COOL TOOLS FOR LEARNING: Data Collection with Go!Motion and Analyzing GeoGebra

KAREN KEENE

NICK FORTUNE

Associate Professor
Mathematics Education

PhD Student
Mathematics Education

I. What are Go!Motion and GeoGebra?

Go!Motion

Go!Motion is used to collect the position, velocity and acceleration data of moving objects. Go!Motion connects directly to a computer or Chromebook USB port making it fast and easy to set up experiments and start collecting a wide range of real-time motion data.
Go!Motion can track objects as close fifteen centimeters and as far away as six meters. The sensor also features reduced noise and temperature compensation to ensure accuracy.

Analyze the motion of a ball, a cart on a ramp, or a pendulum

Adjust sensitivity to track the motion of objects close to Go!Motion or up to six meters away

Attach Go!Motion to a track like the one included in the Vernier Dynamics System to study velocity and acceleration

GeoGebra

Often mathematical programs are one dimensional, functioning as a tool for a single subject such as Algebra, Geometry, or Statistics. Two of the most dynamic, intuitive, and useful mathematical tools include Dynamic Geometry Software (DGS) and Computer Algebra Systems. Since there is such a strong relationship between algebra and geometry, students need a program that has both capabilities. Fortunately there is a software system called GeoGebra that integrates possibilities of both dynamic geometry and computer algebra in one program. GeoGebra is a dynamic geometry program that integrates geometry, algebra, statistics, calculus, and more. What sets GeoGebra apart from other mathematical programs, is its dynamic nature. As one plots functions on the coordinate plane, GeoGebra links this with algebra or statistics. Often students overlook the connection between various areas of mathematics, like geometry and algebra. GeoGebra displays the connection in an interactive and intuitive setting. Additionally, data analyzing is possible in GeoGebra. Data can be copied into the spreadsheet function of GeoGebra and then analyzed by students. Thus, for teachers looking for one technology that is free and open source with numerous mathematical capabilities and functionalities, then GeoGebra is the way to go!

II. How can I access Go!Motion and GeoGebra?

Go!Motion

Go!Motions can be purchased for your school here and for Asian providers click here! Logger Lite is a free software that can be used for data collection (in our activity we then transfer that data to GeoGebra). Or you can purchase Logger Pro.

GeoGebra

GeoGebra is a free and open source software that can be accessed worldwide at http://www.geogebra.org. GeoGebra is available on all computer operating systems (Windows, Mac OSX, and Linux), as well as, all tablet operating systems (Windows, iOS, and Android)! Additionally, there is a Google Chrome App that teachers and students can access with Google Chrome. In addition to the main site there is also a subset of GeoGebra, known as GeoGebra Tube (http://tube.geogebra.org) where educators can upload GeoGebra files they have made to share with the rest of the mathematics (or other disciplines) communities! An account is needed for GeoGebra Tube, but it is free and you just need an email.

III. Go!Motion and GeoGebra Examples: Beginning with the End in Mind

Go!Motion

1. Cooling Water (note this activity used Fathom as opposed to GeoGebra)

Graphical View - functions and relations can be graphed

Algebraic View - keeps track of functions graphed in other views and can have sliders included for dynamic representations

Spreadsheet View - can be linked to the other views and has additional features as well

Multi-representations

2 or 3 different representations from above can be represented at the same time for deeper mathematical connections and understanding.

Functionality

Tool Bar - easy and intuitive with clear pictorial buttons

Menu Bar - simplistic and straightforward menu options

Input Bar - accepts functions, non-functions, relations, parametric function, polar functions, and more!

V. Tutorial

Go!Motion

1. Go!Motion Overview - Vernier Go!Motion is a USB motion detector that includes free Logger Lite software. It's designed for activities about position, velocity, and acceleration.

GeoGebra

1. How I Teach Using GeoGebra - Areas and Quadratic Functions - This video is taken from a sequence of videos a teacher put together to discuss Applications of Quadratic Functions. During the first three clips, the teacher sets up a scenario about a picture behind a square piece of matting. She then discusses with her students how they could use GeoGebra to model the scenario. This is the clip of her translating the word problem into a dynamic workspace. The video illustrates how to change the view, define points, create polygons and sliders, and link points with slider values.
2. How to create an interactive java applet - This is a video tutorial showing how to create an interactive java applet (virtual manipulative) using the free program GeoGebra. The author of the video also shows how to export and upload the interactive worksheet from GeoGebra to a web page as a stand-alone and interactive java applet with questions that students can answer by interacting with the content of the worksheet.
3. How to create piece-wise functions in GeoGebra - This video features how teachers can create graphs of piece-wise functions for use in class. The video can very helpful for teachers for creating their own graphs of piece-wise functions for discussing range, domain, modeling situations, and limits in class. The video also illustrates in detail how to rearrange the steps of constructing and/or displaying the graphs and how to make the graphs look clear and accurate.
4. Why Should GeoGebra be used in the Mathematics Classroom? - This video demonstrates the many different features that make the use of GeoGebra necessary in the classroom. Multiple visuals are presented to demonstrate the use of sliders, rulers, and many other functions.

