I forgot to mention in my first post that I am equally concerned about a
student who pulls out a piece of paper and pencil to compute 10*321.75. and
on the first line put a row of zeros and on the second, put 32175 off-set,
of course, add the columns and count back the number of decimals to arrive
at the answer. I have also had that happen from a student who chooses not
to use a calculator. A person can memorize the process--whether it be
pencil and paper or button pushing on a calculator and still miss the
concept of numbers, arithmetic and reasonable answers.
We can teach arithmetic concepts with hands-on activities, but at the same
time teach the processes of arithmetic, teach efficient calculator use, and
use the calculator to help develop a number sense. It is only when we
think that producing the answer to an arithmetic problem is, in and of
itself, the desired end result of Basic Math that calculators--or pencil
and paper processes-- "water down" the course and work at odds to a
student's developing a number sense.
When we combine a visual look at numbers along with calculator
computations, the calculator can enhance the development of a number sense.
For example, to help a student understand what a reasonable answer to
789.542/0.12, we might start with some rounding. Approximate the problem
as 790/0.1.
Next, we might look at a "ruler", marked in 100's and put 790 on the ruler.
Classroom discussion: How many 1's are in one unit of the ruler? (ans.
100--this is so much easier with pictures) How many 0.1's are in "1"? How
many 0.1's are in 100? How many 0.1's are in 790? End the discussion
with calculating 789.542/0.12 on a calculator. You can alo talk about
multiplying numerator and denominator by 10 and visually see why that gives
you the same answer. In this way, both the calculator and the visual are
used to help develop a number sense.
A number sense is also developed when real data is used. Look up national
debt figures and determine how much each U.S. citizen "owes." Determine
how much each taxpayer owes. Hopefully, you will pull out a calculator in
helping you decide this. Maybe have the students quess the answers to the
questions and move in on a correct answer by guessing and checking.
Perhaps students will naturally understand that division and multiplication
are reverse processes.
>I agree that using a calculator is not "wrong". It's just a matter of a
>student's individual progress before they can eventually make the switch from
>button-pushing to mental calculation.
>I will never take away a calculator from a student. But I try to respond
>quickly when I see someone missing a chance to think. I try to encourage
>students by saying "you knew that already, right?"
>The worst part for me is when I say goodbye to students after only 18 weeks
>of progress. I wish that there was more opportunity to assess number sense
>over the long-term education of community college students.
>
>Mark Harbison
>Whittier, CA