I found an interesting series of blog posts from a college math educator about Wolfram|Alpha. Start with the slides (then you'll understand the figures in a later post). Overlook the typos. Here is a blog post to follow up on the slides. It talks about the same things in more detail.
The main point of the slides is that Wolfram|Alpha can be expected to propagate quickly among students. This is in part because it has virtually no learning curve (it is designed to be used like a browser, which our students are...pretty comfortable with, I'd say.) It is also readily available and at no cost to anyone who already has internet access. Finally, it is easy for students to teach one another and share their Wolfram|Alpha experiences--rather than sharing a program, or a screenshot, or being in face-to-fact contact, they can just send a link.
So what are we going to do about it? The slides don't propose much, except that we need to do something and we need to do it soon. If propagation is as quick as this suggests, we need to be ready to respond soon.
Now check out these interesting Wolfram|Alpha search examples. Moral of the story? The less you ask for, the more you get. This was mentioned in the slides, too. This really sets Wolfram|Alpha apart from CAS devices. You don't have to be specific. But think about the implications! You can fool around on Wolfram|Alpha and find out something interesting. Just by following those links, I found heard the word ``pentatoupe'' for the first time, and was able to look it up and see some cool (combinatorics) graphs.
Another thing I'd like to point out: take a look at the limit problem, and click on ``show steps''--those are some beautiful steps! Sure, it means you had better not ask that problem on homework if your homework is worth points, but it also means that Wolfram|Alpha is a good tutor. I am comparing it to MathZone right now, the ridiculous online homework that comes with Smith & Minton; it explained homework problems in a stupid way that made it easy for the students to score 100% on the assignment without actually learning anything (what dy/dan described as being good at decoding a textbook).
Finally, here is a blog post about how to assess students whom you know are using Wolfram|Alpha. Basically, shift your attention from the answer to the process. We already do this! We already want the students to show their work, but the students have been trained to give answers. They don't understand why their correct answer is worthless to us, and we don't understand why they think it is all that matters.
The solution may be to give students the answer--but ask them to prove it. Mind you, I've seen students miss the point of problems like this blogger suggests. For example, I graded an exam question with the instruction ``Find the sum of the following convergent series''. Half the class tried to prove it diverged.
Another problem not addressed here is homework, or exams if Wolfram|Alpha is allowed during the exam. We have seen that Wolfram|Alpha does a pretty good job of showing steps. Out of curiosity, I tried to get an answer to the following suggested exam question:
Prove that f(x) = (5-2x-x^2)/(3x^2 - 4) has a horizontal asymptote at y = -1/3 by evaluating the limit \lim_{x\rightarrow\infty} f(x) algebraically using appropriate limit laws.
My first attempt just told me the answer and didn't offer any intermediate steps. Darn! Maybe Wolfram|Alpha will show me how to take the limit...huh. For some reason it won't---but I know that in general there would be a ``show steps'' option here. Give it a few weeks, maybe?
The main point of the slides is that Wolfram|Alpha can be expected to propagate quickly among students. This is in part because it has virtually no learning curve (it is designed to be used like a browser, which our students are...pretty comfortable with, I'd say.) It is also readily available and at no cost to anyone who already has internet access. Finally, it is easy for students to teach one another and share their Wolfram|Alpha experiences--rather than sharing a program, or a screenshot, or being in face-to-fact contact, they can just send a link.
So what are we going to do about it? The slides don't propose much, except that we need to do something and we need to do it soon. If propagation is as quick as this suggests, we need to be ready to respond soon.
Now check out these interesting Wolfram|Alpha search examples. Moral of the story? The less you ask for, the more you get. This was mentioned in the slides, too. This really sets Wolfram|Alpha apart from CAS devices. You don't have to be specific. But think about the implications! You can fool around on Wolfram|Alpha and find out something interesting. Just by following those links, I found heard the word ``pentatoupe'' for the first time, and was able to look it up and see some cool (combinatorics) graphs.
Another thing I'd like to point out: take a look at the limit problem, and click on ``show steps''--those are some beautiful steps! Sure, it means you had better not ask that problem on homework if your homework is worth points, but it also means that Wolfram|Alpha is a good tutor. I am comparing it to MathZone right now, the ridiculous online homework that comes with Smith & Minton; it explained homework problems in a stupid way that made it easy for the students to score 100% on the assignment without actually learning anything (what dy/dan described as being good at decoding a textbook).
Finally, here is a blog post about how to assess students whom you know are using Wolfram|Alpha. Basically, shift your attention from the answer to the process. We already do this! We already want the students to show their work, but the students have been trained to give answers. They don't understand why their correct answer is worthless to us, and we don't understand why they think it is all that matters.
The solution may be to give students the answer--but ask them to prove it. Mind you, I've seen students miss the point of problems like this blogger suggests. For example, I graded an exam question with the instruction ``Find the sum of the following convergent series''. Half the class tried to prove it diverged.
Another problem not addressed here is homework, or exams if Wolfram|Alpha is allowed during the exam. We have seen that Wolfram|Alpha does a pretty good job of showing steps. Out of curiosity, I tried to get an answer to the following suggested exam question:
Prove that f(x) = (5-2x-x^2)/(3x^2 - 4) has a horizontal asymptote at y = -1/3 by evaluating the limit \lim_{x\rightarrow\infty} f(x) algebraically using appropriate limit laws.
My first attempt just told me the answer and didn't offer any intermediate steps. Darn! Maybe Wolfram|Alpha will show me how to take the limit...huh. For some reason it won't---but I know that in general there would be a ``show steps'' option here. Give it a few weeks, maybe?