Comments on: What if there was a Google for Math?

By: Wolfram Alpha is up and running « Where the Arts Meet the Sciences

Wolfram Alpha is up and running « Where the Arts Meet the Sciences — Wed, 03 Jun 2009 21:26:10 +0000

[...] Here is some discussion about the site. [...]

By: Wolfram Alpha is up and running « MathBlog: Where the Arts Meet the Sciences

Sat, 30 May 2009 18:27:53 +0000

[...] Here is some discussion about the site. [...]

By: Maria H. Andersen

Maria H. Andersen — Mon, 18 May 2009 23:57:30 +0000

@Alison Not only the students. None of us teach in a vacuum. Personally, I would consider making some major changes to my courses to live in the new WA-world, but … those students then go on to some other instructor, or possibly some other school after me. If they have not adjusted too, then have I done my students a service or a disservice by changing?

There’s an interesting study that was done regarding the effect on students when they had to switch from a traditional precalc to a reform calc, or a reform precalc to a traditional calc. I am going to go dig that study up.

By: Wolfram Alpha: Concept is King! | Mr. Hamada's Universe

Wolfram Alpha: Concept is King! | Mr. Hamada's Universe — Mon, 18 May 2009 16:35:30 +0000

[...] can understand Maria’s point when she says: It does have the potential to seriously wreak havoc on the way we teach math [...]

By: Paul

Paul — Sun, 17 May 2009 18:17:05 +0000

I am glad WolframAlpha is here. I hope this will change the math instruction drastically. Here are two similar assignments.
1. Find the derivative of x^2.
Accepted answer: 2x
Students type in WA and they are done.
No learning or understanding needed.

2. Prove that the derivative of x^2 is 2x.
Accepted answer:
y = x^2 , Increase y by a small bit of y and x by a small bit of x, therefore
y + dy = (x + dx)^2, so
y + dy = x^2 + 2xdx + dx^2 … but we can discard dx^2 because it is a negligible quantity in comparison with the other terms ( a small bit of a small bit of x)
so… y + dy = x^2 + 2xdx … but y = x^2 so we can substitute and eliminate…
y + dy = y +2xdx
dy = 2xdx … dy/dx= 2x QED.
It will take some time before WolframAlpha will do exactly this. At that moment we’re in for another paradigm shift. A.I. at it’s best.
Another example:
1.Calculate (-2)*(-3)
Accepted Answer: 6
2. Why is the product of two negatives a positive?
Accepted answer:
The negative sign indicates direction with respect to the origin. The number indicates magnitude, how far from the origin. Par Example (-2)(-3) = 6 … It tells us that we are operating on the left side of the origin (going West) twice 3 units, so the new position is 6 units away West(left) of the Origin. ( Or bellow sea level)

Another Example:
1.Solve:
x^2 + 4x + 4 = 0
Accepted answer: x = -2
(no problem for WolframAlpha here…nor four your students)

2. Given ax^2 + bx + c = 0, derive the Quadratic Formula
and use it to show that the solution of x^2 + 4x + 4 =0
is x =-2 and explain why is x = -2 a double solution.
Accepted Answer:
…well you know what I mean.

Another Example:
Explain why the Area of a Circle is πR^2, or any of the Areas for that matter. These types of problems are not solvable with WolframAlpha.

So… Maria, you should create a page where we can post types of problems that WolframAlpha would not be able to solve it. This is the Revolution in Math we’ve all been waiting for.

By: Alison

Alison — Sun, 17 May 2009 12:04:25 +0000

I think the question this raises, as will all other newer technologies, is not should there be a change in paradigm but how can it be achieved. I would love to teach my students more creative critical thinking but as all the other educators know many students are not jumping on that bandwagon. So even if we want to change, how do we convince the students to change with us? How can we make the by into the idea that they *must* be smarter then the computer/calculator?

By: Andrew Maynard

Andrew Maynard — Sat, 16 May 2009 20:57:35 +0000

The math side of Wolfram Alpha reminds me a lot of Mathematica – which it should, as it is driven by the symbolic software developed by Stephen Wolfram. I mention this because I have struggled with, sweated over and occasionally got some stunning stuff out of Mathematica for pushing on 15 years now, and if anything have found that it has challenged and stretched my understanding and use of math. It’s about as far from a crutch as you can get!

Of course, there is a danger that some will use Alpha to mindlessly provide answers that they should be working out for themselves. But my sense is that there is tremendous potential here for the symbolic math base to encourage and inspire people to develop a deeper understanding of the subject.

By: Paul Guertin

Paul Guertin — Sat, 16 May 2009 15:21:23 +0000

I certainly plan to talk about Wolfram Alpha to my calculus students next term. I already spend part of the first class wowing them with Maple. I would never think of giving them graded homework consisting of indefinite integrals. I do put a few of those in the exam (usually not all by themselves but as part of a more complex problem), and I give students practice lists (as well as separate hints and answers). It’s up to them to do as many or as few as they think they need.

I have colleagues who still think integral calculus should be mostly a course in how to do indefinite integrals by hand. Lots of textbook authors seem to agree.

I agree that integration techniques are worth teaching. Some indefinite integrals can be nice puzzles to develop problem-solving strategies (fuzzy pattern-matching, splitting into subproblems, backtracking), and working integrals by hand can help students strengthen their algebra skills.

Nevertheless, spending too much time on this has two pernicious effects. It means we have less time to spend on the applications of integral calculus, which is really fun (especially the part about modelizing the real world and seeing where the model and reality diverge), and it gives many students the idea that advanced math (which for them is calculus) is mostly concerned about algebraic manipulations.

By: Walking Randomly » First impressions of Wolfram Alpha.

Walking Randomly » First impressions of Wolfram Alpha. — Sat, 16 May 2009 12:10:17 +0000

[...] Maria is worried about the implications that Wolfram Alpha has for teaching math. It has sparked quite a discussion. [...]

By: Derek

Derek — Sat, 16 May 2009 02:08:37 +0000

Back in World War Two, just before the advent of computers, the term “computer” referred to a human who performed complex mathematical calculations by hand. (The forthcoming documentary “Top Secret Rosies” explores the story of women computers in WW2, http://bit.ly/hS8tn.) Now, a $15 scientific calculator from the drug store can handle a lot of the calculations that once required trained human computers, making the skills once values in human computer obsolete, for the better in general.

What skills will Wolfram|Alpha make obsolete–for the better?