What is Problems-Based Learning?

Problems based learning is an approach to teaching mathematics where problems drive the curriculum and the day-to-day learning. When I was a kid, word problems always came at the end of the worksheet or the end of the text book assignment. You had to figure out how to smush those words to fit whatever math topic you had just learned. What is the variable, what is added, etc.

Problems-based learning is the opposite.

Mathematics is a discipline designed for solving real human problems. So you don’t “learn math” first and then try to fit word problems on top of the topic. Looking for ways to solve problems is how mathematics – and all disciplines – has developed over time.

So in learning math, present problems first. If students have a need for a math skill, then they will use it. So you give them a problem that will require the use of the content standards you need to teach. Essentially, you reverse the order.

By giving students a problem first, you allow them to develop their own ways of thinking, meaning the problem solving approaches are more likely to stick in their brains long term. Problems sort of take the place of your lessons, which might sound strange to some people. Instead of saying I am teaching ___ topic and then we will do a worksheet on it on day 3, you plan to spend three days approaching a problem and you facilitate the learning around it. This works because you will teach the skills students need to solve the problem as you go through the process.

Problem solving framework

This general approach works for any kind of problem and you fill in the specifics with students.

  1. Read the problem. Define the problem. Allow students to have thinking time to process what the words are saying. Have them write down what they believe the problem is asking them to do.
  2. List what you know. What does the problem tell you? What math do you already know that could be useful?
  3. List what you need to know. Is there something missing? Is there more information you need before you can progress? This is a key moment for you as the teacher because you might need to answer simple questions or you might need to teach something once students ask.
  4. List your next steps. Should you make a table, a graph, a picture? What could you do to solve this problem?

Once students have gone through this set up process it is time to let them work. Working in teams is always ideal. Throughout the day/days/week, you might cycle back through this process multiple times. Below, I have a link to a really simple graphic organizer that can work wonders in your classroom. The simple act of having students define the problem and discuss it will change your perspective if you’ve never done it before.

While it seems simple, the problem solving framework
can have a profound impact on your maths classroom.

What I love about problems based learning is that students do more work and I can step back and support them. It is truly student centered, which is perfect for me. I actually hate standing at the front of the room and having people look at me. I hate lecturing.

After students spend time solving the problem, they should have an opportunity to present their approach and solution to their classmates. Do not rush the process though (a mistake I have made many times). Students should have significant time, possibly a few days to work out their solution.


I will be posting more about how I plan for and approach problems based learning in my own classroom, but in the mean time here are my top 3 resources for finding/developing/adapting problems to use in my classroom.

My own problem solving graphic organizer is a worksheet I use with students so they understand that problems are now the work when they get to my class. Something about having a worksheet helps with the psychology of school. I’ve found some students try to opt out of problems at the beginning of the year because they think it is just a brief activity that isn’t graded or doesn’t matter for some reason. But most importantly, it is a record of their thinking that both they and I can refer to throughout the problem solving process.

It also works well to slide the printout into a plastic cover that students can use dry erase markers on. Students love dry erase boards.

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What is Problems-Based Learning?