We Should Wish PhotoMath All The Success In The World

PhotoMath is an app that wants to do your students’ math homework for them. Its demo video was tweeted at me a dozen times yesterday and it is a trending search in the United States App Store.

In theory, you hold your cameraphone up to the math problem you want to solve. It detects the problem, solves it, and shows you the steps, so you can write them down for your math teacher who insists you always need to show your steps.

We should be so lucky. The initial reviews seem to comprise loads of people who are thrilled the app exists (“I really wish I had something like this when I was in school.”) while those who seem to have actually downloaded the app are underwhelmed. (“Didn’t work with anything I fed it.”) A glowing Yahoo Tech review includes as evidence of PhotoMath’s awesomeness this example of PhotoMath choking dramatically on a simple problem.

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But we should wish PhotoMath abundant success – perfect character recognition and downloads on every student’s smartphone. Because the only problems PhotoMath could conceivably solve are the ones that are boring and over-represented in our math textbooks.

It’s conceivable PhotoMath could be great for problems with verbs like “compute,” “solve,” and “evaluate.” In some alternate universe where technology didn’t disappoint and PhotoMath worked perfectly, all the most fun verbs would then be left behind: “justify,” “argue,” “model,” “generalize,” “estimate,” “construct,” etc. In that alternate universe, we could quickly evaluate the value of our assignments:

“Could PhotoMath solve this? Then why are we wasting our time?”

2014 Oct 22. Glenn Waddell seizes this moment to write an open letter to his math department.

2014 Oct 22. David Petro posts a couple of pretty disastrous screenshots of PhotoMath in action.

2014 Oct 23. John Scammell puts PhotoMath to work on tests throughout grade 7-12. More disaster.

2014 Oct 24. New York Daily News interviewed me about PhotoMath.

2014 Oct 27. Jim Pai asked some teachers and students to download and use PhotoMath. Then he surveyed their thoughts.

Featured Comment

Kathy Henderson gets the app to recognize a problem but its solution is mystifying:

I find this one of the most convoluted methods to solve this problem! I may show my seventh graders some screen shots from the app tomorrow and ask them what they think of this solution – a teachable moment from a poorly written app!

M Ruppel:

I we are structuring this the right way, kids (a) won’t use the app when developing the concept, (b) have a degree of comfort with doing it themselves after developing the concept and (c) take the app out when they end up with something crazy like -16t2+400t+987=0, and factoring/solving by hand would take forever.

Sander Claassen:

The point in this case isn’t how well the character recognition is. Or how correct the solutions are. Because it’s just a matter of time before apps like these solve handwritten algebra problems perfectly in seconds, providing a clear description of all steps taken.

The point is: who provides the equation to be solved by the app? I have never seen an algebraic equation that presented itself miraculously to me in daily life.

Kenneth Tilton:

ps. Photomath is just a “stupid pet trick” they did to market their recognition engine.

About 
I'm Dan and this is my blog. I'm a former high school teacher, former graduate student, and current head of teaching at Desmos. More here.

43 Comments

  1. David Cox

    October 22, 2014 - 4:35 am

    Could PhotoMath solve this? Then why are we wasting our time?

    It’d require students to do a little typing instead of taking a photo, but sub “WolframAlpha” for “PhotoMath” and we’re already there.

  2. Michael Pershan

    October 22, 2014 - 5:03 am

    “Could PhotoMath solve this? Then why are we wasting our time?”

    In the future, I’ll give the same shpiel for algebra that I currently offer for arithmetic in the early grades. Technology replaces paper/pencil calculations but never mental calculations. Any calculator can handle 8 + 6, but if a kid can’t do that in his head he’s going to have a hard time noticing patterns, justifying, explaining and doing all that other good stuff.

    Ditto with solving equations. In the future I’ll do a lot of mental equation solving, worry much less about written algorithms for solving equations.

    That’s why I think we need a slightly different line than “If technology can do it then why should we bother with it?” Maybe the slogan should be “Technology can never replace thinking.”

