### Math 1332 Reflection 3: Logic and Representation

At the bottom of our class links page, you will find
a spreadsheet
combining the work of the four small groups who explored the Immigration
problem. This combined spreadsheet will form the basis for this reflection.
- Each of the four spreadsheets predicts the same population of Thartheeans
after one year, but a different population of Thartheeans after 20 years.
What population
*should* the model predict after 20 years?
In order to answer this question, you will have to analyze the logic
of each of the four spreadsheets.
- Obviously at least three of the spreadsheets have errors.
What were the errors? (Each error requires only a minimal change.
Try to make all necessary corrections with as few changes as possible.)
- (Suppose now that we're working with the corrected spreadsheets.)
Each of the groups represented this problem differently.
Group 2 chose a different physical layout and a one-step formula;
Group 4 wrote its formula for new population in a slightly different way.
In other problems this semester we have discussed the equivalence of different
approaches (for example, one-step vs. two-step formulas in the Gradesheets
problem, and making different types of graphs for the same data set earlier
in the semester). How does the difference in representation reflect a
different conceptualization of the problem? How does it affect
how the spreadsheets can be used?

A couple of quick notes: (1) If you have any difficulties, I encourage you
to ask me for help. Of course, you are always welcome to work with classmates
too. (2) You do not have to include spreadsheet printouts unless you need them
as part of your explanations.
*Due in class Thursday, November 14, 2002.*