I know Photo Math is an older App, but I never really played with it until recently. A friend reminded me of the App and then I became more aware of students using the tool. I noticed some students using it to cram some algebra homework in homeroom. I was curious how accurate the tool might be. Like any other tech-geek, I downloaded the app that night, grabbed one of my sons math worksheets he has to do for homework (don't get me started on that) I snapped a photo and viola...answer revealed. At first I was very impressed and jealous that an App like this didn't exist during Calculus III days back in college. I wondered if it would have been able to solve this problem and produce the graph...
Let C be the oriented closed curve in the first octant consisting of three circular arcs: the portion of (x^2 + y^2 = 1, z = 0) from (1,0,0) to (0,1,0), followed by the portion of (y^2 + z^2 = 1, x = 0) from (0,1,0) to (0,0,1), followed by the portion of (x^2 + z^2 = 1, y = 0) from (0,0,1) to (1,0,0). Let G = [y^2, z^2, x^2]; and compute the integral along C of G.d r, both directly and using Stokes' Theorem.
Fortunately the App can't handle this problem, so let's just say I felt pretty good knowing at one point in time I could do math that this App can't do. Well, back to the point, the App was doing homework for students. I wasn't sure if it was cheating, or if it was a great resourceful way to complete the numerous repetitive problems they needed to do. Sure, they probably weren't learning much, but how often is homework used as an avenue for learning? I would argue that most teachers utilize homework as work to do outside of class for drill and practice, or because the classroom agenda didn't allow for everything to get done, so "just do it for homework."
I started thinking more about this tool. Obviously the math teachers must know about this, I mean Wolfram Alpha does the exact same thing, sort of. You have to manually put in the equation, but it will solve it for you, with steps, graphs, charts...etc. It can solve the problem I used as an example (on a side note; the engine behind Wolfram Alpha was the tool I used back in the day in college to create the 3D graph pictured above. If only I knew enough to take the opensource software and host it on a site for everyone to use, I could be rich. Oh well.) So, why am I so flustered by this App?
I arrived at two conclusions, one good and one bad.
The bad one was based off of what I mentioned before. The App does exactly what it sounds like, it accesses your devices camera to scan a math problem and then solves it for you, no thinking involved. Just point, tap, and viola homework done. The tricky thing is, this app most likely won't be allowed on any test and quiz. The way that I have experienced math classes, and the way in which a majority of math classes are still taught, the drill, practice, memorization, and regurgitation is the only way to get through. The app cuts all that out and you are left with only the classroom note taking experience to pass the course.
The good thing about this app, is spawned from the bad. Knowing that students are utilizing this tool might trigger a greater paradigm shift in math education. Instead of the rote memorization of and regurgitation of mathematical process, students are now suddenly required to think and defend their thinking with evidence from their own conclusions! Imagine that, a student using some information provided, identifying the problem, developing a solution and defending that solution with evidence of their own work; sounds like what math class should be. Maybe this app is exactly what teachers need, a little reminder that computers can take our place, unless we shift what we actually teach. Content is merely a vehicle that can be used to teach how to think critically, solve problems, and defend and communicate conclusions. I think we need more apps like this to trigger the paradigm shift education needs to really start teaching students to think, instead of how to play the game to get an A...what is an A anyway? Does an A really matter? Why does regurgitation get me an A?
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