When working with educators to implement project based learning (PBL) in their districts/schools/classrooms, the one subject area that is consistently met with hesitation is math. On a regular basis, math teachers (across all grade levels) ask something to the effect of, “Yeah, this is great. But how does it work in math class?”

Here are two reasons why I believe this skepticism may exist:

**Math textbooks**From my experiences, math is the subject area in which teachers are most likely to march through the textbook from beginning to end, treating the book as if it’s the curriculum (and yes, I have been guilty of this mistake). In reality, the textbook is one tool or resource that a teacher should leverage to meet the needs of students. However, veering away from the textbook (potentially in the direction of PBL) can be uncomfortable.*are*the curriculum, when they shouldn’t be.**Math is inaccurately viewed as black and white.**In other words, answers are either*right*or*wrong*, and a*deep conceptual understanding*of content simply doesn’t matter (or, for one reason or another, it’s not even on the teacher’s radar). And therefore, PBL (which is commonly leveraged to promote deep conceptual understanding), on the surface appears to be nothing but a roundabout way to get to the same old answers. So, why bother with it?

**So, what does project based learning look like in math class?**

Consider this excerpt from *Mathematical Mindsets* by Jo Boaler (a must-read book, which the teachers at my school district’s middle school are currently using for a book study):

In an important study, researchers compared three ways of teaching mathematics (Schwartz & Bransford, 1998). The first was the method used across the United States: the teacher showed methods, the students then solved problems with them. In the second, the students were left to discover methods through exploration. The third was a reversal of the typical sequence: the students were first given applied problems to work on, even before they knew how to solve them; then they were shown methods. It was this third group of students who performed at significantly higher levels compared to the other two groups.

In short, according to this research, first, students should be confronted with a problem *and then* they should learn the necessary material in order to solve the problem.

Sounds like PBL.

**How might we break this down into two steps that are more detailed?**

- Consider the needs of your students and one of your math units that lends itself to exploratory learning. If you typically rely on your textbook, then possibly instead focus on one of its chapters. Then, as a result of the unit/chapter instruction, consider what students should know, understand, and be able to do. (Oftentimes, “know, understand, and be able to do” feels like splitting hairs. So, don’t hesitate to reframe/simplify these particulars as what you want students
*to be able to do and explain*.) - Design a task in which students will have to learn this material in order to successfully get the job done. This task can be something students create (with enough creative flexibility to make it their own), a problem that is given to them, or potentially a problem that they find. Here, the key is to craft your directions in such a way that forces students to “bump into” what they need to learn as they work through their projects. For example, when my students created their own health shakes, they had to (1) make sure its ingredients benefited certain body systems, and (2) display all ingredients in customary and metric weights and capacities. As a result, they learned this content in meaningful context, as opposed to being fed the information, followed by, “Now let’s take what we’ve learned and do something with it!” Also, consider how two classes could be creating the same product or tackling the same problem, but learning completely different concepts as a result of how directions are put together.

Two tips to consider:

**Some direct instruction will be necessary.**In PBL, this direct instruction usually comes in the form of mini-lessons. These mini-lessons can be planned proactively when the teacher, while designing the project’s directions, is able to anticipate what the majority of the class will need. These mini-lessons can also be prepared reactively for students who struggle through their work.**Don’t grade the project.**The research tells us,*if you throw a grade at creativity, you’re going to squash it*. Rather, grade what you want students to be able to do and explain (which should connect to your academic standards). For example, when my students were done with their shakes, they took an open-ended test that assessed their understanding of body systems, measurements, and more.

Finally, I should point out that the above steps and tips can be applied to all subjects, not just math.

**In the End**

Aside from a few tweaks, all we’re really doing here is changing the order of instruction from, “Learn the information, now do something with it,” to, “Let’s do something, now learn the information you need.” Or, as Dan Meyer succinctly tells us in his TEDx Talk, “The math serves the conversation, the conversation doesn't serve the math.”

**What do you think about project based learning in math class?**

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### Ross Cooper

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Tamara Letter says

Excellent post! Teaching math with relevancy is vital for conceptual understanding to stick. I think at the elementary level it’s a bit easier as many units are hands-on application, but I love the mindset of starting with a problem first then figuring out how to solve it (versus “doing it right”!)

Aaron Davis says

Over here in Oz, there is group called Back-to-Front Maths which pushed out a model where students begin with a problem and then unpack their thinking (https://readwriterespond.com/2015/03/problem-based-learning-in-mathematics-my-reflection-on-back-to-front-maths/). Although designed for a different curriculum and context, might still be worth checking out.

Lou Sangdahl says

Great article! Thank you!!