  3. Prof. Wright

    October 22, 2014 - 5:17 am

    “Could a digital camera take a perfect photo of a bowl of fruit? Then why are we wasting our time learning to paint it by hand?”

  4. Matt E

    October 22, 2014 - 5:25 am

    Ditto Prof. Wright.

    Is our primary goal as doers of math to “get answers” as efficiently as possible? If so, then go, PhotoMath, go.

  5. Dan Meyer

    October 22, 2014 - 6:57 am

    Prof. Wright’s counterexample makes little sense to me. The photo and the painting are categorically different.

    Matt E:

    Is our primary goal as doers of math to “get answers” as efficiently as possible? If so, then go, PhotoMath, go.

    It’s precisely because that isn’t my goal that I wish PhotoMath success.

  6. Dan Meyer

    October 22, 2014 - 6:58 am

    Still stewing on Pershan’s comment.

  7. Matt E

    October 22, 2014 - 7:42 am

    An example from Geometry. Suppose I give my students the following task:

    Draw a triangle with sides of length 3 inches, 4 inches, and 8 inches.

    One day, PhotoMath will be able to tell them, “ERROR: NOT POSSIBLE.” Which they will dutifully copy in their notebooks.

    Yes, I could ask them to “Explain.” (And probably get some “PhotoMath told me so”s.) But the discovery that it is impossible has been stolen from them.

    Am I making any more sense?

  8. Dan Meyer

    October 22, 2014 - 7:51 am

    @Matt E, and then our curriculum adapts to the technology, and we start asking questions like, “What combinations of side lengths are impossible to turn into a triangle?” This adaptation, which has been spurred on by technology throughout history, is a healthy development.

  9. Kyle Pearce

    October 22, 2014 - 8:33 am

    I think tools like Wolfram Alpha and PhotoMath (if it actually “works”) are great to help inspire those questions with “fun verbs” Dan mentioned in the original post.

    Most teachers have expressed a concern with tools like Wolfram Alpha because “I’ll never know whether they did their homework or whether Wolfram Alpha did it.” However, if we are working towards authentic tasks that extend beyond the computation and make student learning visible through those “fun verbs,” these tools can only help scaffold students to WANT to develop the deep understanding we dream that all students will have when they leave our classrooms.

  10. howardat58

    October 22, 2014 - 8:52 am

    Shame about the example. Once upon a time x was written in a curly font and multiply was x. Now we have x for ex (how else can I write it?) and a big fat dot for multiply, which the kids will copy as a normal dot, and then interpret as a decimal point, or vice versa. This will keep the machines at bay for a bit longer. Yes, Dan, I’m all for it, but they’ve got some work to do yet.

    New style homework question: Do this problem with Photomath and explain exactly how it arrived at a garbage solution.

  11. Mike Bosma

    October 22, 2014 - 9:25 am

    Dan,
    Good point about how technology should push us as teachers to ask questions that technology can’t answer (more conceptual vs procedural). In precalculus, we are finding roots of polynomials. There are lots of good theorems (Rational Root Theorem, Descartes Rule of Signs, etc) that were much more helpful before the invention of graphing calculators. These theorems tend not to make sense to my students because they can just graph the polynomial. When graphing was slower (by hand), these theorems made problem solving quicker.

    Also, I tried out the app myself and found it didn’t work very well. It had a hard time reading the equation correctly out of my textbook and had trouble solving quadratics and systems. Unless it becomes more user friendly, it will take more time for students to use than for students to actually solve the problem. Wolfram Alpha is much more reliable. Sites like Hotmath have also been around for awhile which also work the problems out step by step. This is one of the reasons why I don’t count homework as a significant portion of a student’s grade in my courses.

  12. Kathy Henderson

    October 22, 2014 - 10:16 am

    Dan,
    Just tried the app with basic, one-step problems I’ve been giving my seventh graders. Wish I could post the screenshots to show the app.

