# Using Mathematica in the Mathematics Classroom

This module is designed for mathematics teachers at the 9 - 14 grade levels who are beginners with Mathematica and who want to learn to use this software package to create transparencies and handouts, computer demonstrations, and interactive student lessons for their mathematics classes. This module is available for both Version 8.0 and Versions 10.0 of Mathematica, with legacy support provided for some older versions. Credit: 2 grad. sem. hrs.

Common Core Standards for Mathemtical Practice that are emphasized include:

• 3. Construct viable arguments.
• 4. Model with mathematics.
• 5. Use appropriate tools strategically.

Using Mathematica in High School Mathematics Instruction was written by Tony Peressini and Debra Woods of the University of Illinois during October 1997.  It has continued to be updated to work with the newer versions of Mathematica (updated April 2016 by Tom Anderson).

Check out some sample projects for this module attached below!

AttachmentSize
Anders.Markov.final_.nb30.74 KB
R1Monke.final_.nb837.5 KB
Stew-series.nb85.55 KB
Tanders.final_.nb30.74 KB

# Detailed Description

The purpose of this module is to familiarize you with the basics of Mathematica programming and its use for generating technology-based classroom materials and demonstrations as well as student tutorials and laboratories.

Mathematica is a very powerful software package that allows you to do complicated numerical calculations, produce and animate beautiful and precise graphical displays, perform messy algebraic and analytic manipulations as well as to do technical word processing. Moreover, all of these capabilities can be used in a single environment called a Mathematica notebook that can be used interactively as an electronic student tutorial, a classroom computer demonstration, or that can be printed as overhead transparency masters or text supplements for special classroom units. As such, it has the power to change the way you teach and the way your students learn mathematics.

To be able to use Mathematica effectively for the above purposes, you need not be an expert Mathematica programmer. It is not necessary or even advisable to study a detailed guide to Mathematica programming such as Mathematica by Stephen Wolfram (Addison-Wesley, 1996) or any less ambitious Mathematica programming guide. Rather, we have found that a mathematics teacher who is a raw beginner with Mathematica can learn to use Mathematica more effectively and quickly with a training program that is structured as follows:

• Step 1: Begin by getting a general idea of some of the things that Mathematica can do by looking at and running some short and simple prepared Mathematica programs that do things that are related to high school mathematics.
• Step 2: Learn a few basic facts about Mathematica syntax to help you to avoid mistakes when you begin writing your own Mathematica programs. (You will still make simple mistakes that are annoying but this step will help to reduce the number of mistakes. It will also help you find and correct the ones that do occur.)
• Step 3: Write some very simple programs to do things that would be useful to you in one of your current classes. Often, you can do this by suitably modifying some program that you have seen in Steps 1 or 2.
• Step 4: Learn how to do some basic procedures that are common ingredients to many classroom projects created with Mathematica such as: writing and displaying text and formulas attractively, creating and running animations, creating lists and tables, entering and using functions, and enhancing graphics so that they are more attractive and informative.
• Step 5: Select and begin a classroom project that you would like to do for one of the classes that you teach. We will provide you with a file that contains many such projects that have been done by high school mathematics teachers who were Mathematica beginners just a few days before they prepared these projects. You can use these sample projects as a souce of ideas for your own project. You can also use these sample projects as a source of Mathematica programs that you can copy and modify to suit your own purposes.

That's it! All of the ingredients necessary to complete these steps are contained in the files that you will download for this module after you complete your registration. Moreover, you can get help when you need it by e-mail or phone from our staff. The Step-By-Step Instructions button below will explain exactly what you need to do to complete this module.

# Required Material

In addition to the general requirements for participating in the Math Teacher Link Course Module Program, this module also has the following requirements:

• Mathematica

To complete this program, you mucst have Mathematica installed on the computer that you will use to complete the coursework. We recommend that new students use Mathematica 10.0, but legacy support can be provided for earlier versions.

More information on Mathematica, including some sample applications, called demos, may be found on the Wolfram webpage at http://wolfram.com . The requirements for running the Mathematica software may also be found on that site.

Students who enroll in a Math Teacher Link course will recieve a UIUC login called a NetID. This login will allow access to the University of Illinois Webstore where Mathematica may be purchased at a substantial discount.

• Courseware

Each of our Mathematica-based courses has a series of files that make up the course's electronic textbook.

Students using Mathematica Versions 8 and 10 may download the files for this course, from our Step by Step Instructions page. Students using older versions of Mathematica should contact us via the Contact link about legacy courseware.

# Step By Step

Registration information may be found by clicking on the Register button above.

