So when doing research, I came across this Java applet that allows for someone to test for primality, pseudoprimes, and carmichael numbers. I think it's pretty helpful, especially since it's all together on one page and can be used to check your work. Also, I was wondering what everyone else thinks about the following: What do you think about technology in respect to mathematics. Obviously, things like calculators are useful for difficult computations, but do you guys think that an applet like this is beneficial, or do you feel some students will fail to learn the material and will use applets like this to find their answers?

It is possible that some students will just use this to find answers, but so long as they need to show their work, they'll still need to learn the material. An applet like this can be used for other purposes (although this particular one has a small limit on the number of digits that n can be). If we are talking about students using this, it is still helpful, because students can calculate primes/pseudoprimes/carmichaels quickly, and perhaps examine the patterns in the numbers instead of just the methods. Of course, it would be smart not to introduce something like this until students have already mastered the methods, and are merely using this as a time saver (or to check their calculations). :)

I also believe technology in the classroom can be very beneficial. I went to a high school where the only thing we learned on a computer was keyboarding and how to write professional letters, but now that I have been in the ED program I totally understand how technology can be beneficial in the classroom. First of all, it allows students to be motivated and excited about the activity and secondly, it engages them to take something out of it. While I was allowed calculators in high school, I can remember my teacher always making us do the homework and tests by hand and then the next day after the test she would show us how to do the work on the calculator. While this was both good and bad because we were able to learn how to do it on the calculator, we didn't have enough time to go into detail about graphs and such. So with respect to technology, I think teachers need to pick and choose which activities they want to use so that the students benefit the most. However, to avoid students completely relying on technology, you can use more of a differentiated instruction type of group activity where students who are more gifted have to figure it the problems using paper and pencil while other students who need more help and visualization techniques can use computer applets.

I agree, technology like this can be very useful for helping students understand concepts. Are there going to be students that learn from using the applet and develop a greater understanding: yes. Are there students that are just going to use the applet to find their answers: yes. This has been a big topic of debate within my education classes. You may find a new way to present a problem, and you are going to think it is great, but you are always going to have students that don't want to take the time to learn the concept and are going to get around having to do all their work. For this reason, I definitely agree with Aviva, that an applet such as this should be revealed well after students are introduced to the topic and have at least a basic understanding of it. Otherwise, you will find the majority of them only using it to get answers and they will not be learning the material as you would have expected.

If you're interested in how technology can be used in education, the University runs a program called Calculus & Mathematica and an associated distance learning program called Netmath. These programs don't use regular textbooks, but instead a bundle of software written for the computer program Mathematica. If you aren't familiar with Mathematica, it is a program designed for doing complex math. It can do may things, like plot functions, compute limits, derivatives, and solve differential equations. So basically, when you sign up for one of these courses you get a tool like that java applet only far more powerful.

One more thing. Obviously, I'm a fan of using technology in the classroom. I'm also a fan of active learning, so here's a link to the wikipedia page on one of my favorite alternative teaching systems- the Moore method.