    -16=d+21

    It gave the correct answer, but when asked to show the steps, it showed:

    -d=21+16
    -d=37
    d=-37

    I find this one of the most convoluted methods to solve this problem! I may show my seventh graders some screen shots from the app tomorrow and ask them what they think of this solution – a teachable moment from a poorly written app!

  13. Yolanda

    October 22, 2014 - 1:22 pm

    I like your thinking, Dan.

    This reminds me of some controversial issues involving algorithms that search for plagarism of student work (i.e. whether or not they just googled their paper). Someone pointed out that if we wanted students to stop googling their papers, maybe we should stop giving them the same papers to write.

    I’ve kind of become of the opinion that if you can solve the problem with a simple search, it’s probably not one worth asking. Or, if you can quickly look it up, it’s probably not something worth memorizing.

    I think it’s time that we start asking deeper questions that only people, not machines, can answer.

  14. Erik Von Burg

    October 22, 2014 - 2:01 pm

    @Yolanda. I agree completely. Once we start examining questions, we are taking the right steps. Questions worth answering are generally not answered quickly…or with little effort.

  15. Jeffrey Gordon

    October 22, 2014 - 3:01 pm

    I must say. The typesetting on that math book in the photo is unacceptable. Variables are italicized in printed text.

    The computer parsed it as a multiplication sign, due to human error – the editor’s not following basic math style guidelines.

  16. David Petro

    October 22, 2014 - 4:31 pm

    Three things
    1) They ripped this app idea off of The Big Bang Theory :-) http://bigbangtheory.wikia.com/wiki/The_Lenwoloppali_Differential_Equation_Scanner
    2) I tried it out with some easy and tougher equations/expressions. There are some issues with the text recognition. But this one was odd. It was a question that had exponents and fractions over fractions. It correctly interpreted the text and started to simplify it correctly but then it dropped a set of brackets as seen in these two steps (https://drive.google.com/open?id=0B0-WU3yuHa7GQWpjeVhZUk01YWs&authuser=0) but interpreted it correctly for the exponent but incorrectly for the 2 out front as seen in these two steps (https://drive.google.com/open?id=0B0-WU3yuHa7GUURlWnhqZjFnQ2c&authuser=0). So this has potential but still needs some work.
    3) Even though it is not perfect I do think it’s shots fired. There are some teachers who see things like this as an apparatus to replace teachers. My statement to them is that if you think this kind of thing can replace you then perhaps you should be replaced. Harsh but I think true.

  17. howardat58

    October 22, 2014 - 5:07 pm

    to David Petro
    There’s no like button so here’s a “LIKE”, especially the last “My statement…”.

  18. jkern

    October 23, 2014 - 5:28 am

    In this rave article, the same problem shows up in their example image. It doesn’t solve for ‘x’, just uses it as a multiplication symbol: http://techcrunch.com/2014/10/23/disrupt-london-finalist-photomath-rockets-to-the-top-of-the-app-store/?utm_campaign=sfgplus&%3Fncid=sfgplus

    But if I’m doing something like a physics acceleration problem, after I already understand the underlying concepts, I might use this app to save myself the time of typing a long equation with exponents and parentheticals into a calculator.

  19. Greg

    October 23, 2014 - 6:00 am

    Tried it… OK so it can solve pretty basic linear equations. The steps it gives are monumentally awful. The only use, as others have said, would be to get students to show where a step could be done better.
    Quadratic equations, say x^2 + 2x – 4 = 0 it gave as an answer x^2 +2x = 4. Congratulations. Seems a very narrow (tiny even) range of problems can be solved. For a few seconds more typing, Wolfram Alpha will get anything done.
    A question that asks a student to form an equation is a problem worth doing, then bring on your Photomath/Wolfram Alpha. I agree that if you think this replacing teaching, I don’t want to be in your class.

  20. Michael Paul Goldenberg

    October 23, 2014 - 6:07 am

    No doubt that the reality right now is underwhelming. Shouldn’t be that hard to combine better recognition tech with powerful CAS to provide what the Vimeo hype suggests is already here.