For Mathematica beginners, it is likely that it will require about 90 hours to complete the module. The time required for the classroom project will depend on the size and complexity of the project you select. However, you should expect to spend at least 15 hours on your final project.  After you have completed and submitted your on-line registration forms, you will be able to download the appropriate module files folder for your operating system (PC or Macintosh) and your copy of Mathematica has been installed, you are ready to begin.

Download all of the files associated with the module at one time by clicking on the appropriate link below. Please note that there are separate versions for Mathematica 8 and Mathematica 10.

AttachmentSize
All Lessons for Mathematica version 8.zip199.57 KB
All Lessons for Mathematica version 10.zip188.74 KB

# Step #1 - Review the notebook: A Mathematica Test Ride

In the zipped file you downloaded is a file called Mathematica Test Ride.  In fact, because you are basically a spectator on this Test Ride, it is a good idea to review it twice with a careful eye to the structure of the commands you are running. (You must have the Mathematica software installed to work with these files.)

# Step #2 - Work through the two minicourses

In these and all remaining minicourses, you are no longer a spectator! Instead, you are asked to do some problems to test and practice your new knowledge. These problems are located in the "Just Do It!" sections of these minicourses. As you do the "Just Do It!" problems of these minicourses , Copy your solutions and Paste them into the Assignment 1 Shell file that is in the download folder for this module.

If you are enrolled for graduate or continuing education credit, submit Assignment 1 through the Module Hand-In System using your MTL login and password before you go on to Step 3.

# Step #3 - Work through the Functions and the Picture It! minicourses, in that order.

In the files you downloaded are two files, one called Function.nb and one called Picture_It.nb.  Work through them in that order.  Remember to do the "Just Do It!" problems as you proceed. Copy your solutions and Paste them into the Assignment 3.2 Shell file.

If you are enrolled for graduate or continuing education credit, submit Assignment 3.2 through the Module Hand-In System using your MTL login and password before you go on to Step 4.

# Step #4 - Work through the Lists, Equations, & Programs minicourse.

Remember to do the "Just Do It!" problems as you proceed. Copy your solutions and Paste them into the Assignment 3.3 Shell file.

If you are enrolled for graduate or continuing education credit, submit Assignment 3.3 through the Module Hand-In System using your MTL login and password before you go on to Step 5.

If you are enrolled as an MTL guest or for continuing education credit, you have just completed the module. Congratulations! Those of you enrolled for continuing education credit will be sent feedback on the three assignments that you were required to submit.

If you are enrolled in the module for graduate credit, you now have the opportunity to put your Mathematica programming skills to work by creating a Mathematica -based Final Project that you can use in your teaching work. Proceed to Steps 5, 6, and 7 for help in selecting, completing and submitting your Final Project.

# Step #5 - Review the projects in the Sample Projects Folder

Review the projects attached below this should help you to elect a project of your own. This review is helpful even if you already have definite ideas about a classroom project or projects because you are likely to find some ideas and Mathematica code that you can borrow and modify to enhance your project. Of course, you are welcome to use these projects, or items from them, in your own teaching independently of your project.

AttachmentSize
brlewis.cycloid.nb15.05 KB
BZecher.functions.nb247.65 KB
G1Teusch.limacon.nb21.2 KB
GeometricDiscovery(93).nb198.42 KB
Johnson.interest.nb13.62 KB
McClar.limts_.nb55.86 KB

# Step #6 - Select a project

Select a project (or projects) that would be useful to you in your teaching, and then e-mail a brief description of your Final Project to us before you begin.

The Final Project must first be approved before you may prepare and submit it. The brief description should include the objective of the project in terms of subject matter and the use of Mathematica to nhance the lesson.

Regarding the use of Mathematica, you must implement the coding and presentation skills you have learned in this course. Specifically, your Final Project must include each of the following six operations.

1. Lists
2. Plotting
3. Tables
4. Functions
5. Two (2) other items from below:
• conditional statements
• arrays
• programming
• animation
• iteration
• recursion
• an operation of your choosing approved by MTL

Ultimately, the Final Project is your opportunity to demonstrate your newly acquired knowledge of Mathematica by developing a lesson that spans two to four days, and through the use of Mathematica make the content more understandable and more interesting to the students.

We also urge you to call us to discuss your ideas - we may be able to make some helpful suggestions. Please email your descriptions to classroom@mtl.math.uiuc.edu

# Step #7 - Complete your Final Project.

Submit an electonic copy of your project as a single Mathematica Notebook through the Module Hand In System using your MTL login and password.

That's it folks! We believe that if you complete these steps, you will acquire the tools necessary to use Mathematica actively in your teaching and that you will have the background necessary to learn more about Mathematica as your needs dictate.