Critical Thinking Course

[Laramie]

I am thinking about putting together a course (honors students, university level) with the objective of teaching/developing critical thinking skills. The course material would be puzzles/brain teasers. We would not just seek to solve the puzzles, but would rather seek to understand processes by which puzzles can be solved.

I would appreciate any thoughts/suggestions anyone might have.

[Vinny]

I think the best thing to teach them would be to recognize what kind of problem they're trying to solve and find the right tools to solve them.

Different problems have different processes to solving them. Some requires running through possibilites, some requires working backward, knowing what the end result would be and what the starting point is and how to get from one point to the next, some requires thinking out of the box, or catching loop holes, some math, some logic, some abstract thinking, etc. The important thing is to recognize what kind of problem it is and to apply the correct process to solve it.

That's what my discrete math Teach would say.

[Vinny]

A neat thing you could do would be to have them write down all the different thought processes in their heads they go through for solving a specific problem. Then they can go back and analyze it later after they solved it to see how they arrived at the solution. Most puzzle have an "a ha!" key to solving it, where you realize something and see the problem in a different light and the direct path to solving it.

I distinctly remember the process I go through to solve the four men and the bridge problem. I'll jot them down real quick for your amusement ...

Here's a link to that puzzle:

http://www.greylabyrinth.com/Puzzles/puzzle069.htm

The problem is to get four people (1M, 2M, 5M, 10M) across a bridge in 17 minutes, with a max of 2 crossing the bridge at the same time, and a flashlight to be delivered back and forth by at least one person.

The first thing I did was to pick the most obvious sequence, namely send the fastest runner back and forth with the flashlight, delivering the other one at a time, to see what the limitations are and understand the problem a bit better. That gave me a total of 19 minutes.

The thing I immediately noticed is that the 5 and 10 minutes guys are the one that's causing the most grief. The key to solving the problem, then, is to minizmize both crossing time. We only want them to have to cross the bridge *once*. The 10M guy will waste 10 minutes no matter what, so if we send 5M across with him, we nullify that 5 minutes altogther. So I tried sending 10M and 5M across, but then I had to send 5M back, and that's not good. I knew that 10M and 5M have to cross together for maximum efficiency, but I needed somebody there to bring the flashlight back so that neither 10M or 5M have to cross a second and third time.

So, 1M & 2M across, 2M came back with the flashlight. Then 5M & 10M, then 1M came back with the flash light. And finally 1M and 2M went across and we are home free.

The "a ha" to that problem was that 10 minute will nullify the 5 minute guy provided that they both only to cross the bridge *once*.

Hmmm ...

I actually enjoyed analyzing my thought processes more than the actual solving of that puzzle. Nifty



[This message has been edited by Vinny (edited 09-07-2002 06:20 PM).]

[Hitchhiker]

What a wonderful idea!

I would say, start with the most traditional kinds of puzzles. Start the class off by presenting them with the puzzle, no hints or clarifications, and get them discussing what kind of a puzzle it is, if there's any ambiguity in the directions, etc.

Or even start them off with a real chestnut, and if they've heard it before, ask them what distracts a person from seeing the solution when it's heard for the first time.

Also, alternate between ones that require different types of thinking: logical, wordplay, algebraic, geometric, lateral, intuitive, etc. The more variety there is, the more likely it is that every student will have something to contribute.

If you get the opportunity to show movie scenes in class, I would recommend Sneakers (the scene when Whistler tells them where on the desk the "black box" is located, using audial input rather than visual, and the subsequent scene when they are breaking into Janek's office to steal the black box: a priceless "Gordian knot" situation), Indiana Jones and the Last Crusade (the "three trials" scene before they reach the Holy Grail), and My Cousin Vinny (when he is questioning the three eyewitnesses).

I used to be the t.a. for an Introduction to Logic course -- I've always wanted to do a course based around brainteasers. If I think of anything helpful from classes I've taken or taught, I'll post them here. Best of luck!

[Beartalon]

One of my required math courses for my BSc degree was "Problem Solving". Of course being based in math, this eliminated all the laterals and most word puzzles. We used the methods of induction, deduction, inference ( not b implies not a implies a implies b), working backwards, contradiction, elimination, and a few more with the healthy dose of logic required to use each.

We touched on number theory, graph theory, optimization/related rates, permutation, statistics, classification (Venn diagrams) and others.

Mostly, we learned how to choose the best tools to solve a problem, even if we didn't fully solve it. Best of all, since it was first year, it didn't require calculus. I wish I could find that book now.

