Re: Algebra (was Re: Half Grades?)

[Judi Hirsch <judih@OUSD.K12.CA.US>]

I agree that we haven't done a good job in earlier grades, and I also wonder
why there needs to be so much pressure to complete courses in one year. I
would rather have depth than breadth and would prefer that we give students
all the time they need to really learn what's important--not just to pass a
test. What do I think is important? To KNOW that one is brilliant, can
figure things out, can solve problems, can work cooperatively, and have a
desire to continue using the skills learned in school once one leaves
school. As with reading, and our desire to have our students choose to read
once they ar on their own, I would hope that student NOT see themselves as
mathematical ignoramuses as so many adults do. This long term perspective is
part of what I consider to be good teaching.
Judi
----- Original Message -----
From: Erwin Morton <e.morton@MINDSPRING.COM>
To: <ARN-L@LISTS.CUA.EDU>
Sent: Tuesday, August 21, 2001 9:35 AM
Subject: Algebra (was Re: Half Grades?)


> Judi--
>
> I think Algebra 1 taught over two years is pretty
> common.  I know we have such courses in our high
> schools, and I know they have them in LA Unified
> (available in 8th-9th and in 9th-10th, I believe).
>
> But I also think (caveat:  this is opinion, not
> research data) the real issue here is that we
> have not done a good job, in the earlier grades,
> of preparing the ground for algebra.
>
> For example:
>
> Most math prior to algebra, in most classrooms, is
> purely procedural.  (I've seen this even in classrooms
> with reform-math materials.)  In such classrooms, the
> equals sign means "do the operations shown and find
> the result".  It's like the "=" key on a calculator.
> "Equations" look like this:
>
>      8 * 7 = ?
>
> ("Math facts" such as
>
>      8 * 7 = 56
>
> are usually procedural, too--in elementary school
> they are usually interpreted to mean "when you
> multiply 8 times 7, you get 56".)
>
> After 8 or 9 years of this interpretation, the
> students hit algebra, and suddenly the equals sign
> has a completely different meaning:  it expresses
> a *relationship*, not an operation.  The equation
> (not in quotation marks this time)
>
>      y = mx + b
>
> is a completely different animal from the first
> example above.  It's no wonder the students have
> difficulty with the transition.
>
> --Erwin
>
> ---
>
> Judi Hirsch wrote:
>
> > This [half grades] sounds like my suggestion to do algebra
> > in two years instead of one---that way, rather than flunking
> > and feeling stupid, students can take all the time they need
> > and really learn [it] once.
> > Judi
>
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