Gregory V. Bard
Associate Professor of Mathematics
Preserving the look-and-feel of the World Wide Web as it was, in 1998.
Interactive Web Applications (Interacts)
for Learning Mathematics
Whether you call them applets, apps, interactive webpages, or interacts, these game-like internet resources
are great for teaching mathematics to college students. These tools allow students to tweak and manipulate
parameters, and therefore teach students how one math object can alter another. Moreover, the visual
aspect can be a great boon---a picture is worth a thousand words! Also, interacts are just plain fun,
and that helps too.
One of the keys to using interacts in teaching mathematics is: DO NOT ATTEMPT TO REINVENT THE WHEEL.
I have on this page a collection of interacts that I've written myself, and further down I have several
links to websites that contain dozens and dozens of interacts written by other people.
And now, here are some interacts that I've written myself, for my students.
- The famous smiley face applet, that shows the role of matrices in computer graphics:
- The feasible region of a system of inequalities: click here.
- To visualize the span of two vectors: click here.
- What is better? 6% compound interest or 8% simple interest? click here.
- Leontief Input-Output Analysis click here.
- An interesting problem about a solvent factory and environmental compliance: click here.
- A simple portfolio balancing problem, risk versus reward: click here.
- Three Linear Equations in Three Unknowns (unique solution):
- [Incomplete] The design of the optimal oil barrel, minimizing the metal used:
- [Incomplete] Step-by-Step, the quadratic equation:
- [Incomplete] Comparing Contour Plots vs 3D Plots:
- [Incomplete] The Behavior of Newton's Method on a Polynomial with Multiple Roots:
- [Incomplete] Visualizing Infinitely Many Solutions in a Linear System of 3 Equations and 3 Unknowns:
- [Incomplete] How the Complex Numbers are used in Signal Processing:
- These rather simplistic interacts are the examples that I used in Chapter 6
of my book Sage for Undergraduates:
- [Incomplete] The Classic Tangent Line Interact:
- [Incomplete] Visualizing the Definite Integral:
- [Incomplete] Optimal Aquarium Design:
- [Incomplete] Amplitude and Phase Shift in Sine Waves:
- [Incomplete] A Simple Polynomial Graphing Interact:
Here are some collections (treasure-troves, really) of interacts from around the net:
- The Sage Interactions Archive is already large, and
growing larger. It is likely that whatever you need, you can find it here.
- The JSXGraph Interacts Archive,
hosted by Universataet Bayreuth in Germany, is quite huge.
- The following mind map (graciously provided by Prof. Hofacker of UW-River Falls)
as part of the Wisconsin Project Next technology training,
is full of exciting internet tools (including interacts) for teaching mathematics---in particular calculus and its prerequisite algerba/trigonometry/precalc
(Just click on Visualization or Interactive Web Activities.)
- While I certainly do not approve of their business practices, the Wolfram Demonstrations Project has numerous
interacts with dazzling graphics, if not always excellent pedagogy. The Wolfram company makes Mathematica.
- At UW-Stout, we have a project called MathWiz, and it has a small but growing collection of interacts.
- The UW-Stout MathWiz page has a bunch of excellent videos too.
- The PhET project at the University of Colorado, Boulder, has many physics-oriented interacts
that are very useable in a calculus-for-engineers classroom.
If you'd like to make your own interacts,
- Chapter Six of my book Sage for Undergraduates, published by the American Mathematical Society in 2014, is
an easy-to-understand tutorial for anyone who wants to build an interact using Sage. (Just click "Sage Stuff"
on the menu to the left to get a free electronic copy.)
- The Sage Community Wiki for Interacts has a lot of demos and examples to get you started.
Last updated July 21st, 2014.