More about Moving on in Math

I got a question in one of the comments on my earlier Right-brained Quote of the Day post and while I was typing up a response, I realized that there was enough there for a post in itself. So i figured that I would use it as a jumping off point for a regular post and kill two birds with one stone.

I am very interested in hearing more about the higher level concepts Jason is learning. What kind of math is he doing?

Actually right now we are mostly working through Life With Fred: Fractions (which is a really good match for right brained kids...he is really enjoying it). What I like about it is that, in addition to the fraction information, he is also definitely getting a lot of "practice" with doing addition and multiplication (which he needs). I just let him use a multiplication chart to look up the facts he is not sure of and he is gradually getting quicker. I think the reason he does not mind doing "the math" with this approach is because the storyline is very humerous and it engages him (as opposed to worksheets which he finds mind-numbingly boring!)

A lot of the other "higher level" math we have done has been through math literature (a la Living Math) He loves books like The Number Devil and The Adventures of Penrose the Mathematical Cat which deal with all sorts of different math concepts. I am sure that some of it goes over his head, but it introduces the concepts and we can go back and revisit the topics. He especially seems to be drawn towards things like Fibonacci numbers. I recently picked up The Joy of Thinking lectures from The Teaching Company and I think there are several topics which will peak his interest.

He has also enjoyed doing some of Hands On Equations (which is a hands on approach to understanding algebra). I hope to go back to this sometime soon.

Then there are some things that he just pretty much picks up on his own. I know that at around 6 he completely "got" the concept of negative numbers. He had asked me one time about a negative sign he saw in front of a number. I showed him a number line to explain. A little later, he showed me that he understood how to subtract a larger number from a smaller and also how to add negative numbers.

He used this understanding to figure out carrying...instead of subtracting right to left, he subtracts left to right and just calculates the negative number if needed. I hope that makes sense...basically he calculates 115-83 as 100-0=100, 10-80=-70, 5-3=2 then 100+(-70)=30 and 30+2=32 (although he does most of it in his head and not quite as sequentially).

One of the things that I am really happy about is that he used to say that he hated math and that math was boring. Now (with my encouragement) he realizes that it is only arithmetic that he finds boring and that there is a whole other world of math out there.

I don't think that math is overly his "thing" or that it will be a deep passion of his, but he definitely has a strong intuitive grasp on mathamatical concepts.

Comments

[MoM]

Thanks! I am going to try some of these ideas with my right-brained guy (he's 10). He's starting to say he "hates math" and is "bad at it" -- which is a shame because he's NOT bad at it, quite the opposite. He learned in a similar way to Jason with figuring out negative numbers on his own then using it in computation to avoid "borrowing and carrying."

[freelearner]

My daughter sometimes does subtraction that way, too. I remember hating borrowing, and she can't stand it either. I think they settled on the conventional borrowing method a long time ago because paper was very expensive, and borrowing uses fewer lines than doing subtotals. Same thing with carrying... you can write the subtotals for each column on separate lines and then do a final add at the end, and actually it makes more sense for kids because it reinforces the ones, tens, and hundreds concepts (e.g. 3 hundreds plus 1 hundred = 400, not 4).

On a related note, I had been accurately doing borrowing for about 2 years before it suddenly occurred to me that the ones, tens, and hundreds were like pennies, dimes, and dollars, and it was really all a matter of making change. Which means that I carried out those computations mindlessly for 2 years without understanding what I was actually doing!

I think you'd like this essay about real math: http://www.maa.org/devlin/LockhartsLament.pdf .

I'm thrilled to hear about those math books, and can't wait to hunt them down. I've been desperate for other ways to do math than just computational worksheets. Yeah, we have various manipulatives... but those are, in fact, mostly a means of illustrating basic arithmetic. I was actually a math major in college, but believe me, that does NOT help me. The most useful books & videos are the ones aimed at non-math people... college math classes are just more computation. Nobody ever asks you to write an essay question on the Fibonacci series and how mystically cool it is.