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

wellis@ti.com

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.