Introduction

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Welcome!

This is Math 221

I’m Doug Baldwin

???

(Watch the output from 4 programs running. One moves a blue bar back and forth, one draws a red spiral, one alternately displays “yes” and “no”, and one prints a sequence of numbers.)

What’s the point?

• To get you to ask questions, particularly ones that lend themselves to mathematical answers, and thereby hopefully come to see that mathematics is a tool for answering questions that come naturally to you.
• Many of the questions are ones that material from this course can help with.

What is the number counting to? Maybe toward 10?

Is there a correlation between the pictures?

What are “yes” & “no” answers to? Which direction the bar moves?

Did the red line start at 0?

Is the red line ever going to overlap itself?

Is the red figure really a 2D view of a 3D shape?

Is the number the radius of the red figure?

What’s making it all happen?

• You were seeing the output of the following 4 programs (none of which you have to look at unless you want to):
  • The red line
  • The blue bar
  • The increasing number
  • The yes-and-no message
• But remember that you do not have to understand these programs, or use them, or write anything like them.

Are you going to have to use these?

• Absolutely not

Learning

How Does It Happen?

(Stars indicate things I expect to use in this course, more stars meaning the item will be more prominent)

* Listening to explanations, including reasons

* Reading explanations

* Seeing examples including reasons and including real-world ones

** Doing examples yourself including real-world ones

* Making mistakes and trying new (imaginative) approaches

Explaining material to others

Discovering material yourself

* Asking questions

* Repeating all of the above

* Working with others on all of the above

What Is the Result?

Being able to apply ideas on your own

Learning processes for finding answers is therefore more important than getting the exact “right” answers on any particular problem.

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