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Topic: fractions, technology
Replies: 1   Last Post: Jun 21, 1995 6:03 PM

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Katherine G. Harris

Posts: 18
Registered: 12/6/04
fractions, technology
Posted: Jun 21, 1995 4:16 PM
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I have been following the discussion on fractions with great
interest since I am one of those high school teachers who
inherits many students who really don't understand any thing
about them. In my school system our students start Algebra I
as early as the sixth grade. Since I teach primarily Algebra I
to ninth through twelfth graders, (and next year will teach an
11-12 class of Algebra I), most of my students are those who
find math painful and have not truly mastered much beyond
operations with whole numbers. I firmly believe that children
must be able to manipulate fractions in order to progress
beyond whole number arithmetic! Of course, it would be ideal
if they also understood why the algorithms worked, but I'll
settle for being able to add, subtract, multiply and divide
fractions and decimals.

Now, about decimal numbers. It is very common for a student to
not truly understand that a decimal is simply another way of
expressing a fraction. To many of them, decimals and fractions
are totally different. They like decimals because any
claculator will work with them. However, with the exception of
usual deciamals like ".5, .25, etc." they have no true
understanding of the actual value of the number. (An
interesting experiment for the classroom is to draw two circles
on the board. Ask one student to color 7/19 of the circle.
Ask another student to color .833333333... of his circle. Even
though 7/19 is a strange amount, that student almost
invarialbly will feel confident. The other student will
usually just guess.) It is essential for a student to
understand operations with fractions in order to work
abstractly, as required in the study of algebra and beyond.
Please, if you teach elementary and middle grades, teach
fractions. And, tell your students the truth. Not everything
they learn in school has a direct relation to "real life" but
everything you learn, period, provides a foundations for future
learning and success. Look at all those people who study the
violin and never play for money. Are they sorry they learned
to play?

Now, for my question about technology. This year I fortunate
to be the "storage" area for our classroom set of TI-82
calculators. After teaching equation solving every possible
way I could think of, I still had a large (50%?) number of
students who were not proficient. Since some of them were on
their third trip through Algebra I, I didn't think that further
drill was going to help. So, I passed out the TI-82's and
taught them to solve by graphing and using the 2nd calc-
intersect feature. (I never showed them the solve feature.)
The results were amazing! Those who had never mastered this
but still wanted to were excited and interested. They were
quite willing to sketch the graphs, worry with the window, and
do anything else required to find the solution. We even solved
higher degree equations and they understood why x^2 = 9 has two
solutions and sqrt x = 9 has only one! So, is it acceptable
for students to move on even if they are technology-dependent?
Not all of the students were successful, but all of those
willing to put in the time were. I really do want to hear
comments on this, since there is an old-fashioned side to me
that says if you canj't do it without a calculator, then you
can't go on. But... (An interesting aside, even though the
use of the calculators was sanctioned, I find that I will not
be the "storage" area next year.)

Sorry this was so long and appologies for all typos!


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