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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 College Saratoga, California wellis@ti.com. An Overview of Technology Used in Mathematics Classrooms. But first. Outline.

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Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding

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  1. Using Inquiry Questions and Action/Consequence Documents to Improve Student Understanding Wade Ellis, Jr. West Valley College Saratoga, California wellis@ti.com

  2. An Overview of Technology Used in Mathematics Classrooms But first . . .

  3. Outline • Teaching Undergraduate Mathematics with Technology • The Action/Consequence/Reflection Principle • Action/Consequence Documents • Inquiry-Based Learning • Comments and Questions

  4. 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

  5. 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

  6. Teaching Undergraduate Mathematics with Technology • Software for • Learning Management Systems • Blackboard, Moodle, Angel, etc.

  7. Teaching Undergraduate Mathematics with Technology • Software for • Learning Management Systems • Blackboard, Moodle, Angel, etc. • Homework Systems • WeBWorK , WebAssign, Maple T.A., etc.

  8. Teaching Undergraduate Mathematics with Technology • Learning Management Systems • Blackboard, Moodle, Angel, etc. • Software and devices for classroom management • TI-Navigator, “Clickers”, SchoolVue, etc

  9. 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”

  10. Podcast

  11. 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.

  12. Teaching Undergraduate Mathematics with Technology • Software for doing mathematics • Maple, Mathematica, Mathcad, MatLab, Sage, Axiom, Minitab, Stella, ODE Architect, etc.

  13. 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.

  14. Software for “understanding” mathematics

  15. 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

  16. The Action/Conseq./Reflection Principle

  17. 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.

  18. 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

  19. 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

  20. Examples Topics • Slope • Radian measure • Graphing a function point by point • Describing function behavior • Derivative functions • Riemann sums • Epsilon-Delta limit definition

  21. Suggested Inquiry Questions • How do you move P2 to get a negative slope? • How do you move P2 to get no slope? • How do you move P2 to get a slope of 0? • What happens when you move P1 to P2 ? • Record the value of the slope. How do youmove P2 to a position that gives the same slope? • What are P1Q and P2Q ?

  22. Inquiry Questions (continued) • 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.

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