# Aimee's Guide

### From www.norsemathology.org

## Guide to teaching from Tannenbaum

I will list below my plan for teaching from this text. You may choose other topics, if you wish, but try to cover about the same amount of the text and at the same depth. I will be trying to set up an online homework grading system and would gladly share my homework sets with you (and get things set up.) But I will only have time for setting up the sections I will be teaching this first semester.

- Chapter One: Voting
- Cover all but the enumeration (pp21-23)
- Students should know about the fairness criteria and be able to apply to examples.
- Students should know about Arrow's theorem

- Chapter Two: Weighted Voting Systems
- Section 2.1 (Don't emphasize Ex 2.2/2.3)
- 2.2,2.3 Students should be able to find power in small examples.
- 2.4,2.5 Skip or replace 2.2-2.3
- This is a nice topic, but the only reason to teach
*both*topics is to show how we can have several ways to mathematically measure the same concept. I don't think this is necessary here.

- First Test (30-50 min.). You don't need to cover everything!
- Chapter 3: Fair division
- 3.1 (Beware student trouble with ratios! Don't avoid these problems, just be aware that they will find such problems difficult.
- 3.2,3.3 A method to divide continuous goods
- 3.4 Skip - redundant.
- 3.5 Optional? This is fun to do in groups, but hard to test and redundant.
- 3.6 Sealed bids - a nice method and not too difficult. Problems arise when adding back in the leftover cash.
- 3.7 Method of markers - this is ok to do, but I will skip it a a redundancy.

- Note: I have marked a number of methods as redundancy. My thought is that I want my students to
*understand*a few methods well, not force them into memorizing lots of methods. We are not training our students to use these methods in real life. We would like our students to look at certain problems in their life and realize that mathematics might be able to solve them. It would be even better if we prepared our students to find such solutions - but we can't do too much in a semester. - Chapter 4: Apportionment
- Before teaching these methods give an apportionment problem to your students and let them come up with a method. They can do it - but you need to give them a problem which can't be done by simple rounding if they are to see why the problem is of interest.
*Make sure they understand why they can't just round the quotas, or they won't ever understand the rest.* - Use the history given at the end of the chapter to make the topic more interesting --your students have all heard of Jefferson, Washington, and Hamilton. And there might be a history major who can fill in some of the context.
- Do all sections, except section 4.5 on Adam's method.
- Work excursion one on the Huntington-Hill method - the method used by the US today. De-emphasize the work on the geometric mean (ya gotta do some), but emphasize the analogy with Webster's method.

- Before teaching these methods give an apportionment problem to your students and let them come up with a method. They can do it - but you need to give them a problem which can't be done by simple rounding if they are to see why the problem is of interest.
- Test 2 (Short again, or longer and reviewing selected topics of Ch 1 and 2.)

## Some guidelines and advice

- From the Instructor's Guide:
- 'Teach algorithms rather than formulas.' I agree with this. If you give this group a formula many will blindly plug in numbers and get nonsense. Teach meaning instead and walk them through the steps. I think the author forgets this sometimes.
- 'Throughout the exercises the ability to solve linear equations, work with percentages, understand scientific notation, etc, ... is assumed.' You have been warned! While all these topics are important, its not true that our students will have a good grasp of them. Be prepared to review, preview, and choose problems wisely.
- 'Because the material is so independent, exams covering more than two chapters may not allow for proper student focus.' I've taught from this text before, and agree. There should be a large number of smaller assessments. They needn't take up the full class period. In addition we need to give a comprehensive final. I assume we will point out the main topics from the course and have the students review these few ideas. Perhaps a larger midterm assessment would help to prepare the student (or review problems on each assessment.)
- The following Prentice Hall websites are worth checking out: