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Re: [Phys-l] innumeracy

I agree that knowing the correct population of your country or the world is
something a bit different from what I'd call 'numeracy." After just a quick
glance at the values below it looks to me that more are in the ballpark than
wildly off.

Years ago I taught a low level algebra class where most of the students were
not up to it. Searching for something more "real-life" to motivate them I
tried having them compute the cost per ounce of pop in different packages
(cans, plastic 2-liter bottles,etc.). It turns out that there is a very
dramatic price difference!

I asked them to give an opinion on whether they would choose the less
expensive packaging. One student compared the prices per ounce (I don't
remember them now, maybe 1.7 cents/oz. And 2.3 cents/oz., say) and said,
"Who cares - we're talking only about pennies." He totally missed the idea
that a large percentage difference scales up to dollars over many purchases.
("A billion here, a billion there ... Pretty soon you're talking real
money." -- wasn't that from Barry Goldwater?)

I also vividly recall going to a talk given by a physics major(!) who
dismissed the difference between two values like 0.0065 and 0.0047 (they
weren't just data points -- they were the end result of curve fits to
different sets of data) as unimportant "because they were small"!

The other problem I gave the algebra class was a telephone magazine ripoff I
remember getting multiple calls about when I was teaching that course. It
was a sort of package deal offering half a dozen magazines at X dollars per
month that perhaps sounded cheap at first but turned out to be a price per
year way above what individual subscriptions would cost.

I related the offer as best I could from memory to the class and asked
whether they thought it was a good deal. The great majority would have gone
for it! Only a very few (who actually had paid for magazine subscriptions
at some point in their lives, I guess) pointed out that it was indeed a
ripoff.

I'm not quite sure how to correctly interpret the students' thinking on
these issues, but it makes me very uneasy.

Steve Highland
Duluth MN




This question is not a test of innumeracy, except possibly at the ends
of the spectrum. It is a test of crystallized knowledge. A real test
for numeracy is to have people compare numbers like 0.5 and 3/8. The
population of a given area is what might be called common shared
knowledge. So if you ask an economist they should know these things,
but does an economist know how many atoms are in 1 gram of hydrogen?
They will not, but all chemists can answer this.

What about the distance from the moon to the Earth? What about the
time it takes for light to travel from the sun to the Earth? This
will be known by those who saw a particular commercial in which the
answer was given to them.

John M. Clement
Houston, TX


Here is another problem you might run into with today's
student--probably
was true in the past too. This one might well surprise you if you
checked
it out even with your science students and engineers--although I
would
expect that group to be better.

The problem is innumeracy--and it is a problem reported to me from
other
disciplines as well. Students have almost NO feel, no instinct for
numbers.
Here is my example. 1st day of my gen-ed Energy class, I give a
little quiz
to see what they know (very little). The first two questions ask
for the
approximate population of the U.S. and the approximate population of
the
world. Here is a list of the answers I got this year.

500 million, 45 billion
600 million, 8.1 billion
1.4 billion, 7 billion
6 million, 13 million
800 million, 5 billion
6 million, 3.8 billion
100 million, 7 billion
600 million, 6 billion
2.5 billion, 7 billion
100 million, 2 billion
4 billion, 42 billion
300 million, 6 billion
300 million, 6 billion (maybe copied from the above!)
2 billion, 25 billion
600 million, 6 billion
5 million, 3.6 billion
3.5 billion, 300 billion
3.4 million, 4 billion
5 billion, 100 billion
4 million, 3.9 billion
28 million, 57 billion
80 million, 1 billion
6 million, 200 million
800,000 , 6 billion
3 billion, 20 billion
300 million, 3 billion
32 million, 500 million
2 billion, 6 billion
4 billion, 12 billion
12.2 million, 8 billion
12 million, 6 billion
60 million, 4 billion
4 million, 4 billion
23 million, 4 billion
7 million, 20 billion
4.5 million, 71 million


Note that they are better with the world than their own country. It
is also
really sad to realize that we are situated about 90 minutes from
Chicago.
Check out all the answers under 10 million!

Anyway, you might want to try something like this (or maybe not).
You can
ask other things like the budget for the U.S. or how much money Bill
Gates
has, or almost anything involving numbers. We also need to deal
with this
in our classes--or at least with students who have so little feel
for
numbers.

Rick

***************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
******************************
Free Physics Software
PC & Mac
www.saintmarys.edu/~rtarara/software.html
*******************************

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Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l