I teach math. I earned my bachelor’s degree in math in 1998 and started teaching high school math in 1999. My first year teaching the math department had a policy of “no calculators” in Algebra (although allowed above Algebra). The reason “because what, will they always have a calculator with them?” Fast forward to 2022… Yes they will. Now we have moved from “no calculators” to “no Google” or “No Photomath.” I would like to argue that Photomath is NOT cheating.

## Is Photomath Cheating?

If you are unfamiliar with Photomath it is an app for a mobile device that when hovered over a math problem, using the device camera, the answer and the step by step solution is displayed.

A staple of the math class has been “show your work.”Photomath shows the work for students. Thus, they are cheating. The work we want is copied down from an app.

## Burying Our Heads in the Sand

In the early 1900’s calculators did not exist. Knowing how to calculate the square root by hand was essential because what is going to do it for you?? You could look up square roots in a book. However, you’re not going to carry around reference books of square root values so we taught students how to use the algorithm for square roots.

When calculators became more prevalent we abandoned the square root algorithm. I am 46 years old and was never taught the square root algorithm. Even as part of my math degree I was never taught the square root algorithm. Other than a party trick there is no value in learning the algorithm and I have no plans to. I will use my calculator.

I went to school in the late 1900’s. We changed the curriculum in the face of calculators. In the 21st century the technology has changed and so must what we value. It is time to stop valuing “show your work.”

Just as the calculator allowed us to stop valuing tedious algorithms, Photomath allows us to stop valuing “show your work.”

Go to Google right now…. Google.com just regular Google search. Use the microphone option to ask math problems “what is y equals 20 x squared minus 8 x plus 20” …. Boom, a parabola comes to you! Need a formula? Literally ASK FOR IT! This technology is not going away and it’s only going to get better. Our students will absolutely ALWAYS for their whole lives have access to technology that will do their math for them.

We have to stop pretending it is the late 1900’s. The world has changed. Google and YouTube exist. Teaching as if they don’t is ignorant. The kids ARE using Photomath. They ARE using the calculators on their phone. They ARE using Google searches. The only value in beating your chest over it is to get the phlegm out of your chest in the morning. If you think this is cheating… You’ve already lost.

## Math Should Be About Critical Thinking

Proof that “show your work” is not critical thinking is that you can hover your phone over the math problem and it shows not only the answer but all the steps. Robots can do this task.

I love the mathematical practices! My favorite is MP3: that students need to communicate and critique the reasoning of others. I am way more interested in students ability to reason mathematically than I am in their ability to compete with calculators.

The mathematical practices are about critical thinking. This is why “show your work” is not number 9. If students can Photomath the math problem then the problem is not hitting the mathematical practices and thus is not cheating.

Any lesson or assignment should be aligned with the 8 practices. If they are not doing any of them, why are we assigning it? The standards do not stand alone from the 8 practices. The list of topics in the standards are in TANDEM with the practices.

## Install Photomath

The first day of school I instruct the students to install Photomath (or something like it). Why is that funny? BECAUSE THEY ALREADY HAVE IT. I am not going to bury my head in the sand and pretend they are not going to Photomath the work. The only difference between requiring it and beating my chest over it is that they do it on top of the desk instead of under it.

## What Changes When Photomath is Not Cheating?

So what happens when you stop fighting the existence of the internet? I would argue that we get to ACTUALLY do mathematics, which is fun and interesting! Math is creative!!! What we’ve been doing for the last 100 years is not math! It was memorizing algorithms without number sense. It was cramming tricks “keep, flip, change” down student throats to help them put the right answer on a line somewhere. Math is not tricks!!! Real math should value THINKING! And if you’re thinking, you should not be expected to get the answer right the first time. Robots follow steps and get the right answer. Mathematicians look for patterns and try to make sense of the world through mathematical modeling (MP4).

If you place Photomath in their hand and tell students it is not cheating… What would that change for you as a teacher? I think it would make us better math teachers.

First realize that tools such as Photomath are not going to go away. These features are being built into tools we use every day. On my phone I have Google Lens. One of the options for me to capture is “Homework.” How can we continue to call this cheating when it is literally built into the tools we use daily. When we can not change the circumstances we must change our perspective.

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## Cheating with Photomath

Try “Solve this problem using Photomath. What is another way you can solve the equation?” or “Instead of starting with the additive inverse, try using the commutative property.” Students WILL be using Photomath, instead of considering it cheating utilize Photomath! Ask them to do it another way, communicate WHY that solution works. Use Photomath on several equations and ask them to find the pattern.

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