online interactivities for precalculus using geogebra and wolfram|alpha
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Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha. Reva Narasimhan Kean University, Union, NJ. What comes to your mind at the mention of equations?. Dynamic geometry – move it and see it Visual and tactile. - PowerPoint PPT PresentationTRANSCRIPT
Online Interactivities for Precalculus using GeoGebra
and Wolfram|Alpha
www.mymathspace.net/geogebra
Reva Narasimhan Kean University, Union, NJ
What comes to your mindat the mention of equations?
www.mymathspace.net/geogebra
www.mymathspace.net/geogebra
Dynamic geometry – move it and see it
Visual and tactileWhat does the algebra problem look like in GeoGebra?
www.mymathspace.net/geogebra
www.mymathspace.net/geogebra
What is GeoGebra?Free and open source software created
Markus Hohenwarter of Austria
www.geogebra.org
A multi-platform dynamic mathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package.
www.mymathspace.net/geogebra
What is GeoGebra?Graphics, algebra and tables are connected and fully dynamic
Can easily create interactive learning materials as web pages
www.mymathspace.net/geogebra
Learning Materials“Crowdsource” – materials contributed by
people all over the world many materials are available in the
GeoGebra WikiAll materials created for GeoGebra must be
non-commercial, unless prior permission is obtained
www.mymathspace.net/geogebra
Solution of EquationsRelate algebraic representation to graphical
representation
Recast an equation as an intersection of the graphs of two functions
Explore nature of solutions
www.mymathspace.net/geogebra
Algebraic Problemx2=2x+ k
For what value(s) of k does this equation have no solutions? One solution?Two solutions?
www.mymathspace.net/geogebra
Solution of InequalitiesRelate algebraic representation to graphical
representation
Recast solution of an inequality in terms of locations on a graph
Explore nature of solutions
www.mymathspace.net/geogebra
Explore nature of solutions – absolute value inequality
Show graphically the solution of |x| - k > 3-5 < k <5
www.mymathspace.net/geogebra
Enabling Guided DiscoveryParameters must be chosen carefullyLimit change of parameters to only one at a
timeStudents need guidance on what to observe
www.mymathspace.net/geogebra
Examine zeros by varying constant
www.mymathspace.net/geogebra
GeoGebra for web based demosThe GeoGebra web page at
www.geogebra.orghas links to many online demos for a variety of topics
You can easily create your own web applets. You will need a web host to host your applet and related files. No programming required.
www.mymathspace.net/geogebra
Exemplary GeoGebra Siteshttp://math247.pbworks.com
http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html
http://www.slu.edu/classes/maymk/MathApplets-SLU.html
www.mymathspace.net/geogebra
Wolfram|Alpha (W|A)W|A is a free online web-based computational
enginewww.wolframalpha.com
Advantage : can be accessed via smartphonehttp://blog.mymathspace.net
Click on link for Wolfram|Alpha widgetsW|A widgets make it easy to visualize
concepts
www.mymathspace.net/geogebra
W|A Exploration: Table of Values of a FunctionQuickly generate a table of values for a
function
www.mymathspace.net/geogebra
W|A Exploration: Trigonometric FunctionsQuickly graph trig functionsExplore effects of period and amplitude
www.mymathspace.net/geogebra
Graphing Two Functions
www.mymathspace.net/geogebra
More widgets …Polar Plotter
www.mymathspace.net/geogebra
ComparisonGeogebra Wolfram|Alpha
Dynamic Yes NoInteractive Yes YesEasy to Use Yes, but a learning
curve existsYes
Syntax Specific Natural languageMobile Device use Only Ipads Tablets and
smartphonesMakes math interesting
Yes!! Yes!!
www.mymathspace.net/geogebra
More informationWeb:www.mymathspace.netClick on links for Geogebra or Wolfram|
AlphaEmail: [email protected]
www.mymathspace.net/geogebra