Jessica Waggener

March 1998

CRYPTOGRAPHY

PEDAGOGICAL EXTENSION

Note: I had a lot of difficulty finding a place in the curriculum where I could feel justified teaching this as a unit or a helpful lesson. In my search, I reviewed a workbook unit entitled "Cryptarithms," but these were not the same kinds of activities we have been discussing. Those activities were puzzles where an arithmetic problem was presented with letters instead of numbers and the goal was to figure out the associated numerical values of the letters. The emphasis was on discovering the usefulness of number properties as "hints" to the puzzle.

In my developing my pedagogical extension, then, I wanted to present a format for assigning independent projects in math class, where cryptology would be one of many options students could pursue. This project would be adaptable for junior high or high school students, with varying levels of expectations. You could have presentations spread out over the course of a few months, depending on your time constraints.

Assignment: "How to be an Expert."

Background: Have you ever watched a trial on TV? Can you recall having seen the use of "expert witnesses"? What are some areas of expertise which are commonly used in courtrooms? Lawyers aren't the only people who call on experts for help. Companies hire expert consultants to come in and tackle specific problems they aren't equipped to deal with. Politicians bring in experts to help them better understand an issue. This assignment is going to give you the opportunity to become\ an "expert" on a subject the rest of us may know nothing about. Suprisingly, many adults become experts on subjects they never really intended pursue, but at some time or another they found themselves needing to know something in order to do their job. So it will be with you. You can pick your profession, but you won't know your topic of research until I reveal it to you. You may choose from the list below. (Information in parentheses not given to students until after choice made.)

• Mailman (graph theory)
• Psychologist (Statistical Analysis in social sciences research)
• Composer (12-tone composition)
• Lawyer (probability, statistics, and the burden of proof)
• Map-maker (Four-Color Problem)
• Insurance Manager (actuarial probabilities)
• Foreign Spy (Cryptography)
• Painter (The Golden Ration, or the influence of perspective on the development of Non-Euclidean Geometry)
• Housewife (Making your own budget on Excel)
• Check-out Clerk (Historical Review of Computation)
• Cowboy (Cost Analysis of running a ranch)
• Astronaout (Orbital trajectories)
  

Details: You will work in groups of two to four people. Some of you have complex topics and will only be able to report historical facts or the importance of your topic in the "real world." Others of you will actually be able to teach us how to DO something. Since everyone's project will be so different, you must meet with me BEFORE you start working so that we can decide together what you will be graded on. In our meeting we will outline specific expectations and grading criteria. In general, I will be considering the following areas:

1. What did you learn, about something mathematical, that you didn't know before?

2. How well can you communicate the importance of your topic to the class? OR How well did you succeed in getting the class interested in your topic?

3. How much effort did you put into appearing professional as an "expert?"

And, in general, each project will contain these minimum parts:

1. Create a pretend context in which the class would need to know what you have to share. Ex: We're a company trying to solve our financial problems and you're a banker.

2. Give some historical background on your topic.

3. Teach us something we can use. OR Make us REALLY curious to learn more about your topic.

4. Give us the references you used so that we can go out and learn about it for ourselves.

5. Evaluate the class to see how well they understood what you taught (and to see how well you taught it!).

Your presentation must be AT LEAST 20 MIN. long, but no longer than one class period.

Evaluation: In addition to receiving a grade for your presentation and grading the class on what they learned from you, you must also design a test for yourself. I must approve the test questions before you answer them. They should reveal what you learned from this project. That might include: new mathematical skills, historical facts, new knowledge about the weird things people learn in life, or new ideas about how math could actually be useful for a real human being.