Date: Oct 1, 2012 12:40 PM
Author: Wayne Bishop
Subject: Re: An Algebra 2 Test

At 08:34 AM 9/29/2012, Robert Hansen wrote:

>I think we have to be careful when using the
>phrase "hidden trick". I know what you mean, but
>my bar is a bit higher. To me the "trick" must
>be very unique to be called "hidden". In the
>case of Dave's problem, all the student needs to
>be aware of is that relationships do not have to
>be explicitly spelled out with the variables,
>they may be implicit in the constants as well.

My concern with Dave's problem (and his expressly
as well) is that someone can know Algebra 2 well
and still miss the trick unless a hint is
given. Our statewide Entry-Level Mathematics has
shown that simplifying a single "rigged" to be
simple but compound rational function (numerator
and denominator each consisting of
sums/differences of rational functions) correlate
so well with future success in anything needing
algebra that it could be a one item
test. Success with such a problem, however, does
not mean that student would spot this problem as trivial.

>Well, this is what I have struggled with, the
>use case. I have not found in people lives in
>general a use case for algebra. I am not saying
>that you couldn't invent use cases (recipes,
>mortgages and such), just that the majority of
>people are not interested in them nor do they
>ever use them. There are paths that do use
>algebra, but if you interviewed and monitored
>100 people's lives, chosen at random, I doubt
>you would find 5 that ever put an x or a y down
>on piece of paper, post school, in their entire
>life. Now spreadsheets on the other hand, they
>beat algebra at making people's lives easier 100 to 1.

That has never bothered me. Out of that hundred,
how many will need to know or ever use who Carl
Sandburg was? And a ton of other such
stuff. What really does bother me - and leads to
the huge inequity at later stages - is being
genuinely algebra ready at algebra time. At that
point, becoming algebra competent or not
(especially at the Algebra 2 level) is probably
irrelevant for those whose ambitions lie other
directions (if known; if not knownÂ…?) Hence my
huge interest in quality K-7 mathematics with K-5
(both math and reading) being the most important
and 6-7 having lots of ratio/percent/etc. word
problems that have to actually be read and
understood for the mathematical content and how
to interpret it back in terms of the original setting.