Math Education

What is learning math all about? What's the basic idea we need to help our children be successful in math? What's the secret to math ability? In the United States, most people, most teachers, most students, believe that learning math is about developing understanding of certain concepts of principles. There is a pervasive belief that a certain type of innate math ability, the much desired trait of "Being Good at Learning Math," is the key to success. And the lack of it is the cause of frustration and failure in this subject.

Just Like Riding a Bike
Think of teaching a child to ride a bike. What are the conditions for success? First, the child needs to have already mastered a set of motor skills that are prerequisite to riding the bike. He or she needs to be able to walk and run already, so that the strength and endurance to turn the peddles are in place. He or she needs the gross motor coordination to hold the handles tight, peddle, and turn the head a bit, all at the same time. He or she needs enough sense of balance so that the potential to stay up is there. So, we need prerequisite skills.
Second, we need developmental readiness. Third, we need some kind of technique to help the child to get going. Like taking the child to an open level place without cars. Like running along holding the back of the bike, gradually letting go for longer and longer.
What about natural ability? OK, a very coordinated child might learn very young. Might teach himself. Think you can look at a bunch of ten year olds, twenty year olds, thirty year olds ... and tell who learnt to ride at four or five or six?
I doubt it.
With unusual talent, the child can learn faster, easier, a bit younger. With the developed skills in place and an OK teaching technique, really almost anyone can learn to ride.
What About Mastering Concepts? You think the child understand how the bike works? I'm sure I don't understand why it's easier to balance when you're going faster than when you're going slower. Natural ability makes it easier, but isn't the main thing. Conceptual understanding isn't the main thing. The main thing is sound prerequisite skills, developmental readiness, and some sensible approaches to instruction.
Now here's the scary part. Most math students in our schools are hitting the material without the necessary prerequisite skills, without developmental readiness, and without satisfactory approaches to education. This is pattern of math education is what is really behind the current "math anxiety" crisis in American schools.