A new member has been added to the Endangered Species list; it is the math teacher of yesterday. At a recent conference I asked the attendees to consider how their teaching would change if their students had an app on their smart phones that would solve a math problem and show the steps simply by taking a picture of it. How much of what we do would be suddenly obsolete?
The truth is, it is here. It is called PhotoMath. It’s fast, it works well, and it’s free. The day I read about it in the news, I shared the article with my students. They asked, “Can we download it now? Why are you telling us this? Isn’t it cheating?” I asked them how they thought they would be doing math once they were out of school–on paper or on computer. They said they would be using technology.
“Can you think of job that would pay you to do your work with pencil and paper?” They were silent. “So,” I asked, “should I teach you how to use technology wisely or not?”
I tested the app and found that though not perfect, it is highly efficient. You simply frame the math problem on the screen and the solution appears in a fraction of a second. You can then scroll through the steps if you wish to see them. It not only worked on simple arithmetic problems, I tried fractions and algebraic equations also. It tested it on this equation:
-8(n + 6) = 2(n + 7) + -22
It correctly delivered n = -4 and showed the steps in detail. Though I did find examples on which the app did not work, my students don’t solve all problems correctly either. For example, the app doesn’t recognize handwritten math problems or word problems at this time. It is inaccurate if the frame also includes the number of the problem in front of it.
In an article in The Guardian dated October 22nd, 2014, Matt Parker reviewed the app and concluded, “PhotoMath is happy solving simple algebraic equations and doing basic arithmetic, but not much else. So it seems fairly safe to say that this app is not going to undermine modern maths education, much like calculators didn’t a generation previously.”
The truth is that calculators have had a tremendous impact on math education! My middle school years were spent gaining expertise with pencil and paper concepts taught in previous grades. We had to get fast at dividing decimals and extracting square roots. Mastering these skills is no longer a viable use of instructional time, and for that reason we see much more algebra introduced in the pre-secondary school years.
When I began teaching in the early 1980’s, our biggest fear was that students might sneak calculators into math class. We patrolled the aisles looking for criminals and their contraband. We told the students that pencil and paper math was still important because, “What are you going to do if you are out in the woods and the battery on your calculator goes dead?” It never occurred to us why you might be carrying paper and a number 2 pencil in the woods or why you were doing math in the wilderness anyway. Nor did we have the foresight to think that one day everyone would have a phone/watch/computer/internet browser/weather station/personal fitness trainer/game console/calculator on their person at all times.
Though this app is not flawless at this time, it reminds me of the days when those ancient AA battery calculators first arrived. Certainly this app and others like it will improve on this process. I look forward to the day when these machines will efficiently do the work of more antiquated calculation methods and maybe save a tree or two in the process.
So the question remains, how will we teach differently when that day arrives? Will we lag behind the technology and insist students still solve the old way, or will we lead students into their technological future?
Here is what I do know. An app may never exist that can solve the types of problems our students encounter in performance tasks or that they will face in life after school. How do we design a trip to Mars? How do we take into account variables such as the weight and thrust potential of different fuels and engines? An app may be able to solve the mathematical content we teach at our grade level, but it is unlikely that one will be designed that can foster the eight mathematical practices any time soon.
This then gives us an idea of how our future trade might look. More and more we will be moving away from procedural instruction, rote memorization, and calculation without comprehension. We will move from emphasizing mathematical calculation to mathematical thinking.
I am looking forward to that day. My joy comes during the “ah-hah!” moments in the classroom. I love when students see the beauty of mathematics in the same way they might see the beauty of a good piece of literature. I anticipate the day when smart phones largely replace pencil and paper calculations and I am creating a generation of mathematical thinkers ready to tackle the world’s problems.
What do you think? I’d love to hear your comments.
“Can you think of job that would pay you to do your work with pencil and paper?” They were silent. “So,” I asked, “should I teach you how to use technology wisely or not?”
I tested the app and found that though not perfect, it is highly efficient. You simply frame the math problem on the screen and the solution appears in a fraction of a second. You can then scroll through the steps if you wish to see them. It not only worked on simple arithmetic problems, I tried fractions and algebraic equations also. It tested it on this equation:
-8(n + 6) = 2(n + 7) + -22
It correctly delivered n = -4 and showed the steps in detail. Though I did find examples on which the app did not work, my students don’t solve all problems correctly either. For example, the app doesn’t recognize handwritten math problems or word problems at this time. It is inaccurate if the frame also includes the number of the problem in front of it.
In an article in The Guardian dated October 22nd, 2014, Matt Parker reviewed the app and concluded, “PhotoMath is happy solving simple algebraic equations and doing basic arithmetic, but not much else. So it seems fairly safe to say that this app is not going to undermine modern maths education, much like calculators didn’t a generation previously.”
The truth is that calculators have had a tremendous impact on math education! My middle school years were spent gaining expertise with pencil and paper concepts taught in previous grades. We had to get fast at dividing decimals and extracting square roots. Mastering these skills is no longer a viable use of instructional time, and for that reason we see much more algebra introduced in the pre-secondary school years.
When I began teaching in the early 1980’s, our biggest fear was that students might sneak calculators into math class. We patrolled the aisles looking for criminals and their contraband. We told the students that pencil and paper math was still important because, “What are you going to do if you are out in the woods and the battery on your calculator goes dead?” It never occurred to us why you might be carrying paper and a number 2 pencil in the woods or why you were doing math in the wilderness anyway. Nor did we have the foresight to think that one day everyone would have a phone/watch/computer/internet browser/weather station/personal fitness trainer/game console/calculator on their person at all times.
Though this app is not flawless at this time, it reminds me of the days when those ancient AA battery calculators first arrived. Certainly this app and others like it will improve on this process. I look forward to the day when these machines will efficiently do the work of more antiquated calculation methods and maybe save a tree or two in the process.
So the question remains, how will we teach differently when that day arrives? Will we lag behind the technology and insist students still solve the old way, or will we lead students into their technological future?
Here is what I do know. An app may never exist that can solve the types of problems our students encounter in performance tasks or that they will face in life after school. How do we design a trip to Mars? How do we take into account variables such as the weight and thrust potential of different fuels and engines? An app may be able to solve the mathematical content we teach at our grade level, but it is unlikely that one will be designed that can foster the eight mathematical practices any time soon.
This then gives us an idea of how our future trade might look. More and more we will be moving away from procedural instruction, rote memorization, and calculation without comprehension. We will move from emphasizing mathematical calculation to mathematical thinking.
I am looking forward to that day. My joy comes during the “ah-hah!” moments in the classroom. I love when students see the beauty of mathematics in the same way they might see the beauty of a good piece of literature. I anticipate the day when smart phones largely replace pencil and paper calculations and I am creating a generation of mathematical thinkers ready to tackle the world’s problems.
What do you think? I’d love to hear your comments.
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