Teaching Calculus
Through Inquiry
CMC-South 2014
Mimi Yang
The Northwest School
My First Calculus Experience
(International School, Germany)

Calculus as a topic within the I.B.
program

Breadth over depth
Calculus:
“Learning Subject” vs.
“Performance Subject”
(@joboaler)
Challenge #1
Calculus classes are highly
heterogeneous
Challenge #2
Limits, theorems, and definitions
can be intimidating and confusing
Calculus language is extremely
precise; our students are not!
Challenge #3
Students can lose sight of the big
picture
Challenge #4
There is less dialogue about
what characterizes effective
Calculus teaching
What strategies do you use to
promote _____________ ?
Motivation
 Understanding of core concepts
 Mathematical Practices
 Students thinking at different
depths

My Current Vision
Vision: Backwards Curriculum
Traditional Calculus:
Possible “Backwards” Calculus:
The Math Dial (@ddmeyer)
Concrete-to-Abstract Continuum
How does this look in Calculus?
Think-Pair-Share
In what order would you teach
the following subtopics within
Calculus?
Vision: My Order of Subtopics
Making and Reading Graphs
Interactive Desmos Activities
Making and Reading Graphs
Parachute Misconceptions analysis
Making and Reading Graphs
Parachute Misconceptions analysis
Making and Reading Graphs
Reasoning with Tables of Values
Reasoning with Tables of Values
Reasoning with Tables of Values
Graphs from @samjshah
Graphing Calculator Tools
“Given the function:
Where is f positive?
Where is f’ positive?
Where is f’ zero?”
Graphing Calculator Tools
Investigating f’(x) formulas via tables
Applying Calculus Formulas
Designing a rollercoaster
Applying Calculus Formulas
Applying Calculus Formulas
Calculating integrals manually
and checking with technology
Applying Calculus Formulas
Modeling and testing 3-D volume
Applying Calculus Formulas
Modeling and testing 3-D volume
Calculus Theorems and Formal
Definitions
Vision: Student-Centered Tools
and Activities
Desmos
 Labs
 Logger Pro
 GeoGebra
 Graphing calculator
 Projects
 WinPlot
 Journaling

Vision: Cycle of Inquiry
Vision: Math Journal

Essential questions

Multiple iterations of revisions

Focuses on the development of
individual understanding
Example Essential Questions

What is a derivative?

What does it mean when the derivative value is zero? Positive?
Negative?

Given a function’s graph, how do we sketch its approximate
derivative graph? Create two examples.

How does steepness from the original graph affect its derivative
graph? Create two examples.

Compare and contrast derivative to the average rate of a function.

When does the derivative value not exist?

Given a derivative graph, how do we work backwards to sketch its
original function (its anti-derivative)? Create two different examples.
Mathematical Practices Focus

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and express regularity in
repeated reasoning
Summary of Strategies
Backwards calculus curriculum
 Concrete to abstract continuum of
subtopics
 Student-centered activities and
tools
 Cycle of inquiry
 Journal on essential questions

Think-Pair-Share

Are these learning strategies
realistic for your classroom?

What suggestions do you have
for improvement?
Let’s keep in touch!
mimi.yang@northwestschool.org
 mimiyang@gmail.com
 @untilnextstop
 http://untilnextstop.blogspot.com

THANK YOU for your feedback!
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Session code
Prepared and knowledgeable? (1-3)
Fits description? (1-3)
Engaged and effective? (1-3)