CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

IDEAS FOR IMPLEMENTATION INTO A MULTIVARIABLE CALCULUS CLASS

Presented by Nicole Schergernschergerelginedu

Elgin Community College

38th Annual IMACC Annual ConferenceAllerton House Monticello Illinois

April 5th 2013

bull Innovation Mathematics programs should be thoughtfully constructed to approach content and instruction with appropriate use of traditional and innovative methods

bull Inquiry Effective mathematics instruction should require students to be active participants

bull Technology Technology should be integral to the teaching and learning of mathematics

CALC3D PLOTTERDesigned by community college professor Paul

Seeburger

Reflects the guiding principles of AMATYC (as expressed in ldquoBeyond Crossroadsrdquo)

Graphs Ideas for Implementation

If teaching in a room with a computer projector and internet access or a computer lab use the Calc3D plotter ldquoliverdquo for classroom demonstrations

Without such access graphs can be inserted into guided notes lecture outlines

Assessments For example create matching or multiple questions (examples included)

Student lab assignments (examples included)

Throughout the following presentation consider the following ideas as a starting point for you to think about the varied ways the Calc3D Plotter

can be implemented into your multivariable calculus class

Graphs Rectangular Cylindrical and Spherical Oh My

Graphs Now in 3D (Glasses Required)

Example (of a

section of matching exercises

)

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Graphs Ideas for Implementation

If teaching in a room with a computer projector and internet access or a computer lab use the Calc3D plotter ldquoliverdquo for classroom demonstrations

Without such access graphs can be inserted into guided notes lecture outlines

Assessments For example create matching or multiple questions (examples included)

Student lab assignments (examples included)

Throughout the following presentation consider the following ideas as a starting point for you to think about the varied ways the Calc3D Plotter

can be implemented into your multivariable calculus class

Graphs Rectangular Cylindrical and Spherical Oh My

Graphs Now in 3D (Glasses Required)

Example (of a

section of matching exercises

)

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Graphs Rectangular Cylindrical and Spherical Oh My

Graphs Now in 3D (Glasses Required)

Example (of a

section of matching exercises

)

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Graphs Now in 3D (Glasses Required)

Example (of a

section of matching exercises

)

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Example (of a

section of matching exercises

)

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Graphs Vector Valued Functions

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Example (of a

section of matching exercises

)

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Graphs of more than 1 surface

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Example

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Example

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Example

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Student Lab Assigments Guidelines

Combine the creation of graphs on the Calc3D Plotter with computational questions to compute by hand or with other technology (such as wwwwolframalphacom )

Create sequences of questions that foster inquiry-based learning with the material

Avoid overly simplistic questions (ie ldquograph this surfacerdquo) that do not increase studentsrsquo level of understanding of the material (and risk becoming ldquobusy workrdquo for students and for you)

Where appropriate share varying student results with the entire class

Sample Student Lab Questions

Dot Product and Cross Product Explorations Students visually reflect on the formulas uv=uvcos(θ) and u x v= uvsin(θ)

Sample Student Lab Questions

Sample Student Lab Questions

Sample Student Lab Questions

actual student responses

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab Questions

Sample Student Lab Questions

Sample Student Lab Questions

actual student responses

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab Questions

Sample Student Lab Questions

actual student responses

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab Questions

actual student responses

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab Questions

actual student responses are they both correct

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab

actual student response

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab

actual student response continuedhellip

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

Sample Student Lab

actual student response continuedhellip

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu

CALC3D PLOTTERhttpwebmonroeccedumanilawebfilescalcNSFJavaCodeCalcPlot3Dhtm

Itrsquos so easy a caveman could do it

Email questionscomments nschergerelginedu