Wolfram Alpha answers Christmas wishes of world's high school students

In other news, world's high school math teachers declare Wolfram Alpha, "dead to us."

Have you ever given up working on a math problem because you couldn't figure out the next step? Wolfram|Alpha can guide you step by step through the process of solving many mathematical problems, from solving a simple quadratic equation to taking the integral of a complex function.

[For example] When trying to find the roots of 3x2+x-7=4x, Wolfram|Alpha can break down the steps for you if you click the "Show steps" button in the Result pod.

Wolfram Alpha: Step By Step Math

(Thanks, Jamesbont!)


  1. I can understand why math teachers find the advent of a “magical math homework machine” unsettling to the practise of teaching math, but I prefer to look at this as a step toward the sort of virtual-handholding that only technology seems patient enough to accomplish.

    The best example of this, from literature, is the Primer from Neal Stephenson’s The Diamond Age. Stephenson sketches a child’s learning relationship with a benign, ever-present tutor that encourages the student to find the answers for themselves.

    If Wolfram|Alpha can do THAT, it’ll be the start of something amazing.

  2. Yeah. I use this for the grunt work of my general chemistry homework, and to check my integrals for calculus. Wolfram|Alpha is the bee’s knees.

  3. Oh, come on, they obviously mean 3x²+x-7=4x, and the first step is 3x²+x-7-4x=0, or 3x²-3x-7=0.

    Or am I missing something? I last did high school algebra in 1977, so maybe I did.

  4. I’m trying to get it to parse Fermat’s Last Theorem for me, because I want to see WolframAlpha start singing “Daisy, Daisy” and then springs and sparks come shooting out of the USB slots and the computer makes a great big “SPROING” noise.

    However, it keeps solving it, which makes me think that I’m not typing it in right.

    -Darren MacLennan

  5. I’m surprised if any teachers actually objected to this.

    They can get the answers from any calculator program on the web. That already exists. But one that can break it down and actually explain it to the students? No teacher would object to a student using this over something that just gave them the answer.

    I guess the only reason would be that it would be easier to make homework look like it was worked out by hand. But that’s what in-class tests are for.

  6. Oh, I thought the gag was printing “3×2” instead of “3x².” ‘3×2’ is more usually written “6.”

  7. I don’t really see a problem. It helps you learn how to do it. if you use it enough, eventually you’ll get the idea and be able to do it yourself. you won’t have wolfram|alpha to use when you’re taking a test.

    1. You won’t have it with you when you take the test, but you might have a TI-92 Titanium. I always do. It’s a real life-saver when you choke and forget something you’ve had memorized for three years prior.

      Most “fun” $140 of scholarship money I ever spent.

  8. To the 3×2 complainers, what makes Wolfram alpha neat is the fact that it disambiguates the two. Type in 3×2 and you get 6. Type in 3×2 + 6x + 5 and you get a plot, some roots, and an integral. Brilliant if you ask me. Go ahead, ask it ‘how many turkeys in turkey’.

  9. I have two daughters in high school taking advanced calculus. When they ask dad for homework help and I can’t remember my coursework from decades ago, I’m the one who consults Wolfram Alpha. Invaluable.

  10. The problem is that it only helps the learning process if you sit down and analyze _why_ the problem may be solved in the way the computer tells you. My experience teaching and working in math help rooms tells me that this is rarely what people do.

    In the end though, graders will be able to detect it pretty easily when they notice that answers from Wolfram Alpha’s do things like use L’Hospital’s rule unnecessarily and long before you cover it. A friend of mine was teaching Fourier analysis has a similar phenomenon with a student who was obviously having a grad student do his homework. Or something stupider, like correctly solve an equation which has been entered with incorrect syntax. i.e. typing x^(2 + 2x +1)=0 instead of x^(2) + 2x +1=0

  11. I used a web-based Mathematica-based program to explain some calculus problems to me last year, when I couldn’t quite figure out some hard problemsn, and it helped me immensely to understand them. It indeed was like having a tutor available. I kept going at those problems until I understood them properly, and I subsequently aced (9/10) the (far too easy, btw) test.

    OTOH, if you use this to make it look like you did your homework, it is a recipe for fail, and it’ll be completely your own fault you failed the test.

  12. Only person who loses when you cheat at homework is yourself. Nobody cares.

    Cheating on the test… well, good luck getting internet access there.

    They don’t do graded coursework on problems like this.

    As for the technology itself, well, it’s nothing new. I was playing with this sort of thing back when I was a student. It’s the first time I’ve seen somebody stick a web interface on it, but that’s about all.

  13. When I went to high school the nightly math homework wasn’t even graded. Quizes and tests were the only thing that mattered.

    We were given a bunch of work to do and if we wanted the teacher to go through it with the class the next day he would.

    Don’t do the homework, don’t get the practice, don’t learn how to solve the problems and you wont pass the quizes or tests.

