Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding
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Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding Wade Ellis, Jr. West Valley College Saratoga, California [email protected]
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Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding. Wade Ellis, Jr. West Valley College Saratoga, California [email protected]. An Overview of Technology Used in Mathematics Classrooms. But first. Outline. - PowerPoint PPT Presentation
Transcript of Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding
Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding
Wade Ellis, Jr.West Valley CollegeSaratoga, California
But first . . .
An Overview of Technology Used in Mathematics
Classrooms
Outline
Teaching Undergraduate Mathematics with Technology
The Action/Consequence/Reflection Principle
Action/Consequence Documents Inquiry-Based Learning Comments and Questions
Teaching Undergraduate Mathematics with Technology
Software 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
Software for 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
Software for Learning Management Systems
Blackboard, Moodle, Angel, etc.
Teaching Undergraduate Mathematics with Technology
Software for Learning Management Systems
Blackboard, Moodle, Angel, etc. Homework Systems
WeBWorK , WebAssign, Maple T.A., etc.
Teaching Undergraduate Mathematics with Technology
Learning Management Systems Blackboard, Moodle, Angel, etc.
Software and devices for classroom management TI-Navigator, “Clickers”, SchoolVue, etc
Teaching Undergraduate Mathematics with Technology
Learning Management Systems Blackboard, Moodle, Angel etc.
Software and devices for classroom management TI-Navigator, “Clickers”, SchoolVue, etc
Software for presenting mathematics PowerPoint, Keynote, Beamer (TeX),
SmartBoard, Tablet PCs, etc. “Podcasts”
Podcast
Teaching Undergraduate Mathematics with Technology
Learning Management Systems Blackboard, Moodle, Angel, etc.
Software and devices for classroom management
TI-Navigator, “Clickers”, SchoolVue, etc Software for presenting mathematics
PowerPoint, Keynote, Beamer (TeX), SmartBoard, Tablet PCs, etc. “Podcasts”
Software tutorials for mathematics ALEKS, MyMathLab, Intelligent Tutor, etc.
Teaching Undergraduate Mathematics with Technology
Software for doing mathematics Maple, Mathematica, Mathcad,
MatLab, Sage, Axiom, Minitab, Stella, ODE Architect, etc.
Teaching Undergraduate Mathematics with Technology
Software for doing mathematics Maple, Mathematica, Mathcad,
MatLab, Sage, Axiom, Minitab, Stella, ODE Architect, etc.
Software for “understanding” math Geometer’s Sketchpad, GeoGebra,
TI-Nspire, Cabri, etc.
Software for “understanding” mathematics
Accepted Tenets of Instruction
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
Students act Students spend focused time on
task Students reflect on mathematics Contexts/Relevance
What students do is relevant to them Mathematical contexts are contexts
Inquiry Question Types 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
1. Slope2. Radian measure3. Graphing a function point by point4. Describing function behavior5. Derivative functions6. Riemann sums7. Epsilon-Delta limit definition
Suggested Inquiry Questions1. 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)
7. What is the comparison between P1Q and P2Q ?
8. Move P2 so that P2Q is 10.
9. Make the distance from P1 to Q 1 unit. What happens when you move P2 ?
10. Move below the x-axis in a rigid transformation? What happens to the numbers?
11. Why does P1 below P2 make the slope negative?
12. How can you move P2 to maximize slope?13. What is slope?14. Where do x 2 and y 2come from? Where do x1
and y1 come from?
15. Make conjectures about Q for P1 and P2.
