The lessons
| Continuity: Epsilons and Deltas | Exploring Jurassic Park:
The Logistic Model and Chaos |
Graph Transformations:
Algebra and Geometry |
| The Curious Tale of Dr. Bias and the Chocolate Factory:
About those Type I an II errors |
How to Make a Hula Hoop, or
Discovering the Fundamental Theorem of Linear Programming |
The Koch Snowflake |
Note: In order to view the following lessons, you will need a Java-capable browser, such as Netscape Explorer 3.0. You will also have to "enable" its Java capability, by going to the Options menu, selecting Network Preferences, then selecting Languages, and clicking on Enable Java and Enable JavaScript.
About the lessons
About HTML/Java/JavaScript
Continuity: Epsilons and Deltas (added June 3, 1997)
This is my first Java-based math lesson with a serious pedagogical purpose. It explains the concept of the continuity of functions starting from the intuitive notion and proceeding to the full-fledged mathematical definition. The lesson includes some animations and an interactive "epsilon-delta" game. All the graphs with green axes are generated on-the-fly by a Java applet (as well as the animation and game, of course). This applet is a 670 line Java program, designed and programmed by the author.
My thanks go to Mary Parker at ACC (Northridge Campus) for suggesting this topic as a lesson.
Exploring Jurassic Park: the Logistic Model and Chaos (added June 12, 1997)
This lesson explores the (discrete) logistic model of population growth, along with some Java-based animated and interactive demonstrations of this model at work. It also explains some of Jurassic Park chaos-mathematician Ian Malcolm's concerns about the idea of predicting and/or controlling nature, and why such endeavors usually don't work very well.
Graph Transformations: Algebra and Geometry (added June 20, 1997)
This lesson explores graph transformations (shifts, reflections, and stretch/shrink) based on several reference graphs: y = x2, y = |x|, and y = sin(x) (also cos and tan). It includes the two ingredients that make such lessons special: interactivity and animation. It assumes that the students will already have been exposed to the notion of "transformation of a graph", but it includes some introductory material that will refresh them on this subject, along with some historical notes.
My thanks to John Thomason at ACC (Northridge Campus) for suggesting this topic.
The Curious Tale of Dr. Bias and the Chocolate Factory (added July 1, 1997)
This lesson explores the statistical subjects of Type I and Type II errors when making tests of hypotheses about the mean of a population. It tells a little story that tries to illustrate (colorfully, I hope) the significance of these kinds of errors, and provides a laboratory for experimenting with the four parameters that define a limited class of tests of hypotheses:
I have found that, as with much of the algebra I teach, Linear Programming eventually boils down to a recipe of rules and steps to follow. I suspect that students don't really understand what they are doing; they are just trying to get the right answer. Worst of all, I often wonder if they understand the key role the Fundamental Theorem of Linear Programming (FTLP) plays in making solving linear programming problems a discrete, rather than an analytic process.
This lesson tries to do both: (1) prescribe the necessary steps and, (2) motivate the steps as they are encountered. The method described is the graphical method for a system with two variables. I will leave the simplex method for a later lesson! Particular attention is paid to the FTLP, and the student is invited to discover it for him/herself.
The Koch Snowflake (added May 10, 1997)
This applet is a demo from the Java Development Kit. It is programmed using Lindenmayer rules (L-systems) combined with a Logo turtle environment (all implemented in Java).
The above math lessons were all (with the exception of the Koch Snowflake) written by me during the summer of 1997, and supported in part by a grant from Austin Community College, entitled Math Instruction Using HTML/Java. They were inspired by my own ruminations about using Internet technology to teach math, as described in more detail in my 1996 paper, Distance Learning, the Web, and HTML/Java: offering new ways to learn mathematics.
Please look at the example lessons and criticize them (send me mail). Positive and negative criticisms are welcome! I know I can make these lessons better if I can get some feedback from interested parties. Or maybe you think the whole idea is a waste of time! Please let me know what you think.
Please send your ideas, comments, and criticisms to me at
e-mail: powens@austincc.edu
For a little information about HTML/Java, read on.
HTML is a language for creating documents that can be transmitted and displayed by Internet browsers (such as Netscape Navigator and Internet Explorer). "Plain" HTML shows only static text. Dynamic (animated) effects can be provided in (at least) two ways:
If you are using Netscape Navigator, you can learn more about JavaScript by selecting Help, and then Handbook. In the future, I will be providing some hints, tips, and examples for math applications.