
I've read many opinions about
delayed math and
delayed reading, and even
delayed potty training. I see the wisdom in it with a child who is struggling. But I think
the terminology is wrong. It isn't really delayed -- just
channeled differently.
Instead of forcing a young child through a traditional reading program, we take a step back and read copiously to the child, help him notice traffic signs, cereal boxes, help him memorize sight words through word games: give the reading context and fun.
Not delaying math, you're really just giving them room to learn some of the intuitive principles on their own, making them come to you when they want to know how to carry the one, how to multiply big numbers, etc.
Through extensive read-aloud time with my oldest child, he began asking about apostrophes at the age of 4 and understood the basics of the contraction at that age. Now, at age 5, he's learning that it can also mean possession and that that's different for plural possessive.
I didn't miss an opportunity by waiting to explain the intricacies of apostrophe usage. Rather, I introduced it as he became interested, and he understood it because he wanted to understand it. At 4 1/2, he was reading at a first grade level. Now, at 5 3/4, he's reading on the cusp of a fourth grade level. We didn't delay reading training. But we didn't force it on an arbitrary schedule either.
Through math play, he's come to addition of double-digit numbers because of his own interest.
Story problems are more of a natural thing as he looks to math to solve questions in his own play: how many blocks can I stack up, how many should make the base of the pyramid so I can end with one on top and use all of them, etc.
So, to ease the troubled minds of parents who read "delayed" and think "problem" and "stunted," think of it in these terms: You're not
delaying crucial life skills.
You're only delaying the formal, rigid structure of the way you were taught reading or math. What you're really doing is
channeling your child's focus into the basic vocabulary, letting her play with the basic tools to see how the pieces fit together and what it means to her personally.
If a child knows enough Latin words, it will be a piece of cake for him to learn the language when he is developmentally ready. That's the principle here, as well.
Give a child a fish and you've fed him for one meal. Teach a child to fish and you've fed him for a lifetime. Hand a child the tool, the fishing rod and the fishy lake, and give him a few hours to himself... and he'll teach himself.
As parents and teachers, sometimes all we need to do is provide the tools, be accessible for questions, and then get out of the way.
p.s. This fits into classical education's trivium stages of grammar, logic, rhetoric, believe it or not. This research only claims that a child's logical faculties aren't ready to absorb complex math principles until 8-10 years of age. That doesn't mean we should delay memorization of math (and reading) facts. Just as students memorize the states and capitals without necessarily understanding that Phoenix is hot and Juneau is cold, they can memorize that 8 x 6 = 48 without understanding that it means six hours of work at $8 an hour earns them $48. The understanding and depth can come later, during the logic stage. But those building blocks can and should be put into place now.
A Thomas Jefferson Education: Teaching a Generation of Leaders for the Twenty-first Century by Oliver DeMille
