We Should Wish PhotoMath All The Success In The World
October 22nd, 2014 by Dan Meyer
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.
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.
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!
My name is Dan Meyer and I like to teach.
It’d require students to do a little typing instead of taking a photo, but sub “WolframAlpha” for “PhotoMath” and we’re already there.
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.”
“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?”
Ditto Prof. Wright.
Is our primary goal as doers of math to “get answers” as efficiently as possible? If so, then go, PhotoMath, go.
Prof. Wright’s counterexample makes little sense to me. The photo and the painting are categorically different.
Matt E:
It’s precisely because that isn’t my goal that I wish PhotoMath success.
Still stewing on Pershan’s comment.
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?
@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.
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.
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.
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.
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!
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.
@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.
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.
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.
to David Petro
There’s no like button so here’s a “LIKE”, especially the last “My statement…”.