    That said, we’ve seen this time and time again. I was at an NCTM regional in Cleveland in 1997 at which Bert Waits gave a talk about “What Will You Change in Your Algebra Curriculum in the Face of THIS?” “This” was the about to be released TI-89, which he had in his shirt pocket.

    I was still in graduate school at U of Michigan, had not yet taught high school mathematics (not counting teaching everything from remedial basic math through precalculus at a community college in NYC for two years), but I could already see the tremendous positive potential for improving how we spent time in classrooms (“we” being both teachers and students). Oddly, the rest of the audience, which I suspect comprised mostly actual h.s. math teachers, seemed less than thrilled.

    Waits told a great anecdote in which he was teaching trigonometric interpolation to a class of Ohio State students back in the late ’60s/early ’70s, when a student in the back raised his hand and said, “Waits, you’re an idiot” (I asked Bert to confirm that when I last saw him in Philadelphia in 2004, which he did). The student had a scientific calculator and was doing in seconds what would take considerably longer with the method Waits was teaching the class.

    And of course, we no longer teach trigonometric interpolation. We no longer have fat tables of trig values, square roots, or logarithms in the back of our textbooks because they aren’t needed (sadly, what those pages have been replaced with is often not worth the paper its printed on, but that’s another conversation. Suffice it to say that I first heard about this PhotoMath ap when Kirby Urner posted about it under the subject line “textbook-obsoleting technology”).

    There are, I’m afraid, a lot of K-12 math teachers, as well as many teaching lower-level mathematics in post-secondary institutions, who like teaching all the dull, mindless arithmetic and algebra that they and their predecessors have taught for. . . ever. And technology annoys and frightens the bejeezus out of them. The reaction to Kirby’s post on the math-teach list serve is enlightening, even though it doesn’t have many actual teachers on it The sentiments expressed there are I suspect, quite typical of the current view of educational technology in some quarters.

    For my money, Dan is right, just as Bert Waits was right, just as Kirby Urner is right. Sure, kids need to have number sense and a strong grasp of arithmetic and algebra, but likely do not need to be bogged down for 13 years, more or less, practicing it at the expense of anything and everything else they could be doing in math classrooms. Today’s “absolute requirements” will mostly go the way of trigonometric interpolation and all those tables in the back of the book. And that’s a good thing.

  21. Dan Meyer

    October 23, 2014 - 7:33 am

    @jkern, I’m missing the error in that article. And I love errors in articles. Help me out.

  22. Sander Claassen

    October 23, 2014 - 11:58 am

    The point in this case isn’t how well the character recognition is. Or how correct the solutions are. Because it’s just a matter of time before apps like these solve handwritten algebra problems perfectly in seconds, providing a clear description of all steps taken.

    The point is: who provides the equation to be solved by the app? I have never seen an algebraic equation that presented itself miraculously to me in daily life. In a real world problem I have to make a translation from the situation at hand to something mathematical. I suppose the 20/80 rule applies here too: 80% of the work to be done in solving a real world problem lies in asking the right questions, making some sort of mathematical model and (after doing some “magimatics” in between) interpreting the outcome: is the solution plausible, what does it mean?

    The 20% of algebra halfway is something apps like this one could do perfectly well. As long as we give the right input to the app, and as long as we can verify the correctness of the app’s output, I think everybody would be happy to leave the boring stuff of calculations to a computer.

    So, although there remains an important task to teach children the rules of algebra (to understand what’s going on in the app’s black box), more important is to teach kids the other 80% of the job. Because that’s something I don’t believe computers will be able to do for us for a long long time.

    And knowing whether your input to the computer actually corresponds with the problem to be solved, and deciding whether the output is correct is something very complicated. Anyone who has ever programmed knows that most of the time in writing a computer program is spent in finetuning the model. Because even seemingly simple tasks often turn out to be quite complicated when they have to be presented in code for a computer. That’s why learning to program is so valuable. Maybe even more important than learning the rules of algebra.