IX. Technology Tools for Teaching Mathematics Content

Core Math Tools New interactive software compatible with the Common Core State Standards for high school mathematics. The tools can be used for
algebra and functions, geometry and trigonometry, and statistics and probability. CPMP-Tools (Similar to the link above, made by same programmers) Downloadable Computer Algebra System, Dynamic Geometry Environment, Statistics Tool, and Discrete Math Tool all in one program. Requires that Java, a free program, be run prior to downloading. NuCal Downloadable Graphing Calculator capable of graphing 2-D and 3-D plots Shodor Educational Foundation Interactive Tools 57 different online interactive tools to use for middle school and high school mathematics content SAS Curriculum Pathways: Mathematics Includes InterActivities, Web Resources, Lessons, and Web Inquiries in four different content areas Illuminations by the National Council for Teachers of Mathematics (NCTM), this site provides Activities, Lessons, NCTM Standards, and Web Links Explore Learning Interactive Applets by mathematics content area. Must have internet access and Shockwave player. Also available for download (30-day free trial). SimCal MathWorlds evaluation versions for TI-graphing calculators and computers

X. Resources to Help with Mathematics Pedagogy

Math Forum Has math help for students, problems and puzzles, a forum for facilitating math talk, and resources and tools for use in your classroom.

COOL TOOLS FOR LEARNING: Data Collection with Go!Motion and Analyzing GeoGebraKAREN KEENENICK FORTUNEMathematics Education

Mathematics Education

I. What are Go!Motion and GeoGebra?

Go!Motion is used to collect the position, velocity and acceleration data of moving objects. Go!Motion connects directly to a computer or Chromebook USB port making it fast and easy to set up experiments and start collecting a wide range of real-time motion data.Go!MotionGo!Motion can track objects as close fifteen centimeters and as far away as six meters. The sensor also features reduced noise and temperature compensation to ensure accuracy.

Often mathematical programs are one dimensional, functioning as a tool for a single subject such as Algebra, Geometry, or Statistics. Two of the most dynamic, intuitive, and useful mathematical tools include Dynamic Geometry Software (DGS) and Computer Algebra Systems. Since there is such a strong relationship between algebra and geometry, students need a program that has both capabilities. Fortunately there is a software system called GeoGebra that integrates possibilities of both dynamic geometry and computer algebra in one program. GeoGebra is a dynamic geometry program that integrates geometry, algebra, statistics, calculus, and more. What sets GeoGebra apart from other mathematical programs, is its dynamic nature. As one plots functions on the coordinate plane, GeoGebra links this with algebra or statistics. Often students overlook the connection between various areas of mathematics, like geometry and algebra. GeoGebra displays the connection in an interactive and intuitive setting. Additionally, data analyzing is possible in GeoGebra. Data can be copied into the spreadsheet function of GeoGebra and then analyzed by students. Thus, for teachers looking for one technology that is free and open source with numerous mathematical capabilities and functionalities, then GeoGebra is the way to go!GeoGebraII. How can I accessGo!Motion and GeoGebra?

Go!Motions can be purchased for your school here and for Asian providers click here! Logger Lite is a free software that can be used for data collection (in our activity we then transfer that data to GeoGebra). Or you can purchase Logger Pro.Go!Motion

GeoGebra is a free and open source software that can be accessed worldwide at http://www.geogebra.org. GeoGebra is available on all computer operating systems (Windows, Mac OSX, and Linux), as well as, all tablet operating systems (Windows, iOS, and Android)! Additionally, there is a Google Chrome App that teachers and students can access with Google Chrome. In addition to the main site there is also a subset of GeoGebra, known as GeoGebra Tube (http://tube.geogebra.org) where educators can upload GeoGebra files they have made to share with the rest of the mathematics (or other disciplines) communities! An account is needed for GeoGebra Tube, but it is free and you just need an email.GeoGebraIII.Go!Motion and GeoGebraExamples: Beginning with the End in Mind

1. Cooling Water (note this activity used Fathom as opposed to GeoGebra)Go!Motion

1. Introduction to the Unit CircleGeoGebra2. Growth of Facebook.com

3. Pythagorean Theorem Proof Without Words

4. Many more at http://tube.geogebra.org !

IV. Key FeaturesGo!Motion

RepresentationsGeoGebra- Graphical View - functions and relations can be graphed
- Algebraic View - keeps track of functions graphed in other views and can have sliders included for dynamic representations
- Spreadsheet View - can be linked to the other views and has additional features as well

Multi-representations- 2 or 3 different representations from above can be represented at the same time for deeper mathematical connections and understanding.

