Numbered Cards for Concrete Abstractions
This web page provides help making numbered cards for use with Concrete Abstractions:
An Introduction to Computer Science Using Scheme, by Max Hailperin, Barbara
Kaiser, and Karl Knight. These cards
are used for comparing two different sorting algorithms.
There are three options for making the cards:
If you have the ability to print a PostScript file, we have a PostScript file, with three pages containing
twelve cards each. You can print that out on cardstock (or normal
paper, in a pinch) and cut it up using a paper cutter. You'll get a
deck of thirty-six cards; that is more than you need, but it means
you'll get some variety if you shuffle it and then count out 32 (or
fewer) of the cards.
Alternatively, we have GIF versions of pages one, two, and three. Most web browsers will let you view and
print this out. Then you can cut it up and use it as above. Although
this option will work for more browsers, the resulting images are
typically more jagged and somewhat smaller.
Finally, it really isn't that tough to make your own cards by hand.
Either 3x5 index cards cut in half or standard sized business cards
work great. (In fact, our PostScript cards are the same size as
business cards.) We recommend writing the number on each card twice,
facing opposite directions, so that while you are sorting you don't
need to worry about which end is up. The numbers we used for our 36
cards are 69, 73, 28, 32, 15, 51, 56, 42, 98, 4, 59, 2, 61, 95, 25,
12, 10, 92, 49, 82, 45, 54, 90, 22, 63, 86, 84, 6, 20, 79, 40, 71, 88,
37, 35, and 76. These numbers have a couple good properties. First,
there are no duplicates, which would introduce an unnecessary
complication in the sorting. Second, there are no consecutive
numbers, which makes it harder for a student to know in advance that a
particular number must be the largest remaining one, when selection
sorting. That means all the comparisons really need doing.
Another option, if you can't tear yourself away from the computer to
deal with physical cards, is to instead use the simulation of card sorting which we
provide as a Java applet (your web browser must support Java 1.1).
Our preference is for the real cards, but the "virtual manipulative"
is better than nothing.
For more information, see the parent web page, or contact Max Hailperin:
Mathematics and Computer Science Department
Gustavus Adolphus College
800 W. College Avenue
St. Peter, MN 56082