More on math not needing to be sequential

Willa posted some thoughts on collaborative learning in which she talked a bit about right brained learners. She and I corresponded a bit about it because I sometimes find that some things in posts on this topic resonate with me (in relation to Tigger) and sometimes I’m not so sure. There was one list (that I can’t seem to find now) which really didn’t seem to fit so I hadn’t explored this topic earlier. But in the discussion with Willa, I decided that maybe I should do a bit of reading. So I got Right-Brained Children in a Left-Brained World: Unlocking the Potential of Your ADD Child by Jeffrey Freed out of the library. I’m not done reading it yet bit it has provided some useful information.

It is interesting, given my discussion in August of Mighton’s Myth of Ability, that Freed suggests giving right brained kids math that is considerably further advanced than their current grade level and then going back and filling in arithmetic as they need it. He actually suggests doing Algebra with grade 4 kids.

For Freed, part of the reason for this is to overcome the disinclination of perfectionists to try new things and to capitalize on the competitiveness that he has observed in these kinds of learners. Tigger, like me, is not at all perfectionist or competitive but there still seems to be some value in this sort of approach.

In fact, Tigger (who would be in grade 4 if she were in school) expressed an interest in algebra last spring and we did briefly consider doing it. But then I think I got worried that I was pushing her and that algebra was way too advanced for her. I recall asking a few people about the Key To … series and when folks said that they assumed knowledge of addition, subtraction, multiplication and division, I thought again about math goals and decided on the homeschoolmath.net e-books. (I really like the books, by the way, and recommend them to anyone looking for good coverage of the elementary school math curriculum.)

We started with Geometry this fall. The book goes from angles through triangles to calculating area. It avoids circles so students don’t need to understand decimals to use it. I had found some dry-erase graph paper that I thought would be useful for the section on area. But the logic of the book made a lot of sense to me so I discouraged Tigger from jumping right to the bit where we needed the graph paper. I told her that in order to do that she needed to know some of the other stuff in the book. It is a very conceptual program and has lots of drawing so she did enjoy doing it. But she got sick of it after a while and we stopped. Before we got to the bit about area.

At a loss for what to do next, I got her to do the pre- test from the Math-U-See website so that I could work out what she could do and what she couldn’t and maybe pick something. I told her why I wanted her to do it and she did some problems and pointed out stuff she had never learned how to do or had forgotten. We then picked out some relevent bits of the e-books to cover some topics she said she’d like to do.

She wanted to learn division so we did that section of the Multiplication and Division II book. I figured we’d go back and do some of the multiplication stuff later. I liked the way division was presented and I think it really helped Tigger understand the concept of long division (and some alternatives) but I’m not sure I should have made her do all of the practice problems. There was a lot of resistance. And I almost lost her before we did the thing she had wanted to learn.

Some of the problems suggested checking your answer by multiplying and we skipped that because she didn’t know how to multiply in columns. But she decided that would be good to learn so we went back and did that. We did the lesson on distributive property. I let her skip some of the practice. Then we did multipling in columns (one of the factors is a one digit number). Then I was reading Freed.

So, the next day I took a piece of paper and we did one problem like the ones we did before. Then I gave her a 3 digit by a 2 digit number and showed her how to do it. I showed her with carrying (previously we had done the ones on one line, then the 10s on the next, and so on), using the same problem we just did. Well, I started to show her and then I had a phone call and she worked it out. She was very proud of herself. So then I got her to do the harder problem we’d just done. And then I gave her a 4-digit by a 3-digit. She looked at it and started to back away. It’s too hard. The numbers are too big. I reminded her that she’d just worked out how to do the other one and this wasn’t really any harder. She reluctantly bought that and tried it. We checked it with the calculator and she had done it right. She was happy. We stopped. She said that we shouldn’t use the books; that I should just teach her myself.

Then I read more Freed. I thought more about the algebra thing. I talked to Tigger about it, explaining what Freed had said. She is interested. But I then felt like I should make sure she knows how to do the things we just learned. So I printed out some review pages from the Multiplication and Division III book. She has been resistant but she’s done some. The first time, though, she forgot what to do and didn’t go look it up or ask for help but worked herself into a state about it. I think we’ve fixed that. (Her resistances have some of the flavour of what Freed describes of perfectionists but she is pretty easy to talk out of them and she doesn’t show other signs of perfectionism.)

As an aside, I used to be worried about how to get her to learn her multiplication tables but she seems to have learned them more or less. Not sure how. We haven’t done that much practice but a lot of them are in there. And I’ve encouraged her to count on her fingers when she doesn’t know them so she figures them pretty quickly. I asked if she can visualize the sequences (she doesn’t know them as times tables but as skip counting sequences) and then find the right number but she says she can’t.

So I’m back to the algebra idea. It seems like it might be fun. She likes that conceptual stuff. I think she likes that it is supposed to be hard. I have no idea where to start. I did a bit of searching and like the look of this novel (which is not in my library) and this which also comes with a workbook. Except that in the excerpt available there is a bit about how you learn algebra in middle-school because that is when your brain is ready that is feeding my anxiety about pushing too hard or going too fast.

And then I check one of the links in Willa’s post that I didn’t check the other day for some reason, and Stephanie has a list of right-brained and left-brained traits that puts algebra in the left-brained side. Freed does say that it is often taught in a very left-brained sequential way but doesn’t need to be. And Tigger isn’t strongly right-brained though she does have some traits (as do I, thanks Willa for pointing that out). And she does get excited about the idea of algebra.

I’m not sure where this is going but I wanted to get these thoughts out there because there are folks who will probably leave helpful comments. Some of the difficulty is with me letting go. Though, like Willa, I think a bit of structure helps and doing some math is a good thing to provide some structure with. I have also seen her enjoying math and school really kicked that out of her and I would like her to get to a place where she recognizes that she can enjoy it (we have had some glimpses of that). I also think that maybe if we do some stuff that is more advanced than anyone would expect her to be, it will help me relax a bit about whether we are doing it regularly or not. I don’t have anyone really challenging my decision to homeschool or my methods but I am still not totally confident. There is some weird gremlin whispering things that is bugging me. Probably the same gremlin who is whispering things about pushing her when I know that mostly I’m trying to meet her needs, which often are ahead of where kids are expected to be at her age.

Thanks for listening.

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4 thoughts on “More on math not needing to be sequential

  1. Until this year, I would probably have told you to just follow the order of things. But I met an amazing math teacher at co-op, and saw that his pre-algebra class has 3 4-5th graders in it. THey are using MathUSee pre-algebra, and we discussed it. He told me that he feels pre-algebra fits better at this level, to get the brain thinking in that fashion. Fractions and decimals can come later, but often kids are more open to algebraic thought if introduced younger. These kids proceed to advanced fractions and decimals, with review of multiplication and division, in later years. I am now considering getting Girlfriend started earlier than traditionally planned as well.

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  2. Not sure how you’d do any harm by giving it a try, so long as you try to relax about how it goes. As you would if you were, say, trying a new sport. Is this for you at this time? No? OK, back to basket ball.

    And though I think the whole right brain/left brain stuff is interesting – I wouldn’t get fixated on whether a particular thing is a ‘right brain’ or ‘left brain’ activity. most tasks/activities probably have more than one way to perform them so perhaps are either or, and anyway, who cares? Why create a new category? I feel as if ‘I’m right/left brained’ could be a bit like ‘I’m good at sports/academic’ – unreal categories.

    Just my take. I’d relax about the whole thing (as I know you would like to!) – imperfection is ok.

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  3. As usual, your posts make me think.

    I had some algebra in sixth grade. The teacher wanted to demystify the A word, I guess, so he gave us a little unit on it in preparation for middle and high school. I loved it and still remember the rush I felt realizing that math wasn’t just boring long division. That enthusiasm carried me a long way and I never did develop the math anxiety that many others do. So I thought what Freed said made sense.

    Realizing that the strict sequential math approach hadn’t been very successful with my two middle ones, I have tried to pull in a variety of different things with my younger ones and they have responded well.

    But doing it in an flexible way as you are doing is useful because if the child isn’t into it, you can back off and try something else.

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  4. Hi – I checked back to see if you’d gotten more comments on this post. I didn’t have any words of wisdom, but I am intrigued with all your ideas. I just finished reading Freed’s book. I hope you will post a follow up on Tigger’s math studies.

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