Another posted response:

> No one gives specific examples, just "play with numbers"
> how does that help?

It helps because one of the most important things is being comfortable, really comfortable, with numbers and how they relate to each other. Basic arithmetic needs to be something that not only can you do, it's part of how you think.

> I never played with numbers so don't understand.

Play games. Play with dice. Add numbers in your head. Factor numbers in your head. Play with things like dividing something, then multiplying it to get back where you started. This sounds simplistic, but it really matters.

> " lots of music stuff," my kids play three instruments, how does this
> help with higher math?

Music and math share the concepts of recognizing and creating patterns. Really. Music theory is math in a different form.

Look at improvisational music- how is that done? The player has to know what key he is in, and what that means, and how to stay within that framework- or if he wants, where to go outside of it and still have it sound good. The listener has a part in this, too, because part of what makes music beautiful and meaningful is an intrinsic understanding of music theory on a basic level- what sounds in tune, what sounds discordant, where things sound like they should be going. You can hear a chord resolve in your head, even if it doesn't actually resolve in the music, because you expect it to be that way. Good musicians play with your expectations, and surprise you some of the time. Your experience of the music involves what you've just heard, keeping it in your head, and adding to it the new sounds happening, and making them relate in your mind.

Did you think I was going to fall back on the time signature as the math in music? Sure, that's part of it, the rhythms, but it's the notes and chords and their relationships to each other that is part of higher math.

Listen to counterpoint, baroque music, minimalist music. Listen to music in different tonal systems (like Gamelan or different Eastern music forms). Sing arpeggios. Play duets, or rounds. Try having two people play the same piece, but one play it twice through, twice the speed- how do they sound together that way? Why?

Go look up the Pythagorean Scale, see where it came from, how it changed and why. Then listen to early Bach. Listen to my favorite Bach- The Well Tempered Clavier (where did the name come from, and what does it mean? Why is that important?) Try to find a performance on pre-Pythagorean instruments.

I really am beginning to believe that part of this culture's problem with math fear and deficiency is that the educational system largely ignores music and art. Back during the time of the most famous mathematicians, music was considered one of the most important academic subjects. I think listening to and interpreting music, lots of different styles, is part of what helps our brains learn and practice making the connections they use in math. Trying to teach math without that background is almost like expecting a child to speak who has bever been spoken to.

> I am not being contrary, I am SERIOUS here. I want to let my
> children have a happy learning experience, and if I am the culprit of them
> not having that, then I want to do something about it.

You are not the culprit- more likely, what was done to you as a child is the culprit.

You can undo it, just like your children can if they have had negative math experiences.

The book "Family Math" is a good starting place. (I hear they have a couple of new versions out, one for younger kids, and one for older, but I haven't seen those) It's full of games. Try some. Start with easy ones, progress through whichever catch your interest. The important thing is to have fun with them. Once you're having fun, think about what you're doing, really think- why do things work that way? What is easier or harder for you? Why? Where are your personal math blocks?

You may want to doodle while you think, or draw or sing or talk with someone or whatever helps stuff to stick in your head.

One of my favorite things to do, and to tell people to do, is to play with converting numbers into different forms. Go from decimal to fraction to percentage to ratio and back again. Get comfortable with numbers in their different forms, so that you can take advantage of which form most easily lends itself to a certain situation. (Decimals are good for money, for example) Be as comfortable manipulating fractions as anything else.

See math as a game, not a chore. A playground. A tool, if you have to, or if you like tools.

Go look at stuff like fractals and complex geometric shapes, see the intricacy and beauty of math.

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