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 What does the algebra problem look like in GeoGebra?

What is GeoGebra? Free and open source software created Markus Hohenwarter of Austria A multi-platform dynamic mathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package.

What is GeoGebra? Graphics, algebra and tables are connected and fully dynamic Can easily create interactive learning materials as web pages

Learning Materials “Crowdsource” – materials contributed by people all over the world many materials are available in the GeoGebra Wiki All materials created for GeoGebra must be non- commercial, unless prior permission is obtained

Solution of Equations Relate algebraic representation to graphical representation Recast an equation as an intersection of the graphs of two functions Explore nature of solutions

Algebraic Problem x 2 =2x+ k For what value(s) of k does this equation have no solutions? One solution? Two solutions?

Solution of Inequalities Relate algebraic representation to graphical representation Recast solution of an inequality in terms of locations on a graph Explore nature of solutions

Explore nature of solutions – absolute value inequality Show graphically the solution of |x| - k > 3 -5 < k <5

Enabling Guided Discovery Parameters must be chosen carefully Limit change of parameters to only one at a time Students need guidance on what to observe

Examine zeros by varying constant

GeoGebra for web based demos The GeoGebra web page at has 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.

Exemplary GeoGebra Sites us/GeoGebraCalculusApplets.html SLU.html

Wolfram|Alpha (W|A) W|A is a free online web-based computational engine Advantage : can be accessed via smartphone Click on link for Wolfram|Alpha widgets W|A widgets make it easy to visualize concepts

W|A Exploration: Table of Values of a Function Quickly generate a table of values for a function

W|A Exploration: Trigonometric Functions Quickly graph trig functions Explore effects of period and amplitude

Graphing Two Functions

More widgets … Polar Plotter

Comparison GeogebraWolfram|Alpha DynamicYesNo InteractiveYes Easy to UseYes, but a learning curve exists Yes SyntaxSpecificNatural language Mobile Device useOnly IpadsTablets and smartphones Makes math interesting Yes!!

More information Web: Click on links for Geogebra or Wolfram|Alpha