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Interactive Precalculus Learning with GeoGebra and Wolfram|Alpha

Explore innovative online interactivities designed to enhance your precalculus understanding using GeoGebra and Wolfram|Alpha. This dynamic mathematics software integrates geometry, algebra, statistics, and calculus in a single platform, enabling students to visualize and manipulate mathematical concepts interactively. With resources contributed globally, learners can access engaging materials and guided explorations on equations, inequalities, and trigonometric functions. Connect algebraic and graphical representations while developing problem-solving techniques that promote deeper comprehension and discovery.

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Interactive Precalculus Learning with GeoGebra and Wolfram|Alpha

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  1. Online Interactivities for Precalculus using GeoGebra and Wolfram|Alpha Reva Narasimhan Kean University, Union, NJ www.mymathspace.net/geogebra

  2. What comes to your mindat the mention of equations? www.mymathspace.net/geogebra

  3. www.mymathspace.net/geogebra

  4. Dynamic geometry – move it and see it Visual and tactile What does the algebra problem look like in GeoGebra? www.mymathspace.net/geogebra

  5. www.mymathspace.net/geogebra

  6. What is GeoGebra? • Free and open source software created Markus Hohenwarter of Austria www.geogebra.org • A multi-platform dynamicmathematics software that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. www.mymathspace.net/geogebra

  7. 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

  8. 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 www.mymathspace.net/geogebra

  9. 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 www.mymathspace.net/geogebra

  10. Algebraic Problem x2=2x+ k For what value(s) of k does this equation have no solutions? One solution? Two solutions? www.mymathspace.net/geogebra

  11. 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 www.mymathspace.net/geogebra

  12. Explore nature of solutions – absolute value inequality Show graphically the solution of |x| - k > 3 -5 < k <5 www.mymathspace.net/geogebra

  13. 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 www.mymathspace.net/geogebra

  14. Examine zeros by varying constant www.mymathspace.net/geogebra

  15. GeoGebra for web based demos • The GeoGebra web page at www.geogebra.org 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. www.mymathspace.net/geogebra

  16. Exemplary GeoGebra Sites • http://math247.pbworks.com • http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html • http://www.slu.edu/classes/maymk/MathApplets-SLU.html www.mymathspace.net/geogebra

  17. Wolfram|Alpha (W|A) • W|A is a free online web-based computational engine www.wolframalpha.com • Advantage : can be accessed via smartphone http://blog.mymathspace.net Click on link for Wolfram|Alpha widgets • W|A widgets make it easy to visualize concepts www.mymathspace.net/geogebra

  18. W|A Exploration: Table of Values of a Function • Quickly generate a table of values for a function www.mymathspace.net/geogebra

  19. W|A Exploration: Trigonometric Functions • Quickly graph trig functions • Explore effects of period and amplitude www.mymathspace.net/geogebra

  20. Graphing Two Functions www.mymathspace.net/geogebra

  21. More widgets … • Polar Plotter www.mymathspace.net/geogebra

  22. Comparison www.mymathspace.net/geogebra

  23. More information Web: www.mymathspace.net Click on links for Geogebra or Wolfram|Alpha Email: RNARASIM@kean.edu www.mymathspace.net/geogebra

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