FunctionalityV. Tutorial

1. Go!Motion Overview - Vernier Go!Motion is a USB motion detector that includes free Logger Lite software. It's designed for activities about position, velocity, and acceleration.Go!Motion

1. How I Teach Using GeoGebra - Areas and Quadratic Functions - This video is taken from a sequence of videos a teacher put together to discuss Applications of Quadratic Functions. During the first three clips, the teacher sets up a scenario about a picture behind a square piece of matting. She then discusses with her students how they could use GeoGebra to model the scenario. This is the clip of her translating the word problem into a dynamic workspace. The video illustrates how to change the view, define points, create polygons and sliders, and link points with slider values.GeoGebra2. How to create an interactive java applet - This is a video tutorial showing how to create an interactive java applet (virtual manipulative) using the free program GeoGebra. The author of the video also shows how to export and upload the interactive worksheet from GeoGebra to a web page as a stand-alone and interactive java applet with questions that students can answer by interacting with the content of the worksheet.

3. How to create piece-wise functions in GeoGebra - This video features how teachers can create graphs of piece-wise functions for use in class. The video can very helpful for teachers for creating their own graphs of piece-wise functions for discussing range, domain, modeling situations, and limits in class. The video also illustrates in detail how to rearrange the steps of constructing and/or displaying the graphs and how to make the graphs look clear and accurate.

4. Why Should GeoGebra be used in the Mathematics Classroom? - This video demonstrates the many different features that make the use of GeoGebra necessary in the classroom. Multiple visuals are presented to demonstrate the use of sliders, rulers, and many other functions.

VI. Mini-TaskTuesdayWednesdayVII. ReflectionVIII. Additional Resources

Go!Motion SiteGo!Motion

GeoGebra TubeGeoGebraGeoGebra Blog

Using GeoGebra in Your Middle School Mathematics Classroom

Using GeoGebra in the Classroom

Getting Started with GeoGebra - Tutorials, Examples, and More

Wiki of GeoGebra Activities

GeoGebra Activities

Mathematics with GeoGebra

GeoGebra Samples

## IX. Technology Tools for Teaching Mathematics Content

Core Math Tools New interactive software compatible with the Common Core State Standards for high school mathematics. The tools can be used for

algebra and functions, geometry and trigonometry, and statistics and probability.

CPMP-Tools (Similar to the link above, made by same programmers) Downloadable Computer Algebra System, Dynamic Geometry Environment, Statistics Tool, and Discrete Math Tool all in one program. Requires that Java, a free program, be run prior to downloading.

NuCal Downloadable Graphing Calculator capable of graphing 2-D and 3-D plots

Shodor Educational Foundation Interactive Tools 57 different online interactive tools to use for middle school and high school mathematics content

SAS Curriculum Pathways: Mathematics Includes InterActivities, Web Resources, Lessons, and Web Inquiries in four different content areas

Illuminations by the National Council for Teachers of Mathematics (NCTM), this site provides Activities, Lessons, NCTM Standards, and Web Links

Explore Learning Interactive Applets by mathematics content area. Must have internet access and Shockwave player. Also available for download (30-day free trial).

SimCal MathWorlds evaluation versions for TI-graphing calculators and computers

## X. Resources to Help with Mathematics Pedagogy

Math Forum Has math help for students, problems and puzzles, a forum for facilitating math talk, and resources and tools for use in your classroom.

## XI. Resources for AP Mathematics Content

College Board's AP: Calculus AB website

College Board's AP: Calculus BC website

College Board's AP: Statistics website

XII. ReferencesNCSU. (2015). Review of GeoGebra. Retrieved from: http://ems581spring2015.wikispaces.com/GeoGebra+Group+1.

NCSU. (2015). Review of GeoGebra. Retrieved from: http://ems581spring2015.wikispaces.com/GeoGebra+Group+2.

Vernier Go!Motion is a USB motion detector that includes free Logger Lite software. It's designed for activities about position, velocity, and acceleration.