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Open Source Math Software For Education?
Rui Carmo writes "Now here's something you don't get asked every day, but which a friend happens to need for her kids: If you had to suggest Open-Source software for mathematics - somewhere from high-school to freshman level, and not merely for 'pure' mathematics, but also applicable to physics and statistics (the kids are considering going into Applied Maths and Engineering), what would you point people toward, assuming they have access to both Linux and Windows? I know this is a niche thing and that there is nothing out there that even comes close to Wolfram's excellent Mathematica (which I used on my old NeXTCube), but surely something along the lines of (or simpler than) Calculation Center exists?" The Knoppix-based Quantian might be a good place to start; what math software do you recommend?
The whole technology upgrade the schools have been getting doesn't seem to be making learning more efficient. It seems like a big waste of money.
If a kid doesn't spend time studying his books, why would he start studying his software?
What are these "kids" trying to learn?
They can explore lots of stuff just with gnuplot.
bc is also pretty good - simple to learn and use.
Who needs all the flashy stuff?
Stephan
http://stephan.sugarmotor.org
There were no computers in my middle/high school math classes and I learned math just fine. What is your friend trying to do that couldn't be done better with pen and paper and old fashioned teaching? Computers aren't a panacea.
Give me Classic Slashdot or give me death!
I wouldn't recommend software at all. I would recommend something we call "pencil and paper." Learning mathematics (and reading music, and a number of other such undertakings) is as much a mechanical skill as an intellectual one and the quickest way to the brain is through the fingers.
Come back when they're in college and ask again.
KFG
I know this is a bit off-topic, but it can't be overemphasized:
If possible, students should learn the principles behind the math before they are allowed to use fancy tools like calculators and computers.
My high school teacher made us learn logarithms and trigonometry using a pencil, graph paper, and tables, THEN we got to use a calculator. As for calculus, we did all our graphs by hand, sub-$200 graphing calculators weren't available back then.
I hope you get some good answers in this thread.
Knowledge is how to play a game, intelligence is how to win, wisdom is knowing what game to play.
There are any number of ways to learn math; most of them involve exploring the relationships between numbers and the physical world. This means teaching someone how to think about things. Math software does not teach anyone how to think; it is a tool for accomplishing a goal. First the student learns arithmetic, then algebra, geometry, trig, calculus, and so on. Once the concepts are understood, the foundation is sound, and the student *knows* math, then, and only then, does math software become useful. It becomes a shortcut, a means to an end. It is a tool used to solve a problem. You have to know how to use the tool to get to the answer. You can train someone to input numbers into some piece of software and watch other numbers get spit out, but that person won't *understand* what they are doing. If the person already understands the math, and is looking for a tool to accomplish some problem solving, then the programs mentioned in this topic become useful. As far as using software to learn math, I don't think any piece of software, open source or otherwise, can currently take the place of a good math teacher. And by that I don't mean someone who drills you in math problems, but someone who can help you discover for yourself the power and elegance of mathematics.
Just wondering
I have mod points and I am not afraid to use them
Educational versoin is around $150/yr which includes the symbolic toolbox. That, I must say, is a darn good deal for MATLAB, considering it does a whole helluva lot. Everything that a high schooler would ever need to do, and a lot more. If you want math software, shell out the $150 (less than the cost of a textbook) and get Matlab, it's the best math software possible
That being said, the best software for math is no software at all. Paper and pencil, that's it. Over at my college, all engineers are required to go through four semesters of math (2 calc, diff eq. and linear algebra), and no calculators or tech tools are allowed for either course. And yes, we did need to plot slope fields, draw 3d representations of functions, etc... It's more important to know the concept of doing a problem than crunching numbers. The only time I use MATLAB is when I'm working on my design project-- I do the design, I setup the equations, MATLAB crunches the numbers for me.
Remember, number crunching != real math. Theory is the most important thing to learn.
I will grant: Pencil and Paper are great if you're working on learning math skills. Even then, however, there are times you're going to want something to do the arithmetic and/or graphing and/or solve the integral for you. If I've know how to add already, I don't want paper and pencil, I want an open source calculator so I don't have to. If I know how to do Integration by Parts already, I don't need to do it every time...of course, studying math won't mean you have to do Integration by Parts all the time (unless you're in DiffEQ or something), which brings me to my "But":
But: Paper and Pencil aren't gonna cut it as far as taking an engineering course is concerned. Nor as far as a physics course is concerned. If I'm trying to "learn the concepts" of a non-calculus class, then having to do all these pesky integrals isn't going to help any! It's just taking up my time. Even better, there are going to be cases where you can't do the work without some hefty numerical computations that would take you faaar too long to do by hand. Sure, you should do the first one on paper, but do you want to do every calculation of magnetic field by hand? Want to do this line integral for the 7th time? Not yet bored of 2 page solutions? Really want to follow Newton's method by hand?
Furthermore: The age when everything could be done on paper and pencil is now part of the "good old days(TM)", and such technology is no longer the only mainstay.
Finally: I was in a graduate program for mathematics, and yes, even doing "pure" mathematics, we used software. The programs that pop immediately to mind were Maple (cheaper than mathematica) and McCauley (it's algebra. I don't know much else). I also wrote a C program to handle card shuffling, so we could look at various results - sure, you could do it by hand, but it'd take a *lot* longer. In one course, I even wrote Public Key Encryptioni/Decryption software in Maple - an easy way to get a hands-on feel for the concepts, and you don't even have to handle arbitary-length modular multiplication by hand...
Don't get me wrong, Paper and Pencils are great, but so are math packages!
--LWM
Full disclosure: I work for Wolfram Research. But oh -- the irony! I am also a columnist for Math Games at maa.org, and I wrote an article about the Quantian Distribution. I didn't want a spammer to start using quantian.org just as the distro was getting popular, so I bought it, and provided a redirect to the main Quantian site. So now, I'm getting doubly Slashdotted. Huzzah. A student should definitely be getting Mathematica for Students -- but check with the college first. They might be on a Mathematica Campus, and can get it for free.
How do you know you're better off for it? Maybe, if calculators had been allowed, you'd've been able to get to deeper concepts faster. Maybe you'd have been able to play with function and form and plots, and discovered chaos.
'Course, maybe not. But it seems to me that a blanket statement like yours is essentially unsupportable, and generally counterproductive. There's room for pen-and-paper, or even just brain work, but IMHO, there's room for integrators and plotters.
Put another way: When I took math in grade school, I had a teacher who also didn't believe in "high tech" -- like the pencil. We did everything in ink. Her theory was, if it was in ink, you couldn't correct a mistake -- so you wouldn't make any. It was an insane educational theory, of course, and bore no relation to what actually occured.
The Mongrel Dogs Who Teach
The next question is whether or not a symbolic math package is useful at highscool/freshman level. Maple and Mathematica can look really flashy when you see them for the first time, but after half an hour you end up asking a question that can only be solved if you spend a lot of time looking through the manual, trying to understand all the list operations.(I don't know if Maxima is advanced enough to create this kind of problems) When using Matlab or Octave it is easier to guess what is possible and what is not. This way the students have a better chance of trying to do something on their own hand.So even if Octave cannot integrate it may still be the better education tool in a highscool computer lab. If I understand correctly the the poster just wishes to give his students a glimpse of what computers can do in mathematics. Therefore I would advice him to use Octave. By the way you can also find a great deal of very specialized java applet on the web. Perhaps they are more accessible to the students than Octave.