The Crystal Task

The contents of this page are the handouts when the crystal task was used for Math 300-

Mathematical Writing. Most of the students in this class were college seniors majoring in mathematics and computer science. Several different ideas were addressed by this assignment.

1. Distinguish between a definition (average grain indicator or average area) and a procedure (a specific procedure for determining either of the above.

2. Describe a procedure well.

3. Understand and be able to explain the use of proportionality in using scale factors.

4. Understand that the ranking of a set of data can be done in different ways. (One can compute either the average area or the number of grains per unit area. In one case big value is good; in the other a low number is good.)

5. The eventual aim (acheived by most of the students) was to understand that while the different procedures for computing the same indicator produce the same ranking; changing indicators

(from average area to agi) might change the ranking.

Guide to handouts:

Crystal Task I and II are the original version as used by 7^th graders - just in different formats.

Essay 3 is the description of the assignment for this class.

Average grain indicator (pdf) is the original assignment from Purdue describing the average

grain indicator and referring to the computer program (which we did not have).

AGI and Average Area I and II are a couple of attempts to show the effect of shape on the

computation of the agi (while average area is invariant). This introduced shapes which

were very regular and may have been misleading.

Definitions, Procedures, and explanation is an activity designed to make the distinctions between these modes of mathematical writing explicit.

Proportion analyzes the notion of the `diameter' of a plane figure (polygons as well as circles). It should be particularly appropriate for teachers.

Random is a collection of definitions of random. We didn't really have time to get into this

topic.