Problem Based Learning

I hear, I forget. I see, I remember. I do, I understand.

—Chinese Proverb

This process of "learning by doing" recommended by the proverb has come to be called problem based learning or PBL. It dates back to the early 1970's when it was developed for the Medical School at McMaster University in Hamilton, Ontario. It was then adopted as the organizing principle for the University of Limburg in Maastricht, The Netherlands, and has subsequently been used in a variety of forms in countless other professional, undergraduate and secondary schools. The central premise is that problems are intended not to test understanding but to assist in the development of the understanding itself.

Learning by doing problems is the focal point of this course.

Homework / Classes

Working together in study groups of 3-5 students is strongly recommended.

Groups of no more than 5 students may submit a single written assignment by clearly indicating the members of the group on the first page. Group memberships may change from assignment to assignment.

For a person's name to be listed on an assignment, it is required (honor code) that the person have seriously attempted all of the problems on the assignment and participated, at least by being present, at all group discussions of the problems on the assignment.

Each class period will be devoted to a discussion of the assigned problems lead by randomly selected students. You may, on at most two occasions during the course, request an exemption from being selected to present by emailing me at least two hours before the beginning of class.

You may wait until the end of the class session to turn in your written answers so that you will have access to them during the discussion. You should not, however, add notes to your written answers or modify them during the class session.

A ten minute break will be taken approximately half way through each of the class sessions.

Books

The electronic Math Camp for Economics is the principal reference for the course and the source of all assigned problems. Please use Simon and Blume as a backup reference. Often it is very helpful to read the same thing expressed in different ways and Simon and Blume's treatment of a topic is often very different than mine.

Mathematica

Mathematica is a symbolics software program that bears much the same relationship to calculus and algebra that a calculator does to arithmetic. Its use will be emphasized in the course and required for many of the assigned problems. Get it today from

http://www.oit.duke.edu/comp-print/software/license/index.php

Getting a working knowledge takes about 30 minutes. Go to the course web site at the url given above and check out the 3-part introductory movie and "Introduction to Mathematica". There is also an introductory appendix in Math Camp for Economics. Have it running while you are working on the homework assignments, try it out on simple things to see how it works and you'll soon be addicted.

LaTeX

Though not required for this course, this scientific document preparation tool is ultimately essential for every professional Economist. There are introductory materials in

http://www.duke.edu/~dgraham/LaTeX/

Grades

Your grade will be based upon your your class participation and your homework after dropping your two lowest grades.

Habits Worth Making

Excellence is an art won by training and habituation. We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly. We are what we repeatedly do. Excellence, then, is not an act but a habit.

—Aristotle (Nicomachean Ethics)

Habits made now will likely last a lifetime. One of my "meta" goals for this course is to suggest the ones that I think you will ultimately be happiest to have acquired.

Be Disciplined.

Many disciplines, and Economics is no exception, are based upon a few central tools and concepts with a very broad range of applicability. The goal is to discipline yourself to rely upon these tools and to use them in a controlled and habitual way when confronting a new problem.

Science is nothing but trained and organized common sense, differing from the latter only as a veteran may differ from a raw recruit: and its methods differ from those of common sense only as far as the guardsman's cut and thrust differ from the manner in which a savage wields his club.

—Thomas Huxley (English Biologist 1825-1895)

Have Fun.

Gritting your teeth and racking your brain when working on a problem is something to be avoided. No one has enough mental discipline to sustain a thought process that isn't fun - the mind invariably wanders to more pleasant matters. Remember that the bottom line is not the effort expended but the results obtained. The less effort expended and the more fun experienced, the better.

Keep It Simple.

A problem will be simple when you think about it the right way. Spend your time looking for the right way - not beating your head against a wall trying to make the wrong way work.

Ask good questions.

Ask yourself good questions. How is this problem like others you have seen? How is it different? What do you know? What do you want to know? What series of steps would take you from the former to the latter? The key to getting the right answers is to begin by asking yourself the right questions.

Plan Ahead.

In the words of a sign I once saw prominently displayed on the dashboard of a truck, "Engage brain before starting engine!" Resist the urge to jump right in (plug and chug) and begin instead by making a plan about how you intend to solve a problem. With a minimum expenditure of time and effort you can discover whether or not an approach will work and, if it will, obtain a map and compass that will lead you to the solution.

Write It Down.

Always think with a pencil in your hand. No less an authority than Nobel laureate Paul Samuelson once observed that "I never know what I'm thinking until I write it down." Your brain, like a computer's processor, has relatively limited storage capacity and, pursuing the metaphor still further, can benefit greatly by having access to some additional memory. Store and organize your ideas on paper. And to make this storage medium effective, make your notation and drawings clear and simple. One glance should be sufficient to reload the information into the brain.

Use the Force.

Your conscious mind is little more than a link to your real imaginative and creative power center - your subconscious mind. Consciously consider the problem while maintaining a relaxed awareness that your subconscious mind will produce the solution. You'll be amazed how often the solution will just pop into your head when you least expect it.

Be Self-Aware.

Intellectual skills are harder to develop than physical ones. Hit a tennis ball and you immediately get to see the result. Better still, a video tape will show how you actually swung the racket. Comparable aids for sharpening mental skills are hard to find. One trick is the Zen-like device of "meta-cognition" in which you devote a part of your mental processing power, say 10%, simply to being aware of what the other 90% is doing. Such awareness enables you to repeat what works for you and to avoid what doesn't.

Expect Success.

One of the outstanding lessons of sports psychology is that your endeavors tend to turn out as you expect they will. Want to sail over the high bar? Then imagine yourself doing just that before you jump. Imagine yourself dribbling the ball off your foot at the worst possible time and you will likely experience this outcome as well. The effect of positive (or negative) thinking may be even greater for mental than for physical activities.