[Edu-sig] Algebra 2

[Matt K]

*To Anna:*
Thanks for the clarification. I can understand that punchcard *should* be
clear to me - but to me I've never seen or used one in my life; I only hear
of them in fairytales with abbucusses and dragons.

*To Kirby:
*You can always subscript with words instead of just letters! That enables
you to have more meaning.
(more below)

*To Kirby and Andrew:*
I really like the idea but it sounds like you guys are talking at far far
higher levels that I can achieve. The *stronger* students I'll be teaching,
who *choose* to do an elective in computing, will come to properly
understand loops only in about 2 years. I've tried to teach recursion to
about 4 students while I've been a teacher, and only 2 have ever worked it
out - and those students were exceptional. Things like classes are hidden
from the students almost entirely until the final year, and even then they
are only taught "as needed".

Which is why things like generators and classes for fractions are out. The
syntax for that would just be too confusing. We're looking at the level of
algebra with these kids where they have mostly learnt to add like terms and
are perhaps beginning to factorise a simple common factor. Nothing like
difference of two squares... just the beginnings. They'll start to do
algebraic fractions and perhaps begin to appreciate the form y = mx + b.

But, it sounds like you've both done it with some success with significantly
older (and smarter) students. I think you've motivated me to try it and see
what happens!

*To Andrew:
*I wouldn't expect to see results in a test. Really, if they're trying to be
good at tests, the *best* way to do it is by rote. But if we're teaching a
deep understanding (which we of course are!) then this will perhaps help -
although I wouldn't expect the results to be apparent for a while. A solid
understanding of algerbra will really help them once they get into the
graphing topic intensely, which is 2 years later.

Further thoughts are welcome of course!

Thanks heaps!
Matt


On Wed, Oct 8, 2008 at 2:36 AM, Anna Ravenscroft <annaraven at gmail.com>wrote:

>
>
> On Tue, Oct 7, 2008 at 7:18 AM, Matt K <matt.kameron at gmail.com> wrote:
>
>> Anna, is what you describe programming (as in Python)
>>
>
> Back then it was basic. ;-)
>
>
>>  or using graphing software (as in Maple/Matlab)?
>>
>
> Never used it.
>
>
>>  I am not certain which you are referring to by reading your email.
>>
>
> Sorry - I thought the punchcards was pretty telling... ;-)
>
>>
>> I think the difference is significant - the latter converts an equation to
>> a graph, the former might show students the generalisation of an algorithm.
>>
>> The downside you describe won't be an issue these days (at least in my
>> school) - Python is so powerful that kids will start playing around with it
>> out of my control - plus they always see what the kids who are older than
>> them are doing.
>>
>> Yep. It's nice to have a language you *can* do more than just equations
> with without it being painful.
>
>
> --
> cordially,
> Anna
> --
> Walking through the water. Trying to get across.
> Just like everybody else.
>
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