Open Source Applications for Math Teachers

In addition to all the technology ramblings I post here every month, I am also a student. This is my final semester in an undergraduate mathematics program with a secondary in education. I believe free open source software (FOSS) is the way of the future and should be used in schools as much as possible. In addition to being free of charge, having code be open promotes learning (as future computer students can see how the internals of a program work).

Part of my final semester was student teaching at a local high school. Technology is very much a part of the classroom in 2011 and I used a number of open source tools to aide in my teaching. The following is a collection of some of the best open source tools around that you can use to enrich your mathematics class.

Geogebra
Task: Interactive Geometry Software
Platforms: Linux, OSX, Windows

I believe Geogebra is easily one of the best pieces of educational mathematics software around. It is easily comparable to Geometer's Sketchpad and performs many of the same functions. One of the largest advantages of Geogebra is that because it is written fully in java it can be run 100% in the webrowser, requiring no installation.


KAlgebra
Task: Function Plotting
Platforms: Linux

KAlgebra is a calculator that has both symbolic and analysis features that lets you plot 2D and 3D functions. In the 2D function plotting tagent lines along a function are also easy to display simply by moving the mouse.


wxMaxima
Task: Computer Algebra System
Platforms: Linux, OSX, Windows

wxMaxima is a Computer Algebra System (CAS) that is a GUI front end to Maxima. It has a wide range of features which I've described in more detail in my post here.


XCAS
Task: Computer Algebra System
Platforms: Linux, OSX, Windows

XCAS describes it's as the "swiss knife of mathematics" - which isn't too far from the truth. It has all the features you would expect from a CAS and then some! One of the most notable features though is that it comes with a "maple syntax" option - so those coming from the closed source Maple will feel right at home using XCAS.

Qalculate!
Task: Multi-Functional Calculator
Platforms: Linux

Qalculate is easily one of the best scientific calculators around. It stores every calculation you make so you can easily go back and find numbers you have crunched in the past. Qalculate also includes a wide range of scientific constants to easily perform calculations with. This is an application no science or mathematics major should be without.


LibreOffice Math
Task: Mathematics Document Creation
Platforms: Linux, OSX, Windows

In addition to providing a full office suite (Word processor, Spreadsheet, Presentation, and data base) LibreOffice also provides a fantastic mathematics writer. Excellent for creating worksheets and exams that look professional, LibreOffice Math is easy to learn and a great tool to have.


Xournal
Task: Digital Notebook
Platforms: Linux, Windows

Xournal + a cheap tablet computer + a projector = a fairly cost effective interactive white board. The main benefit to putting lecture notes down in a digital form is easily saving them for later. As a teacher writing notes on a tablet computer is beneficial due to the fact that you can face the class as you write instead of having your back turned.


Do you have an open source mathematics application you like to use that I did not list here? If so drop a comment below letting me know what it is so I can check it out!

~Jeff Hoogland

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HOWTO: wxMaxima on Nokia N900

I mentioned in a post at the beginning of the year that I was attempting to get my favorite CAS functioning on my N900. I am happy today to say that it is indeed possible to run wxMaxima on your N900! The following is a short HOWTO on getting it running.

First - if you have not already done so, install the rootsh package from your application manager and enable the extra-devel repository.

Next, crack open a terminal and run the following in order:

sudo gainroot
apt-get update
apt-get install easy-deb-chroot

Next open your menu and locate the Deb Img Install icon (if you use categorize it is located under System). Upon launching this it will ask you if you want to install the Debian image to your MyDocs or your SD card - pick which ever you prefer just know that it will take up at least 2gig worth of space. Let the package download and extract, the download size is about 300megs and it takes awhile to extract (seriously, go play a video game or watch TV while it does this).

Once that has finished, open up terminal again and run:

debbie sudo apt-get install wxmaxima

Select Y when it asks you to install the packages and then let apt work it's magic. Once it is finished you can access wxMaxima by running

debbie xbindkeys && debbie wxmaxima

Now due to how the N900 keyboard maps it's keys you will need to go to Edit->Configure and check the box Enter Evaluates Cells. After doing this you should be able to enter an equation and have it be evaluated by pressing shift+enter on your N900 keyboard.


