It was towards the end of the third marking period a few years ago when my Math teachers in our middle school came up to me.
“AJ, I think we’ve got a problem, hoping you can help.”
“Sure”, I said, “What’s going on?”
“Well, it’s kind of weird. Almost all of our students are turning in their homework. We usually check for completion, but when this started happening it was unusual.”
I responded, “That’s a good thing, right?”
“Yes, it was good that they were turning in homework. But, the odd piece was that it was all correct. All of the steps were right, the solution was right.”
I waited to hear more…
“And we think they are cheating. We aren’t sure how, but something is going on. Even the online homework we are assigning is coming back correct, so it’s not like kids are copying each other on the bus like the old days.”
“Ok, I can check into it and see what we find.”
At that point, I wasn’t sure what was going on, but it did seem odd. I know from when I was teaching, and now being an administrator, normally you don’t get 100% of the students turning in homework.
A few weeks later, they came back to me.
“It hasn’t stopped. And now we are getting complaints from parents.”
I laughed, even though they seemed serious.
“Why are you getting complaints?”
“Well,” she said, “Our kids are getting 100 percent on every piece of homework, and yet, they are not passing the quizzes and tests. Parents are wondering how this is possible, and quite frankly, so are we.”
Hmm. I thought for a moment before responding, “Let’s ask a student, and see what they say. Can’t hurt!”
The next period I headed to the library commons area where some students were working on Math during a study hall. I asked one of the students what was going on with Math homework, and if she was getting all the answers right.
The student said, “Oh yeah, I think everyone just uses PhotoMath now. We are allowed to use it, right? It’s just like a calculator, right?”
I asked to see it in action.
What happened next caught me by surprise. Not because I couldn’t believe it, but because it changed the way I viewed math forever.
She would pick up her iPhone (or maybe it was an Android) and open up an app. Then flicking over to a clear screen, she would hover the phone over a specific problem in her textbook.
It was nothing short of magic. If by chance, someone had been transported here from even 20 years ago they might not have believed it was possible.
The phone immediately (I mean it was quick!) overlayed the problem, multiple steps, and a solution all in a row on her screen. She jotted down the answers on her piece of paper and went on to the next problem.
“That is PhotoMath?” I questioned.
“Yep. It’s a free app.”
“Are you allowed to use that? Is it something your teacher uses in class?”
“Um, I don’t think Ms. Carter knows about it…but no one ever said we couldn’t use it. Am I in trouble?”
I told her she wasn’t in trouble at all and continued to ask a few more questions about how the app worked. But there wasn’t much to learn. It worked just as I saw it work. I quickly googled the app on my phone and found this video (which is eerily similar to what I saw in the library that day):
Photomath 2.0 from MicroBLINK on Vimeo.
We tend to hear stories all the time of computers doing “human things” and impacting productivity but this time it was different.
And PhotoMath is not the only app out there that does it. In fact, it may not be the best at this process.
This Verge author wrote about his experience with Socratic (another math solving app that answers questions from other subjects as well), that seems to take this process to the next level:
I pointed it at 2x + 2 = 7x – 5, which I wrote down at random, and it gave me a 10 step process that results in x = 7/5. It has trouble with word problems, but if you can write down a word problem in math notation it shouldn’t be an issue. I also tried it on a weird fraction from an AP algebra exam, which it kind of failed at, but then I swiped over and it was showing me this graph, which included the correct answer:
I love this app, not just because it would’ve helped 8th grade Paul out of a jam, but because it’s such a computery use of computers. You use the tiny computer in your pocket to be basically smarter than you already are. It’s technology that augments a human brain, not just a distraction.
The creator of Socratic just open sourced its step-by-step solver, called mathsteps. There are a lot of computer-based algebra solvers out there, but for Socratic they had to do some extra engineering to get at the steps a human would need to solve the same problem.
This is a serious evolution of the calculator. No human input needed to solve equations, only a smartphone, and the app with a camera.
So, I went back to my Math teachers, ready to show them the app that would end Math homework as they knew it…forever.
A New Way to Do Math Homework
I know there is a big debate over the practicality of homework in general. I also know that this is not the first time someone has tackled the idea of doing Math homework differently (Flipped Classroom anyone?).
That being said, when I came back to our Math teachers to show them PhotoMath, they took a long hard look at their instructional practice, and what they could do to change things up in order to give kids a better learning experience.
It was not about what would be easy to do on their end.
It was not about using the latest and greatest technology to combat PhotoMath.
