Posted by: Kriston

## Math intuition, math without books - 04/22/08 08:30 PM

Please bear with me a bit on this post. It has two goals, which may or may not coincide neatly:

1) I'm trying to digest a presentation my local POGS put on by a brilliant mathematician/inventor/teacher tonight so I can apply his methods for teaching math to my DS6.5, and

2) I'm trying to share his insights with anyone here who is interested.

I may have to muddle through 1) before I can share much that's useful to meet goal 2).

I'm both excited and terrified by this notion. It lines up very neatly with what I'm seeing and feeling about my own experience of teaching math to my son--my fear that my approach is killing math for him, my dissatisfaction with "book-learning" (even the good curricula!) for math, etc. This gives me a totally different way to attack math, and a very child-directed way at that. It fits neatly with a unit study sort of approach, which I've been considering for next year, since the wholly hands-on tack lends itself to combining math with science, history, sports, etc.

OTOH...

I'm still more-or-less terrified of math, and I'm not at all sure that I can teach calculus to a 7yo, even if it's very basic and I don't call it calculus! It's going to take a whole lot more effort on my part to make this work, and I'm not sure I have it in me to do it even a little bit well. It's a whole lot easier to cover a workbook than it is to really teach math.

Of course, writing the situation out like that makes the choice obvious, doesn't it? I can teach math in a way that makes perfect sense to me and that my DS has literally been asking for, or I can be lazy and probably kill his love of math. Well, that's a no-brainer!

I foresee a long summer of planning for me...

1) I'm trying to digest a presentation my local POGS put on by a brilliant mathematician/inventor/teacher tonight so I can apply his methods for teaching math to my DS6.5, and

2) I'm trying to share his insights with anyone here who is interested.

I may have to muddle through 1) before I can share much that's useful to meet goal 2).

- In effect, Dr. F. said that most people--schools, teachers, homeschool parents, etc.--mistake teaching arithmetic or showing kids how to "do" math for teaching mathematics, and that that's wrong. Doing math and getting math are two very different things.
- Instead of using canned problems out of a book, we should teach kids math only through natural methods, through science experiments like pendulums and bouncing balls, graphing changes in history, the weather, election results, etc. on Excel, and so on. Ask them how many oranges can fit in a box. Have them estimate the value of pi as closely as they can using only geometrical shapes and a ruler.
- Rather than teaching math facts or requiring memorization, we should encourage kids to derive their math facts every time they do a problem until they have internalized them. No memorization ever. If it takes longer to do the problems, then so be it; just do fewer, deeper, harder problems. Memorization kills intuition, and should be banned.
- Start with the big picture. Teach calculus to the littlest kids, but don't call it that and don't expect them to understand it all in one bite. Give it to them until you lose them and then move on to the next topic. It's the spiral method of teaching at its best: every 2 or 3 years, come back to calculus (or stats or trig or geometry or whatever), only with the next layer of complexity, picking up wherever the child stopped during the previous rotation of the spiral (if that makes sense, as I'm explaining it badly).
- Above all else, teach them that math is beautiful and encourage them to use their intuition.

I'm both excited and terrified by this notion. It lines up very neatly with what I'm seeing and feeling about my own experience of teaching math to my son--my fear that my approach is killing math for him, my dissatisfaction with "book-learning" (even the good curricula!) for math, etc. This gives me a totally different way to attack math, and a very child-directed way at that. It fits neatly with a unit study sort of approach, which I've been considering for next year, since the wholly hands-on tack lends itself to combining math with science, history, sports, etc.

OTOH...

I'm still more-or-less terrified of math, and I'm not at all sure that I can teach calculus to a 7yo, even if it's very basic and I don't call it calculus! It's going to take a whole lot more effort on my part to make this work, and I'm not sure I have it in me to do it even a little bit well. It's a whole lot easier to cover a workbook than it is to really teach math.

Of course, writing the situation out like that makes the choice obvious, doesn't it? I can teach math in a way that makes perfect sense to me and that my DS has literally been asking for, or I can be lazy and probably kill his love of math. Well, that's a no-brainer!

I foresee a long summer of planning for me...