The long rambling philosophical introduction

What you’re holding in your hand is much closer to a set of detailed lesson plans than to a traditional textbook. As you read through it, your first reaction may be“Who does he think he is, telling me exactly what to say and when to say it?”

Please don’t take it that way. Take it this way instead.

Over a period of time, I have developed a set of in-class assignments, homeworks, and lesson plans, that work for me and for other people who have tried them. If I give you the in-class assignments and the homeworks, but not the lesson plans, you only have⅔of the story; and it may not make sense without the other third. So instead, I am giving you everything: the in-class assignments and the homeworks (gathered together in the student book), the detailed explanations of all the concepts (the other student book), and the lesson plans (this document). Once you read them over, you will know exactly what I have done.

What do you do then? You may choose to follow my plan exactly, for a number of reasons—because it worked for me, or because it looks like a good plan to you, or just because you have enough other things to do without planning a lesson that I’ve already planned. On the other hand, you may choose to do something quite different, that incorporates my ideas in some form that I never imagined. This book is not a proscription , in other words, but a resource .

OK, with that out of the way…suppose you decide that you do want to follow my plan, exactly or pretty closely. Here’s what you do.

• Right now, you read this whole introduction—despite the title, it really does contain useful information about these materials.
• Before beginning each new unit, you read my“conceptual explanation”of that unit, so you know what I’m trying to achieve.
• Each day before class, you carefully read over my lesson plan (in this document), and the in-class assignment and homework (in the student book), so you know what I’m doing and why I’m doing it.

A typical day in mr. felder’S class (…And why you care)

At the risk of repeating myself, let me emphasize—I’m not trying to insult you by suggesting that my way is the only right way to run a class. But it will help you understand these materials if you understand how I use them.

I begin each day by taking questions on last night’s homework. I answer any and all questions. This may take five minutes, or it may take the entire class period: I don’t stop until everyone is perfectly comfortable with last night’s homework.

Why is that so important? Because, very often, the homework introduces new concepts that the students have never seen in class before . For instance, very early in the first unit, I introduce the idea of“permuting”graphs: for instance, if you add 3 to any function, the graph moves up by three units. This concept never comes up in class, in any form—it is developed entirely on a homework. So it’s vitally important to debrief them the next day and make sure that they got, not only the right answers, but the point.