Speaking of factoring, I promised some of you that I would report how the
first day of class went in the Graphing Calculator approach to college
algebra with the factoring exercise. Here is what I did and how it went.
I gave each student 3 colors of index cards--these are used for voting on
this and other class discussion questions. Each student was given a slip
of paper that said,
"Each of the following are wrong answers for factoring x^2 - x - 6.
a. (x-2)(x+3)
b. (x-6)(x+1)
c. (x-3.1)(x+1.9)
Which answer is the 'best answer' for the factored form of x^2 - x - 6?"
The students had about 30 seconds, without discussion, to look at the
problem and vote with their note card. Everyone had to hold up a
card--pink for (a) yellow for (b) and white for (c). I counted the votes
and 24 students chose (a) for the best answer and 6 chose (c) for the best
answer. No one chose (b). I then had them discuss the problem with
someone else and tell them why they made their choice. Then they
revoted--one person changed from (a) to (c). I then showed them the graphs
of the original quadratic function on the graphics calculator and compared
it to the graphs of all of the wrong answers and used this as an
introduction to what the graphics calculator can tell us about traditional
mathematics that we might miss if we focus with binocular vision on the
procedures.
I thought it was a great start of the night and set the tone that we will
be looking at traditional topics differently as well as do things such as
data collection that we never could do before. I had never used the note
card voting technique, but liked that also. I borrowed the idea from a
book I had read. Since everyone had to vote, we got the opinion of
everyone at the same time, not just the one or two vocal students. I used
the note cards later when reviewing the famous -2^2 question of whether the
answer is -4 or 4 and how the calculator handles the problem and how that
appears to differ from most scientific calculators. In my class, about 23
thought the answer was 4, and 7 thought the answer was -4 The voting
brought home that the majority is not always right and got everyone to
commit to an answer without being singled out.
On the complex number question, I was taught that a+bi where a and b are
real numbers is a complex number and bi where b is not 0 is an imaginary
number. I learned that pure imaginary and imaginary meant the same thing.
The imaginary numbers do not form a group, have closure, etc.
Martha
>Good, all us mathematicians should go on a holy war in like vein at all
>the would be pic-n-saves!
>
>Regards,
>
>
>On Mon, 2 Jun 1997, Roberta S. Lacefield wrote:
>
>>
>> >And .25 cents...my students tell me that this is a quarter everytime.
>> >They can't seem to grasp hundredths of a cent. Do others encounter this
>> >also?
>> >
>> >Just wonder?????
>> >
>> >
>> I was nearly tossed out of a Pic-n-Save once for trying to convince the
>> manager that he was confusing my students by letting his employees write
>> things like .89 cents and 3 for .99 cents. I tried to explain it to him
>> but he just thought I was an escapee from an insane asylum. Now that the
>> Pic-n-Save is closed, his employees are wreaking havoc at the local Walmart
>> and my students continue to be confused.
>>
>> Roberta
>>
>> ____________________________________________________________
>> Roberta S. Lacefield RSLace@mail.way.peachnet.edu
>> Waycross College http://members.tripod.com/~Roberta/index.html
>> 2001 S. Georgia Pkwy (912) 285 - 6027
>> Waycross, GA 31503 fax: (912) 287-4909
>>
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>
>A. Jorge Garcia
>****************************************************************************
>Teacher/Professor Applied-Mathematics/Computer-Science Baldwin-SHS/Nassau-CC
>http://freenet.buffalo.edu/~aj317
>mailto:aj317@freenet.buffalo.edu
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Martha Haehl
Maple Woods Community College
2601 N. E. Barry Rd.
Kansas City, Missouri 64156
(816)437-3147
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