This document provides guidance on developing effective lesson plans for calculus instructors. It recommends starting by defining specific learning objectives and assessments. Examples should be chosen carefully to illustrate concepts and engage students at a variety of levels. The lesson plan should include an introductory problem, definitions, theorems, examples, and group work. Timing for each section should be estimated. After teaching, the lesson can be improved by analyzing what was effective and what needs adjustment for the next time. Advanced preparation is key to looking prepared and ensuring students learn.
2. Introduction
We need to cover the section on the
product rule.
Students hate the product rule
What to do?
This “problem” exists for every topic
of every course
3. Why plan lessons? (apologies
to Andy Engelward)
PPPPPPP
Proper Planning and Preparation Prevent
Pretty Poor Performance!
Be an effective teacher
Make yourself look smart
5. Lesson Styles (continued)
Problem-oriented
Example
Example
Definition
Theorem
Proof?
Example
Example
Example (repeat as
necessary)
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7. Start with the end
“Students will be able to” (SWBAT) points
Context, Big Picture
Assessment
What class activities will determine if you have
met your goals?
What homework problems are going to be
assigned after this class?
8. Sample Goals
“Understand the interplay between
logarithms and exponentials”
(conceptual)
“Use the product rule to take
derivatives of elementary functions”
(technical)
“Recognize when to use logarithmic
differentiation” (strategic)
9. Then go to the beginning
Introductory Example (Hatsumon)
here’s a problem you can’t do now, but
will be able to do at the end of the class
Big Question that you plan to answer
10. Anticipating Questions
What will students
find difficult?
What examples will
illustrate and
illuminate?
Practice and
experience will
improve this skill
11. End with the middle
Fill in the big idea
Proof?
Use your knowledge of students
backgrounds to fill in your examples.
12. Choosing Examples Wisely
Vary degrees of simplicity
and complexity
Try to find ways to involve
students
Choose them to be
interesting to them
Consider alternatives to you
doing them at the board
Work them out ahead of
time!!
Make sure they’re not too
complicated
Make sure they illustrate
your point
13. Scripting your Lesson
Consider writing out
some parts verbatim
Important diagrams
can be practiced
ahead of time
Depends on
experience and
language skills
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14. Time Management
Know how much of
your notes
corresponds to how
much class time
Put a timeline in
your lessons
“accordion”
sections
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24. Postmortem
Assess your Class!
Analyze
What went right
What went wrong
What you’d do next
time
Keep for posterity
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25. Cheats and Hacks
Look in (different)
textbook
Reuse old lesson
plans
“Borrow” someone
else’s lesson plan
Collaborate on
lesson plans
Lesson Study
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27. References
First Day to Final Grade: A Graduate
Student’s Guide to Teaching (Curzan,
Damour)
Learning to Teach and Teaching to Learn
Mathematics: Resources for Professional
Development (Delong, Winter)
How to Teach Mathematics (Krantz)
Notes de l'éditeur
Lesson: what happens in a class period. This is chosen to include not only lectures but interactive classes, which of course we encourage.
It’s important to note that this is not the only way to teach a class. If the only way you can do a class is
theorem-oriented, and you can do it well, great. But we believe this is an effective way to teach a “service” calculusclass to non-mathematics majors
Class activities: students do examples on board, ask questions of students,etc.
SWBAT: The things you want your students to come away with
Difficult: remembering that the product rule is NOT just the product of the derivatives
Example: a simple function that if the product rule is applied, will give an answer which is known to be wrong.
Practice, experience: and memory! Think about when you were a student.
Proofs are not always necessary. I like formal proofs that show the idea. For instance, two ways to prove the product
Rule are the rectangle and the old add-and-subtract-the-same-thing trick.
Avoid deltas and epsilons. This doesn’t mean avoid all infinitesimal arguments, but make sure to keep the language informal.
Avoid extreme simplicity: differentiating the zero function might be confusing if it’s the first thing you do.
Choosing examples: find things that you can get the students to feed you
Work them out: you don’t want to end up with an irreducible quadratic or cubic
Think about writing the first paragraph out.
My (bad) example of teaching the method of Lagrange Multipliers, missing the key sentence to drive the essential idea home
Nonnative speakers may employ this technique more often. Don’t wory about being Shakespeare; concentrate on getting the sentences coherent.
Consider colored chalk--not just “using it”, but which colors will stand for what
Nothing against you, but students have other classes to get to!
Accordion sections expand or contract to fit the time
TRANSITION: “These are the basic ideas behind buildiing your lesson. But there are other pieces which go into how your lesson is delivered”
Re breaking up: can do it geographically, by interest, randomly, by fiat
Yielding the chalk breaks the structure of class-as-television.
Silly stuff like board races may be well-received.
SS: “So we’ve seen that the product rule is a necessary and important tool for computing derivatives. It’s not the most obvious thing, but it is easy to memorize with the right mnemonic…”
Hand out Winter & DeLong WS
Breakout
Analyze: whether your timeline was appropriate. Whether your assumptions about their level pre-lesson were appropriate.
Keep: We’re all about saving time. So save it and save yourself the couple of hours you just spent next year. But it’s much more useful if you take that extra step
Different is pretty important. Students will feel a little cheated if all you put on the board are worked-out examples from the book.
Preceptors are working on archiving lesson plans.
Math 301 does one lesson collaboratively, per year!
Your records consist of your own lesson study program