    So, summarizing, let’s spend more time in math education on modeling and interpreting the plausibility of outcomes. And teach kids to program.

  23. Jenna

    October 23, 2014 - 12:32 pm

    Sounds like a good app to use for error analysis.

  24. Adam Poetzel

    October 23, 2014 - 1:33 pm

    I think PhotoMath and Wolfram Alpha are useful tools to have us reflect on our classroom assessments. Take a look at the last math assessment you gave: What percent of the questions could be solved immediately by these tools? What percent of the assessment is evaluating computational skills vs. conceptual skills and applications?

    That question leads to a more important question: What percent of questions on our assessments should be able to be solved by tools like these?

  25. M Ruppel

    October 23, 2014 - 1:46 pm

    I’ve been stewing a bunch over MPershan’s comment too – I think there is value in both the elementary settting (arithmetic) and the middle/secondary (algebra) in doing things that the technology can do a little faster, a little more accurately.

    Take factoring: Although a computer can more quickly find two binomials that give me a product of x^2+9x+14, noticing those little patterns and connections and developing your own little algorithm is creative, rigorous work. What’s not rigorous work is the teacher saying “Find two numbers that add to 9 and multiply to 14” and then having students try 10 on their own without understanding. The point isn’t to be able to factor, it’s to find a method to factor, and understand what we mean by “factors”

    The fact that a computer can do it better doesn’t mean we shouldn’t “teach” it – I think it just means that some of the fluency was less critical than it used to be. We should focus on getting kids to do the creative, investigative, work, and “fake-world” math is a nice conduit for it.

  26. M Ruppel

    October 23, 2014 - 1:49 pm

    What I should note is that, if we are structuring this the right way, kids (a) won’t use the app when developing the concept, (b) have a degree of comfort with doing it themselves after developing the concept and (c) take the app out when they end up with something crazy like -16t^2+400t+987=0, and factoring/solving by hand would take forever…

  27. Dan Meyer

    October 23, 2014 - 2:45 pm

    Extraordinarily helpful comments from M Ruppel and Sander. I’ve added them to the main post.

    I also like the idea Jenna expresses (which has popped up on Twitter for time to time) that the app basically gives us some interesting errors for lots of different problems. Those errors will, of course, be largely computational or related to optical character recognition, rather than conceptual. But I like the idea. I’m not sure PhotoMath would love it for their marketing materials, though.

  28. J Pai

    October 24, 2014 - 5:30 am

    When I saw it, I had always been thinking about this development as a good thing. It’s not to say that I don’t understand where all the angst and worry is coming from, but I think about it differently.

    “sub “WolframAlpha” for “PhotoMath” and we’re already there.”

    The first comment by David Cox was on the money. I don’t think calculators should be hidden from students during tests, the same way I don’t think we need to confiscate phones. Of course, I just gave a poor comparison of two items, but what I mean is that: if tests are what we are worried about, then:
    1) we should be designing tests differently anyway, and include problems that have a wider range of opportunities instead of just calculations.
    2) both teachers and students should be thinking about tests differently — as opportunities to demonstrate what they understand
    3) Maybe tests aren’t, and has never been, the best venue for demonstrating certain aspects of understanding.

    What has concerned me most, since the beginning of all of this, was the perception of the roles of math teachers in our current classrooms. Is our roles really just to show students the steps of solving an equation? It seems to be what the app description claims – that having this would be like having a math teacher in your pocket. As we have reduced the roles of math teacher to demonstrating a single way of solving algebraic equations.

    Is there actually discontent amongst teachers? I imagine there would only be discomfort if that’s all the teachers are doing in the classrooms.

    I actually think the launch of this app provides a good opportunity for us (those of us that haven’t already) to change our fundamental understanding of what teachers do in a classroom. Much like I thought Wolfram Alpha could have done for us when it came out a while ago.

    I am showing and inviting my students to think about this today. I will share what happens there.