It was not about taking the focus away from mathematical concepts.
It was about the learning.
The teachers quickly made up their mind. There was no reason to continue giving the same homework each night to students who could answer every question with PhotoMath.
Were there times they would still give problems and practice them in class? Of course.
Were there times students would take problems home to work on and study? Of course.
Yet, in the long run, something needed to change in order for the students to be successful.
They brainstormed a number of options which included three viable solutions:
- Give no homework and only optional problems they could solve and work on at night
- Flip the classroom (watch instructional videos for homework)
- Have students create their own video tutorial (screencasts) explaining how they solve problems
Although options 1 and 2 were still going to be used, our teachers selected the video tutorials as the main focus for homework moving forward in most math classes.
The Nightly Math Project
The Buck Institute describes Project Based Learning as a teaching method in which students gain knowledge and skills by working for an extended period of time to investigate and respond to an authentic, engaging and complex question, problem, or challenge.
The Gold Standard PBL Essential Elements are as follows:
- Key Knowledge, Understanding, and Success Skills – The project is focused on student learning goals, including standards-based content and skills such as critical thinking/problem solving, communication, collaboration, and self-management.
- Challenging Problem or Question – The project is framed by a meaningful problem to solve or a question to answer, at the appropriate level of challenge.
- Sustained Inquiry – Students engage in a rigorous, extended process of asking questions, finding resources, and applying information.
- Authenticity – The project features real-world context, tasks and tools, quality standards, or impact – or speaks to students’ personal concerns, interests, and issues in their lives.
- Student Voice & Choice – Students make some decisions about the project, including how they work and what they create.
- Reflection – Students and teachers reflect on learning, the effectiveness of their inquiry and project activities, the quality of student work, obstacles and how to overcome them.
- Critique & Revision – Students give, receive, and use feedback to improve their process and products.
- Public Product – Students make their project work public by explaining, displaying and/or presenting it to people beyond the classroom.
We were already making the shift as a district towards authentic PBL across subject areas, and our teachers believed this was the perfect opportunity to give PBL a shot at tackling the math homework issues.
For each unit, our teachers would now define a math project that would last the entire unit but would be worked on nightly by each student (or group of students depending on the class, subject, and age).
Each project had three phases.
First, students would create their own video tutorials (screencasts) solving math problems that were relevant to the concepts being taught during the unit.
This would include math problems that were teacher provided, problems they found online, and in a textbook or resource.
The teachers would have students share their screencasts with other students during the class and reflect on the steps they took to solve each problem, pointing out teachable moments throughout the video.
The second part of the project involved choice. The student (or group) had to create their own word problem or puzzle that represented the mathematical concepts. The goal was to create a problem that was challenging for others students to solve, and would be one they would have to work through.
In order to do this, the students had to go through a sustained inquiry process in which they tested different problems and ways to display the problem (as a puzzle or word problem). This involved having test groups to answer their problem and developing ways to make sure it was “PhotoMath” proof.
The last part was all about problem-solving with time constraints. The students had a chance to solve each other’s word problems or puzzles and time how long it took them to solve it correctly (if they could). The result would be in one group winning the prize for difficulty and clarity.
By far the most important piece of this last phase is what happened after the challenges were solved and completed. The students would get together in roundtable reflections and talk about what went well, what didn’t, and what they learned about this concept throughout the process. The final project created opportunities for more learning and students mastered the skill of not only solving these problems but also creating them.
How Are We Solving Our Problems?
These teachers took a creative approach to solving the problem of the world changing rapidly and their practice being impacted at its very core.
They could have easily tried to continue giving the same type of math homework knowing that programs like PhotoMath existed.
They could have balked at PBL in math class and focused on a more traditional I do, We do, You do approach.
But they worked together to solve a problem with a better way of doing things.
Not an easier way.
A better way.
Project-based learning takes a lot of work to plan and put together on the teacher end. It takes time to tweak and iterate and make better during and after the project is complete. Yet, that is what we are here for.
We are here to provide students with learning opportunities that they could not get somewhere online. We are here to give kids the support and challenge they need to be successful in any type of environment.
When we see challenges, do we treat them like opportunities to do things better, or hope for a solution that can get us back to an old way of doing things?
I’d love to hear in the comments how you are doing new things in new ways in your classroom and school. We all need to hear each other’s stories and strategies to give kids awesome experiences that they could only have with an adult who understands how to engage and empower on a daily basis.
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