One thing I have started doing differently which has made a substantial
change in the way I teach the algebra sequence is to priortize the topics to
determine which topics need more in-depth coverage and which ones can be
treated as overviews. This is a break from many years of looking at the
sections of the book to be "covered" and proportioning them out linearly
throughout the semester. Here are some of my thoughts on priorities of time
spent.
In beginning algebra, I approach "what is a variable" in many different
settings, from pattern recognition to calling a variable the name of a
storage location. The textbook definition, "a variable is a letter which
represents a number" is only understood after the concept is built.
(Without an understanding first, there is no difference by that definition
between a letter that represents a constant or a letter that represents a
variable.) Understanding a variable and how to substitute values into a
formula is the biggest first building block of algebra which we generally
cover abstractly in a few days and then move on.
We can't hit at graphing, lines, slopes of lines as a physical slope or as a
rate of change enough. Students measure physical slopes, determine whether
the ramp is legal, stage races and clock speeds and plot the data. I
supplement the text with applications, visual lines of good fit, theoretical
problems like give students a graph of a line on a graph that has different
vertical and horizontal scales, have them estimate the slope and other
critical information.
I have created worksheets to give an overview of topics such as simplifying
radicals. I also give an overview of adding, subtracting, multiplying, and
dividing rational expressions. Students no doubt do not need to see every
possible scenario with every possible factoring combination to learn the
concepts or skills need for working with these or understanding about domain
limitations and vertical asymptotes.
How do some of you make room in a traditional curriculum for more indepth
explorations, whether they be applications or theoretical mathematics?
Martha
----- Original Message -----
From: Laura Bracken <bracken@LCSC.EDU>
To: <mathedcc@archives.math.utk.edu>
Sent: Thursday, October 28, 1999 6:01 PM
Subject: RE: [MATHEDCC] Why Johnny can't do math
> I agree, teaching math in context using applications is motivating and
> wonderful. However, is the only mathematics worth knowing and teaching
> applied mathematics? Isn't mathematics as a human accomplishment in
itself
> worth studying? Certainly many other disciplines that we make part of the
> core curriculum include topics that are not necessarily "real life" and
> "useful to solve problems".
>
> Besides, we all know that the mathematics used in applications is often
> developed using pure mathematics that isn't "useful". One of the reasons
> that we have so many contrived word problems is that textbook writers are
> trying to meet the call for problems with context in situations where
there
> are few if any applications.
>
> I'm still wondering about intermediate algebra. What skills/techniques
> should we eliminate from this curriculum under the situation in which we
> must work -- our students must succeed in the next math course or in the
> other courses for which this is a prerequisite. Lets get away from the
> theoretical for a bit and talk reality. Next semester, what should I do
> differently?
>
> --Laura
>
> ____________________________________________________________________
> Laura Bracken bracken@lcsc.edu
>
> Division of Natural Science and Mathematics Office: 208-799-2484
> Lewis-Clark State College Fax:
208-799-2064
> 500 8th Avenue
> Lewiston, ID 83501
> _____________________________________________________________________
>
>
>
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