### Teaching

Teaching is a challenge. I think of the classroom as a performance space and expect the students to be actors too, not the audience. In the past few years I have developed a few tricks to create that dynamics, not always with full success. Giving puzzles in the class helps.

For graduate students, this may be math problems. They typically listen, register the problem, tilt their heads, scratch their chin or stare nowhere, scribble on the notepad, do whatever stance each individual adapts when they solve problems, and typically don't talk unless they have questions or ideas. This *is* being part of the performance that is the classroom.

The undergrads are a different challenge and math puzzle may not help. I typically use "lateral puzzles". These are descriptions of instances in everyday life; the instance sounds strange and inexplicable, but there is a rational explanation. The puzzle is to find the explanation. The solutions are more grey than black and white math puzzles. Further, students can not typically proceed to solve these puzzles without asking questions for more clarity which gets them to talk in the class, a big step forward. Finally, when you give math puzzles, during the course of the semester, one or two well-trained solve most of them; with lateral puzzles, any one can solve them even without training, and many of the students in the class end up solving a puzzle or two during a semester, which is cool.

ps: There are six eggs in the basket. Six people each take one of the eggs. How can it be that one egg is left in the basket?

pps: Once, a long time ago, I remember playing a game with cards that involved lateral puzzles with Peter Winkler, Joel Spencer, Robin Pemantle and others, but don't remember how the game ended.

For graduate students, this may be math problems. They typically listen, register the problem, tilt their heads, scratch their chin or stare nowhere, scribble on the notepad, do whatever stance each individual adapts when they solve problems, and typically don't talk unless they have questions or ideas. This *is* being part of the performance that is the classroom.

The undergrads are a different challenge and math puzzle may not help. I typically use "lateral puzzles". These are descriptions of instances in everyday life; the instance sounds strange and inexplicable, but there is a rational explanation. The puzzle is to find the explanation. The solutions are more grey than black and white math puzzles. Further, students can not typically proceed to solve these puzzles without asking questions for more clarity which gets them to talk in the class, a big step forward. Finally, when you give math puzzles, during the course of the semester, one or two well-trained solve most of them; with lateral puzzles, any one can solve them even without training, and many of the students in the class end up solving a puzzle or two during a semester, which is cool.

ps: There are six eggs in the basket. Six people each take one of the eggs. How can it be that one egg is left in the basket?

pps: Once, a long time ago, I remember playing a game with cards that involved lateral puzzles with Peter Winkler, Joel Spencer, Robin Pemantle and others, but don't remember how the game ended.

## 5 Comments:

ps. is easy. you didn't say anything about when people took the eggs. so it is fair to presume that some of the eggs may have hatched and become chickens which themselves lay eggs which the humans pick out. you could rephrase the question to have seven eggs left.

Lateral Puzzles do help a lot. One of my Professor at undergraduate level made us solve very good problems[big problems] in the class. Surely it is very difficult to do so. He provided us with a sound problem statement and made us think in a particular direction by giving real life scenarios to solve the problem. I liked the way he taught the course. I wish every course should be like that.

Suppose the solution did not involve hatching of the eggs?

You didn't say they each took a different egg. Might as well be the same one egg they passed around.

As for keeping students engaged, I like giving them (somewhat) real life problem (somewhat) related to the current material and forcing them to work in groups for 10 minutes. Fun to watch, especially in a big class

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