*Note: This is the third post in a series focused on practical ways to do PBL in every subject and grade level. Read the first and second here.*

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.and**Authenticity**– The project features real-world context, tasks*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**–

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.

**Phase 1**

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 screencasts would be created using tools such as Screencast-o-matic or Screencastify, and they would have the students’ voice overlay the writing of a problem and solution on a whiteboard.

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.

**Phase 2**

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.

**Phase 3**

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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Are there any examples of the maths questions used with the PBL approach available to view?

Thanks

I really like this blog post to explain questions at the Elem level: https://performingineducation.com/2017/03/driving-questions.html

This was a problem several years ago in our district as we went 1:1 with technology. PBL was our solution also. Although it is not completely integrated into all math courses we definitely have come a long way.

I wrote a blog response to this several years ago. It’s interesting how technology works its way around the world.

http://schommermath.blogspot.com/2015/09/what-this-means-for-math-education.html

Thanks for sharing Mark, love seeing your process in this post!

Interesting post, AJ!

I suppose the knee-jerk reaction will be to seek out apps like PhotoMath and block them. Hooray for your students – I hope their resourcefulness sparks further discussion about what Alan November calls “unGoogleable” questions.

Happy Holidays,

Bob

Bob, I agree, that would be the initial reaction. But, it’s almost impossible to block them when kids are at home! Just as the calculator changed how we teach Math, so too will apps like Photomath. Interesting times!

Caution-pretty big pent-up rant follows:

The end of math homework can’t come soon enough for me. As a high school science teacher, I have always hated the way the math department, with their massive drill and practice that counts heavily in students’ grades, monopolizes all my students time and makes it really difficult for them to read an article or a short story or just stop for a minute and think about something really hard for once.

I also hate how it has shaped their view of what is important. EVERYTHING in their academic schedule is triaged through the filter of how many “points” it is worth in their grade. It has made implementing standards-based grading a nightmare.

Worst of all, doing 30 – 50 textbook problems every night does NOT increase their understanding of the concepts. I have a hundred examples of students who are in pre-calc and calc and have always gotten A’s or B’s in math who cannot, to save their souls, interpret physical data that shows a linear pattern. They can solve y = mx + b problems all day long, automatically, even solve systems of two equations without exerting any mental effort…it’s just a sequence of button pushes on a TI-84, after all. But they don’t have a clue what it means that a relationship between two quantities has a definite slope. Or a vertical intercept. I have to teach them the math, because all their math teachers have taught them is how to do problems.

But now that I have two children of my own in high school, it REALLY hate it. My son gets math pretty easily. English literature is much more of a struggle for him and he should spend a lot more time reading and writing for that class than he does. But every damn night, calculus homework (that he doesn’t need to do in order to understand how the calculus works) consumes the bulk of his night and leaves him with a few minutes to do what he needs to do the most.

Just yesterday, I had a conversation with the most advanced math student our high school has ever had. He had just finished the final exam for his independent-study differential equations class and came to my chemistry classroom early to get a jump on a lab he was working on. He said, “I’m finally done with math forever. I will never again do any of the stuff I have spent all those hours on for the last 5 years. Nobody but math teachers solves those kinds of problems over and over again and thinks they’ve accomplished something.”

I have said the same thing to math teachers repeatedly. The conversation usually goes something like this conversation with a calculus teacher:

Me: “Why do you guys assign all these problems and give a grade for them?”

Math: “If we don’t grade them they won’t do them.”

Me: “But if you grade their understanding of concepts, won’t they do what they need to to learn the concepts?”

Math: “But they need to do lots of problems, and they’ll quit before they’ve had enough practice if we don’t grade it.”

Me: “Why do they need to do lots of problems if they understand the idea?”

Math: “So they can get faster at doing the problems.”

Me: “Why is that important?”

Math: “Because you have to be able to work quickly to get all the problems on the test done in time.”

Me: “Why is that important?”

Math: “Because there are lots of problems on the test.”

Me: “Why do there have to be so many problems on the test?”

Math: “We have to know if they can do all the kinds of problems in the homework.”

Me: “OK. But why does there have to be a time limit.”

Math: “Because it’s not fair if some people take more time.”

Me: “Fair?”

Math: “Well, if I give somebody the same grade for work that took an hour and a half as somebody else took an hour to do, that’s not fair.”

Me: “So the grade isn’t really reflective of having understood the concepts?”

Math: “Well the better you understand the concept the faster you can do the problems.”

Me: “Really? Is there evidence for that? Because what I remember about calculus problems was there being one conceptual step followed by a boatload of simplifying algebra. Why is the basis of a kid’s calculus grade based on speed in doing algebra?”

Math: “Well it’s important to be able to do the problems fast.”

Me: “Why?”

Math: “Because when these kids get out in the real world they will not have extended deadlines”

Me: “Well, they also won’t have to do textbook math problems in the real world either.”

Math: “But they will have to use this stuff, if they become engineers or scientists or economists…”

Here’s where the argument gets a little unfair, because I am a former engineer.

Me: “Um, all the way through my engineering program in college and all the way through my career, I never integrated or differentiated a function one single time after I finished my math prereqs. The only value in my calculus training was that the conceptual underpinning helped me to read my textbooks and understand my lectures in the engineering and physics classes.”

Pause.

Math: “Um. Well, the students who are doing all the homework faithfully aren’t having trouble getting the tests done in time.”

So the bottom line was the way they do their testing is justified primarily by the way they assigned their homework…which was justified by the way they do their testing… No thought was given to the purpose of learning calculus or what it even meant to understand calculus. I even asked what the learning standards were for the current unit. They only could respond in phrases that resembled textbook chapter subheadings. They didn’t even have a clear understanding of what their instructional goals were for the students. The only real goal was being fast at solving textbook-type problems.

And we wonder why kids hate math. And don’t understand it.

This is amazing! Thanks so much for taking the time to write it all out for the benefit of the rest of us! I love hearing your science teacher and parent perspectives. You have articulated some very good points which I hope help shed light on this issue for some math teachers out there!

I think the new idea of asking students to explain their steps helps get around the use of apps such as photo math because it requires they do more than just copy the steps down.

Yes! I wish I could shout this post from the rooftops! When I was an elementary Math Interventionist my eyes were opened wide to the reality of the points Dave Eckstrom addressed in his comment. AJ, I’m wondering if there were any teachers who weren’t in agreement about the changes and if so, how the teachers dealt with that resistance. Also, I’m wondering if any students were outspoken about the changes since it meant they would have to work harder and in more meaningful ways than simply solving problems with their app…which BTW I’ve used PhotoMath with my own 6th grade son to check his AP Math homework when he’s confused.