Making Lesson Plans

Calculus Instructors Orientation

September 13, 2005Matthew Leingang

Copyright ©2005 The President and Fellows of Harvard College

IntroductionWe need to cover the section on

the product rule.Students hate the product ruleWhat to do?This “problem” exists for every

topic of every course

Why plan lessons? (apologies to Andy

Engelward)PPPPPPP

Proper Planning and Preparation Prevent Pretty Poor Performance!

Be an effective teacherMake yourself look smart

Lesson StylesTheorem-oriented

DefinitionTheoremProofExample

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Lesson Styles (continued) Problem-oriented

Example Example Definition Theorem Proof? Example Example Example (repeat as

necessary)

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Basic Lesson Planning

Start with the end“Students will be able to” (SWBAT)

pointsContext, Big PictureAssessment

What class activities will determine if you have met your goals?

What homework problems are going to be assigned after this class?

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)

Then go to the beginningIntroductory 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

Anticipating QuestionsWhat will

students find difficult?

What examples will illustrate and illuminate?

Practice and experience will improve this skill

End with the middleFill in the big ideaProof?Use your knowledge of students

backgrounds to fill in your examples.

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

Scripting your LessonConsider writing

out some parts verbatim

Important diagrams can be practiced ahead of time

Depends on experience and language skills

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Time ManagementKnow how much

of your notes corresponds to how much class time

Put a timeline in your lessons

“accordion” sections

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Methods (aka Choreography)

Group WorkBreaking up

studentsPreparing

worksheetsBig

problems/small problems

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Student Board WorkWork out an exampleRaces

Polling/Discussion organizing

InformalPRSGet students to

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TransitionsMoving from one thing to the nextSimple SummaryNot necessarily delivered by you!

Breakouts: Develop a Lesson for your class

Debriefing

DiscussWhat ideas did you hear that you

hadn’t thought of?What principles of lesson planning

did you take away?

AssignmentThink about your lesson in the next

couple of daysFill in the restMeet in your group and share

PostmortemAssess your

Class!Analyze

What went rightWhat went wrongWhat you’d do

next timeKeep for posterity

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Cheats and HacksLook in (different)

textbookReuse old lesson

plans“Borrow” someone

else’s lesson planCollaborate on

lesson plansLesson Study

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Closing RemarksPPPPPPPOntogeny recapitulates phylogenyThe more you teach, the smarter

you get, but students stay the same!

ReferencesFirst 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)