  14. Math teachers worried about kids mindlessly plugging in their homework, thereby getting around the heretofore insurmountable “show your work or no credit!” rule, are sadly overestimating kids who plagiarize. (Or just “cheat”, as I suppose you’d call it with numbers.)

    Take it from a humanities professor. These so-called “digital natives” who turn in papers where the font suddenly changes formatting and every other sentence ends in a blue [citation needed] are not magically going to become super-savvy with copying math symbols that they understand even less than they do words. I could use half the electrons in the whole internet just to tell the best 10% of my PLAGIARISM FAIL! stories, and everyone else in my job has just as many.

    They’ll mistranscribe half of it and still come up with the right answer. Or they’ll type in the question wrong and end up miraculously solving a partial differential equation instead of 2x + 2 = 8. I mean, I don’t know exactly what will go wrong, but then again I never thought a student would swear up and down, to my face, that he had personally written an especially brilliant paragraph that he’d copied off the internet… from my own university web page. (It even had my picture on it!)

    So yeah, I don’t think there’s much cause for alarm.

  15. I am a high-school maths teacher. This kind of functionality has been available for some time, and it hasn’t really been much of a problem so far.
    The really interesting thing about this technology is how we, as a profession, are going to deal with this kind of calculating ubiquity. So far, we’ve (obviously I’m excluding a lot of work done by a lot of forward thinking people) ignored its existance, collectively putting our thumbs in our ears and humming the ‘we can’t hear you’ song. The problem that we face is that, in the face of portable devices that basically do everything that we are attempting to teach our students to do, we need to shift our focus for learning 180 degrees. Maths teachers talk a good game when it comes to saying that we teach for understanding and problem solving, but in fact we’re all smart enough to know that the kids (and, by extension, ourselves) are only judged by the results they take home in narrow, content-based testing. These technologies will change that, but don’t imagine that it will happen any time soon, or without significant resistance from the stakeholders in education (I’m thinking about ‘old-school’ teachers, politicians out to make some quick political capital by stressing the ‘educational values’ of the past, and, most importantly, from parents, who seem to think that if they had to go through the misery of learning 50+ formulas and methods, then so should their offspring).

  16. I would say that the problem with this would be that it doesn’t represent the learning math as a process. It is possible a student could look at how it was solved and reflect on that process and learn something. But, this is far from an automatic teaching tool (which I don’t think there really is such thing).

    Learning by being given the next step bases too much on the final solution and not on the process. Unfortunately, you can’t compare this with or justify it by the traditional classroom because traditional classrooms also base too much on the final performance or memorizing an equation than it does the understanding of core concepts and transferring those concepts to other areas or other problems.

    It is a matter of Behaviorist learning theory and Constructivist learning theory. Traditional classrooms are based on behaviorism (eg. B.F. Skinner) and couldn’t give a crap about the student’s process, as long as they can repeat back the proper answer. Constructivists (eg. Dewey, Piaget, Bruner, Vygotsky, Noam Chomsky) believe that a student goes through a process including reflecting in order to construct the knowledge. It is more likely that they will be able to apply that knowledge in other areas of life, beyond the test.

  17. I used to help my sister with her calculus homework for 4 hours a week, now there’s Wolfram Alpha.

    But seriously, in this specific case it’s great, because she’s a smart girl and she just uses it as a homework checker to make sure she got the right answer, and see where she went wrong if she did. For me it’s great because I only need it when I’m doing my own projects and I screw a calculation up.

    However, once the middle and high schoolers who don’t care about math just want to get their algebra I homework done find out about this…

  18. What a weird way to solve a quadratic equation. I’d simply calculate the discriminant and then roots.

    1. agree. galois noticed a while back, it’s all related to the structure of the group of automorphisms of a field extension, sadly the symmetric group on more than 4 things contains some nasty subgroups, so shopping postponed due to math hardness in the general case. ruffini is a cool name tho.

  19. Wolfram has been selling a Mathematica add-on (Calculus Wiz) for over 10 years with this functionality and more. I am delighted that it can now be done from free on wolframalpha, so that it is available to all students. (I only hope that the CalcWiz developer is making some money out of it.) Since it first appeared I have shown my Calculus students wolframalpha and encouraged them to use it to check their answers or do the grunt work on difficult non-mechanical problems. I don’t see it as a classroom threat in any way.

  20. This has provided much amusement and astonishment in the office. Some questions that were answered included:

    How many angels can dance on the head of a pin?

    What is the sound of one hand clapping? Although I disagree with the answer and prefer Bart Simpson’s explanation better…

    If a tree falls in the woods and no one is around, does it make a sound?

    How many licks does it take to get to the center of a tootsie roll pop?

    Knock, knock.

    What is the nearest start? Cubicle mate brain farted when he did that one – it’s the sun of course. He should have asked for the second closest star…

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