  29. Kenneth Tilton

    October 24, 2014 - 6:03 am

    “Because the only problems PhotoMath could conceivably solve are the ones that are boring and over-represented in our math textbooks.”

    The interesting thing is that half the population cannot solve those problems. And they *are* easy. I would not say boring, but then I enjoy pure maths for itself.

    So why cannot so many solve those problems, even young adults paying a lot of money to community colleges and desperately trying to learn to solve them?

    I suspect the learning problem they have transcends algebra, and neither PhotoMath (or any algebra-solving web site) nor dropping the Algebra requirement altogether will solve the larger learning problem.

    ps. Photomath is just a “stupid pet trick” they did to market their recognition engine.

  30. Michael Paul Goldenberg

    October 24, 2014 - 10:25 am

    @Kenneth Tilton wrote in part: ” I would not say boring, but then I enjoy pure maths for itself.”

    So do many of us. But I’m not sure that simple arithmetic or algebra problems that require nothing more than exercising an already-mastered skill fall into the category of “pure maths for itself.” Nothing wrong with ENJOYING nearly-mindless number-crunching for its own sake. We all have hobbies and guilty pleasures (and not-so-guilty but clearly idiosyncratic pleasures), but let’s not try to justify them by making them sound like more than they are. Even doing easy derivatives and integrals as a form of doodling shouldn’t be confused with doing real problem-solving of the pure or applied kind. To my thinking, it’s important to distinguish between a puzzle and a mystery, and between an exercise and a problem that isn’t simply the mechanical application of steps we’ve been trained to do with near-automaticity.

    I would also dispute some of what you write about community college students but I’m not 100% certain what the learning problem is to which you refer or, for that matter, where you think it lies. So absent elaboration on your part I’ll hold my peace on that for the moment.

  31. Kenneth Tilton

    October 24, 2014 - 11:24 am

    Sure, “already mastered” would be drudgery, but I do not remember such a thing from when I was in school and I aced Algebra without a problem.

    The only problem was then sitting thru a class period during which the teacher went over each problem step-by-step to help the rest.

    Either way, competency-based learning solves this sort of problem. Once I have mastered a topic I move on, no drudgery.

    And then we always have the pleasure of coming up with that nice neat answer, say, x=42. That was always a kick for me, and I think it would be for any kid if they could just do it.

    But a huge fraction no longer can. Not sure what you are disputing about community colleges, but it is so bad the AMATYC is voting in three weeks on a position paper stating there is no need for TYC students in non-STEM majors to pass Algebra (since half of them cannot): http://www.npr.org/blogs/ed/2014/10/09/354645977/who-needs-algebra

    The state of Florida IIANM is directing state colleges to drop the Algebra requirement, and apparently California has done the same.

    As for what are the learning problems, well, for one they do not even know their number facts. Fractions? No way. And one CC prof told me his kids expect to pass just because they are taking the class. They do not realize they will actually have to master the subject.

    What that does not explain for me is the ones who try and fail five times before dropping out, ending up with a student loan to pay off. Those students are making an effort, and Algebra is not that hard, so …?

  32. Matt E

    October 25, 2014 - 5:51 am

    I’ve been ruminating on this for a few days now. What’s frustrating to me is that I feel I’m being lumped into the category of teachers who “like teaching all the dull, mindless arithmetic and algebra.” I don’t like teaching anything that is dull and mindless. I guess my main argument is that there is value in repeated calculation–not for its own sake, but for the sake of having students discover patterns, relationships, and shortcuts on their own.

    I am about to start a section in my Discrete Math class on graph coloring and chromatic numbers. I am presenting my students with around 20 “blank” graphs, and having them try to figure out on their own what the chromatic number of each graph is. I imagine that, five years down the road, they’ll be able to snap a picture of a graph and have an app determine the chromatic number. So why should I make my students “suffer” and try to figure it out on their own? Because I hope to have them try to give words to any patterns or rules they are noticing, so that we can write them down, organize them, debate them, and maybe prove them. That is doing math. That is why I don’t want them to “just Google it” or “just [insert spiffy new app] it”. Then again, these are conversations I have with my students regularly. I ask my Advanced Topics students to not use calculators or computers unless they get expressed permission from me. Obviously I have no control over what they do outside of class (or even inside it), but once they understand my motives, they are amenable.