[Chuck]

How to Solve It by George Polya is considered to be an excellent book for teaching problem solving.

[CrystyB]

wow i wish i had BT's first-year schedule instead of mine!

[morrisonlucas]

Sorry that this is coming so long after your original post. There is a lot to read in the GL. This sounds like a good idea for a course.

Once I was interviewing for a couple of management consulting jobs, and they all use a "case interview". For example, they will ask: "How much rubber does the United States consume annually?", or "How much money does a Starbucks make in a day?". You then need to answer as closely as possible without looking anything up. You do well if think of the correct numbers to ask for, and better if you provide reasonable estimates for those numbers.

[example]
"How much rubber does the United States consume annually?"
Assume: most rubber is used in car tires
Estimate: 250,000,000 people in the country,
Estimate: 1.5 people/car
Estiamte: 10 years/car
Known: 4 large + 1 small tires/car
Estimate: 15 lbs/tire
Therefore first estimate: 1.25 billion lbs/year
[/example]

Even if your gueses are wrong, you get a pretty good idea of the magnitude of the issue. It turns out that once you have worked a few of these, you can quickly estimate a lot of numbers in your head. (such as, "Is $1billion a lot of money in the national budget"?)

I believe that this is a useful skill for people to have, and this might be a forum to present it. Although it doesn't directly revolve around puzzles.

[EEEM]

If you could get your hand on and International Baccaluareate Theory of Knowledge book, there's some great stuff about perception when approaching written, verbal, and visual problems, including puzzles and optical illusions. Plus lots of general thought process/problem solving stuff. And it's just damn interesting.

[Hitchhiker]

For puzzles and insightful essays about the nature of intelligence, I'd recommend

Games for the Superintelligent and More Games for the Superintelligent by James F. Fixx

all the Mensa Genius Quiz books

Aha! Insight by Martin Gardner

(...or almost anything else by Martin Gardner)

[Beartalon]

CrystyB, yes, that was first year. It helped a LOT when I started programming in VB and breaking larger problems down into smaller ones until I could solve them. It was very analytical and most students that did well in that course did much better than the rest of the students overall, right up to graduation.

[Laramie]

Thanks for the great advice, everyone. I'm making progress in getting it on the books, but I need to come up with reasonable ways to test/grade the students. Any thoughts on that, keeping in mind that my students are extremely bright (average SAT in the class would probably be around 1450)?

[Beartalon]

From my course: There was no mid-term or final exam, per se. There were two large scale problem solving assignments, one was individual for 20%, one large group (5 student) project for 30%. 30%was for several individual assignments to develop skills in each type of solving method. 5% was for class participation and the remaining 15% was a small group (3 student) project. It's designed so that you will pass just on the individual portions.

Left to our own devices, we probably would have helped each other with individual assignments. These assignments were done during class-time, on a fixed day, usually the last day of the week.

The individual problem solving assignment was more a report on famous problems - like the Konigsberg 7 bridge problem - rather than solving problems, so the cheating factor was low.

The large group project was similar to a GL Potpourri's puzzles. Not only were we marked on final presentation of solutions, but each person had to show their work. Marks were assigned in this manner:

• Multiply the number of percentage points X the number of people in the group.
• Then allow each group member to individually distribute those points based on how they feel everyone, including him/herself contributed.
• If Joe Blow does very little, you can give him less and distribute the points to the more deserved.
• Take the papers, add each persons points from all group members and determine each person's average.

Wow. I'm surprised I can remember all that.

One of the problems in our large group project was trying to define a solution for the Instant Insanity cube game. Another was a difficult logic problem as you'd find in a Dell logic puzzle magazine.

[This message has been edited by Beartalon (edited 10-24-2002 09:51 PM).]

[Legion]

Checked out the work of Alec Fisher from University of East Anglia in the UK?

Here's a book

http://books.cambridge.org/0521009847.htm

[Brave Margaret]

In working with gifted youngsters aged 7-14, I have often used puzzles. I see a lot of great sources have already been posted, but you might want to start with some physical puzzles such as the peg board ones. After allowing some "play" have students generate the parameters, ie, how many jumps to win? Allow them to develop a design for "researching" the correct sequence, since most will continue to make unsuccessful moves. They can devise an annotation system and by process of elimination, devise the correct sequence.

[Legion]

Margaret, have you tried the Word Class Arena?
Was it any good? beyond the demo site I mean
http://www.worldclassarena.org