Using Inquiry Questions and
Action/Consequence Documents
to Improve Student Understanding
Wade Ellis, Jr.
West Valley College
Saratoga, California
wellis@ti.com
But first . . .
An Overview of Technology Used
in Mathematics Classrooms
Outline
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Teaching Undergraduate Mathematics
with Technology
The Action/Consequence/Reflection
Principle
Action/Consequence Documents
Inquiry-Based Learning
Comments and Questions
Teaching Undergraduate
Mathematics with Technology
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Software
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Learning Management Systems
Homework Systems
Software and devices for classroom
interaction
Software for presenting mathematics
Software tutorials for mathematics
Software for doing mathematics
Software for “understanding” mathematics
Teaching Undergraduate
Mathematics with Technology
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Software for
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Learning Management Systems
Homework Systems
Software and devices for classroom
interaction
Software for presenting mathematics
Software tutorials for mathematics
Software for doing mathematics
Software for “understanding” mathematics
Teaching Undergraduate
Mathematics with Technology
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Software for
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Learning Management Systems
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Blackboard, Moodle, Angel, etc.
Teaching Undergraduate
Mathematics with Technology
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Software for
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Learning Management Systems
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Blackboard, Moodle, Angel, etc.
Homework Systems
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WeBWorK , WebAssign, Maple T.A., etc.
Teaching Undergraduate
Mathematics with Technology
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Learning Management Systems
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Blackboard, Moodle, Angel, etc.
Software and devices for classroom
management
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TI-Navigator, “Clickers”, SchoolVue, etc
Teaching Undergraduate
Mathematics with Technology
„
Learning Management Systems
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„
Software and devices for classroom
management
„
„
Blackboard, Moodle, Angel etc.
TI-Navigator, “Clickers”, SchoolVue, etc
Software for presenting mathematics
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PowerPoint, Keynote, Beamer (TeX),
SmartBoard, Tablet PCs, etc.
→ “Podcasts”
Podcast
Teaching Undergraduate
Mathematics with Technology
„
Learning Management Systems
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„
Software and devices for classroom management
„
„
TI-Navigator, “Clickers”, SchoolVue, etc
Software for presenting mathematics
„
„
Blackboard, Moodle, Angel, etc.
PowerPoint, Keynote, Beamer (TeX), SmartBoard, Tablet
PCs, etc.
→ “Podcasts”
Software tutorials for mathematics
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ALEKS, MyMathLab, Intelligent Tutor, etc.
Teaching Undergraduate
Mathematics with Technology
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Software for doing mathematics
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Maple, Mathematica, Mathcad, MatLab,
Sage, Axiom, Minitab, Stella,
ODE Architect, etc.
Teaching Undergraduate
Mathematics with Technology
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Software for doing mathematics
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Maple, Mathematica, Mathcad, MatLab,
Sage, Axiom, Minitab, Stella,
ODE Architect, etc.
Software for “understanding” math
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Geometer’s Sketchpad, GeoGebra,
TI-Nspire, Cabri, etc.
Software for
“understanding” mathematics
Accepted Tenets of Instruction
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Students learn by doing
Focused time on task is important
Students remember what they think
about
Contexts/Relevance help students learn
The Action/Conseq./Reflection
Principle
Action/Consequence Documents
. . . are environments where students can act
on mathematical objects and transparently
observe the consequences of their actions.
‰Teachers create the classroom settings
where students are confident in answering
and asking inquiry questions that extend
mathematical environments so that they can
understand the underlying mathematics
through their own reasoning and reflection.
Tenets and the A-C-R Principle
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Students act
Students spend focused time on task
Students reflect on mathematics
Contexts/Relevance
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What students do is relevant to them
Mathematical contexts are contexts
Inquiry Question Types
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Compare and Contrast/Similarities and
Differences
Predict forward and backward:
What action gives . . ./Given this action . . .
Analyze a connection/relationship
This happens when . . .
Make a conjecture
Require Mathematical Reasoning/
Justify a conjecture/Prove a conjecture
Examples Topics
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Slope
Radian measure
Graphing a function point by point
Describing function behavior
Derivative functions
Riemann sums
Epsilon-Delta limit definition
Suggested Inquiry Questions
1. How do you move P2 to get a negative slope?
2. How do you move P2 to get no slope?
3. How do you move P2 to get a slope of 0?
4. What happens when you move P1 to P2 ?
5. Record the value of the slope. How do you
move P2 to a position that gives the same slope?
6. What are P1Q and P2Q ?
Inquiry Questions (continued)
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What is the comparison between P1Q and P2Q ?
Move P2 so that P2Q is 10.
Make the distance from P1 to Q 1 unit. What
happens when you move P2 ?
Move below the x-axis in a rigid transformation?
What happens to the numbers?
Why does P1 below P2 make the slope negative?
How can you move P2 to maximize slope?
What is slope?
Where do x 2 and y 2come from? Where do x1 and
y1 come from?
Make conjectures about Q for P1 and P2.