    I’m a big fan of this quote from Neil Postman (in Technopoly):

    We are currently surrounded by one-eyed prophets who see only what new technologies can do and are incapable of imagining what they will undo.

    All I ask is that those heralding PhotoMath and all of its siblings and eventual descendants just take a minute to try to imagine what these new technologies might undo.

  33. Kenneth Tilton

    October 25, 2014 - 6:55 am

    @MattE I remember when I was learning Algebra and doing 15-20 homework problems and sometimes I would spot a shortcut that turned out to be the next day’s lesson. I always thought I had discovered something. :)

    Lots of quotes favoring practice here: http://www.goodreads.com/quotes/tag/practice

    This one is short and sweet: “For the things we have to learn before we can do them, we learn by doing them.” ― Aristotle, The Nicomachean Ethics

    The thing about sufficient (not excessive) practice is that there is a difference between consciously knowing something like the distributive property and having internalized it through practice. The latter is necessary to perform at a higher level where the skill is taken for granted, and indeed I think that is what we mean by learning.

    Anything hard we can do requires us first to do in our sleep what goes into it. Successful hockey players do not think much about how to skate, i like to say.

    Conrad Wolfram discusses the issues in great depth here http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers?language=en, coming down in favor of using computers wherever possible (except for number facts).

    Of course he sells a product that does Algebra for us and I sell a product that helps us learn to do Algebra ourselves, so no surprise on our disagreement. :)

  34. Dan Meyer

    October 25, 2014 - 10:04 am

    @Matt E, thanks for coming back by and updating us.

    All I ask is that those heralding PhotoMath and all of its siblings and eventual descendants just take a minute to try to imagine what these new technologies might undo.

    Again, I do imagine what they might undo and I hope for it.

    But I think M Ruppell and Michael Pershan have helped me see my final kiss-off to problems that Hypothetical-PhotoMath-That-Doesn’t-Suck can do was too strong. Exercises as a means to an end of conceptual understanding of numbers and operations sounds great. That’s true even of basic computational exercises. Exercises as an end unto themselves is what I hope Hypothetical PhotoMath will undo.

  35. Matt E

    October 26, 2014 - 12:30 pm

    Exercises as a means to an end of conceptual understanding of numbers and operations sounds great. That’s true even of basic computational exercises. Exercises as an end unto themselves is what I hope Hypothetical PhotoMath will undo.

    I’m totally on board with that. My worry is that that’s a fine distinction, and that the false dichotomy of “computation bad, concepts good” may mean that the baby gets thrown out with the bathwater.

  36. Michael Paul Goldenberg

    October 26, 2014 - 12:48 pm

    @Matt E.: I might agree with you if in fact the last 25-30 years hadn’t shown that it goes just the opposite: the thoughtful stuff gets tossed; the computational stuff dominates. With the exception of classrooms taught by people like Dan Meyer and others who blog about their practice that reveal a great deal of deep thinking about math and teaching.

    PhotoMath is for the most part a gimmick that nonetheless highlights questions about technology vs. paper-and-pencil computational math. It barely touches, if at all, on what mathematicians do on a daily basis. And those whose work involves primarily loads of computations, particularly if large numbers are involved, are using technology extensively to probe further into what’s out there. But of course they use the technology to pursue questions that no technology is going to ask or evaluate in the first place.

  37. Sasa Skevin

    October 27, 2014 - 5:59 am

    I’m part of PhotoMath dev team and would like to thank everyone for samples which didn’t scan well. We welcome users to report bugs, send problems and give feedback. Our team will take everything into consideration and try to make PhotoMath more robust with less bugs and add new features over time.