February 4th, 2016 by Dan Meyer
In math education, the fields of handwriting recognition and adaptive feedback are stuck. Maybe they’re stuck because the technological problems they’re trying to solve are really, really hard. Or maybe they’re stuck because they need some crank with a blog to offer a positive vision for their future.
I can’t help with the technology. I can offer my favorite version of that future, though. Here is a picture of the present and the future of handwriting recognition and adaptive feedback, along with some explanation.
In the future, the computer will recognize my handwriting.
Here I am trying hopelessly to get the computer to understand that I’m trying to write 24. This is low-hanging fruit. No one needs me to tell them that a system that recognizes my handwriting more often is better than a system that doesn’t.
But I don’t worry about a piece of paper recognizing my handwriting. If I’m worried about the computer recognizing my handwriting, that worry goes in the cost column.
In the future, I won’t have to learn to speak computer while I’m learning to speak math.
In this instance, I’m learning to express myself mathematically – hard enough for a novice! – but I also have to learn to express myself in ways that the computer will understand. Even when the computer recognizes my numbers and letters, it doesn’t recognize the way I have arranged them.
Any middle school math teacher would recognize my syntax here. I’ll wager most would sob gratefully for my aligned operations. (Or that I bothered to show operations at all.) If the computer is confused by that syntax, that confusion goes in the cost column.
In the future, I’ll have the space to finish a complete mathematical thought.
Here I am trying to finish a mathematical thought. I’m successful, but only barely. That same mathematical thought requires only a fraction of the space on a piece of paper that it requires on a tablet, where I always feel like I’m trying to write with a bratwurst. That difference in space goes in the cost column.
That’s a lot in the cost column, but lots of people eagerly accept those costs in other fields. Computer programmers, for example, eagerly learn to speak unnatural languages in unusual writing environments. They do that because the costs are dwarfed by the benefits.
What is the benefit here?
Proponents of these handwriting recognition systems often claim their benefit is feedback – the two-sigma improvement of a one-on-one human tutor at a fraction of the cost. But let’s look at the feedback they offer us and, just as we did for handwriting recognition, write a to-do list for the future.
In the future, I’ll have the time to finish a complete mathematical thought.
If you watch the video, you’ll notice the computer interrupts my thought process incessantly. If I pause to consider the expression I’m writing for more than a couple of seconds, the computer tries to convert it into mathematical notation. If it misconverts my handwriting, my mathematical train of thought derails and I’m thinking about notation instead.
Then I have to check every mathematical thought before I can write the next one. The computer tells me if that step is mathematically correct or not.
It offers too much feedback too quickly. A competent human tutor doesn’t do this. That tutor will interject if the student is catastrophically stuck or if the student is moving quickly on a long path in the wrong direction. Otherwise, the tutor will let the student work. Even if the student has made an error. That’s because a) the tutor gains more insight into the nature of the error as it propagates through the problem, and b) the student may realize the error on her own, which is great for her sense of agency and metacognition.
No ever got fired in edtech for promising immediate feedback, but in the future we’ll promise timely feedback instead.
In the future, computers will give me useful feedback on my work.
I have made a very common error in my application of the distributive property here.
A competent human tutor would correct the error after the student finished her work, let her revise that work, and then help her learn the more efficient method of dividing by four first.
But the computer was never programmed to anticipate that anyone would use the distributive property, so its feedback only confuses me. It tells me, “Start over and go down an entirely different route.”
The computer’s feedback logic is brittle and inflexible, which teaches me the untruth that math is brittle and inflexible.
In the future, computers will do all of this for math that matters.
I’ve tried to demonstrate that we’re a long way from the computer tutors our students need, even when they’re solving equations, a highly structured skill that should be very friendly to computer tutoring. Some of the most interesting problems in K-12 mathematics are far less structured. Computers will need to help our students there also, just as their human tutors already do.
We want to believe our handwriting recognition and adaptive feedback systems result in something close to a competent human tutor. But competent tutors place little extraneous burden on a student’s mathematical thinking. They’re patient, insightful, and their help is timely. Next to a competent human tutor, our current computer tutors seem stuttering, imposing, and a little confused. But that’s the present, and the future is bright.
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