If you would like an icon for wxMaxima in your N900 menu (instead of launching it from terminal) run the following in terminal:

sudo gaintroot
apt-get install leafpad
leafpad /usr/share/applications/hildon/wxmaxima.desktop

The last line will open a blank text file, enter the following as it's contents:

[Desktop Entry] Encoding=UTF-8
Name=wxMaxima
GenericName=wxMaxima
Exec=debbie "xbindkeys; wxmaxima"
Icon=maxima-icon
X-Osso-Type=application/x-executable
X-HildonDesk-ShowInToolbar=true
Terminal=true
Type=Application
StartupNotify=true

Press ctrl+s to save the document and then close out leafpad (note you may need to restart your N900 for this icon to appear).


It's just that simple! Enjoy using your N900 as a pocket computer algebra system :)

~Jeff Hoogland
Note: I do not take credit for coming up with this method, I just reorganized the information in an easier to understand matter. The two articles I pulled information can be found here and here.

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(wx)Maxima - An Open Source CAS

The original use for computers when they where first created was to have them compute numbers. When they first came about computers where contained in large rooms and where only able to make the most basic of calculations, as time has progressed how ever our systems have steadily gotten smaller and more powerful. At this point in time there is very little (given enough time) our computers cannot calculate.

How exactly do we make our computers run such calculations? Our systems are useless without software to run on them - enter the world of CASes or Computer Algebra Systems. A CAS is a type of software that allows the computer to perform calculations such as algebra, calculus, generation of two and three dimensional graphs, as well as more simple computations such as basic addition, subtraction, multiplication, and division.

Maxima is an open source, cross-platform, computer algebra system. On its own Maxima is simply a command line interface (CLI) that gives you access to a whole slew of different commands that allow you to perform just about every type of useful math function you can think of. From Maxima's homepage:

"[Maxima] is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors."

From personal experience as a math student I can say that having a CAS at my disposal both in class and for take home work has been invaluable. Such software allows the user to better focus on the new lesson at hand rather than get caught up in sticky, time consuming applications from long past lessons such as algebra.

The syntax for Maxima commands is extremely easy to pick up, especially if you have any kind of programming experience (in fact for the most the the function syntax largely resembles the python scripting language). Maxima also does a great job of defining functions and variables, so if you have a certain complicated number or complex function you are going to be making multiple calls of you do not have to fully type it out more than once. One of my favorite features of Maxima is how it labels inputs (%i1) and outputs (%o1). For each additional input/output the number value is increased by one. By labeling them all as such it makes it very easy to recall a certain value you obtained earlier on, thusly reducing the amount of typing needed and greatly lowering the chance of human error (such as transposing or leaving out numbers/decimal places).

Now a CLI is fine and dandy if you are intimately familiar with the software, however for the beginning user this is not so useful. One solution to such an issue would be to dive in reading documentation detailing the different functions and their syntaxes, however this can be a cumbersome task and for the average user - especially if you just want to do a few calculations and get on with the rest of your work. A more viable solution is something along the lines of wxMaxima, an open source, cross-platform, GUI (graphic user interface) front end for Maxima.

wxMaxima does a good job of organizing the different functions Maxima provides into different categories such as: Equations, Algebra, Calculus, and Plots. Such organization allows for someone who has never used the software before to quickly find the function they are looking for and provides easy dialog boxes for entering the inputs the function requires to be used properly. wxMaxima also helps teach a user the CLI as they use the program, as each function is called it displays how the syntax should look when the command is run. The last feature I want to mention that wxMaxima provides is saving your work, if you have a set of functions you plan to use on a regular basis you can save the file to be reloaded at a later date. Also present is the option to export your work to either an HTML file or a LaTeX file if you wanted to send it to someone else to view.

All in all I think Maxima is a fantastic piece of software and it is easily on par with commercial CASes such as Maple. If you are a math or science student or someone who works with complex functions and numbers in the field Maxima is definitely worth taking the time to check out.

~Jeff Hoogland

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