PBL and Learning through Problem Solving

In preparation for our upcoming CPLC meeting I’ve been reflecting quite a bit on part of Cathie’s video on Project Based Learning. In differentiating between project-based and project-oriented courses, she discusses whether the learning is the “main course” or simply the “dessert”. This got me thinking about a topic that’s foundational in mathematics education and that has guided a lot of work in program revision. In math ed we like to talk about the difference between learning for problem solving and learning through problem solving. My goal in writing this is not to do a deep dive into philosophies that guide mathematics education, but rather, to discuss how this principle has influenced my understanding of project-based learning and how I see it impacting my work going forward.

Learning for vs Learning through Problem Solving

First, a quick overview. Traditionally, mathematics is taught to children with a teaching for problem solving lens. The idea is that in order to solve meaningful problems, students need to first gain all the foundational knowledge and memorize all the facts and algorithms that they would bring to bear on those bigger problems. It’s a perfectly reasonable idea. You’ve surely seen this approach in action. Think back to your math textbooks and learning experiences. You were probably taught a strategy, then you had a page full of problems to solve, and then, at the very end, there were a couple of story problems. The good problems, the potentially meaningful and useful problems, were saved for the end. What we’ve found is that the isolated memorization of facts and procedures rarely transfers well to other situations. So, a student can tell you that 5 x 3 is 15, but has no idea how many available seats are in 5 rows of 3 seats. Worse still, memorization is often tedious, leaving students completely disinterested in the content. When we treat the real meaningful work as the dessert, we’ll often find that students are so put off by our cooking that the dessert holds little interest.

The flip side of this approach is learning through problem solving. When children grapple with mathematical ideas by jumping right into meaningful problems, they regularly problem solve their way through it, even when no one demonstrated a specific solution pathway. Their early solutions are inefficient and error-prone, but as they share their thinking and refine their ideas collaboratively, they build a far more nuanced and transferable understanding. I like the main course analogy, though I think we’re really dealing with the combination of the main dish and all the sides. The meal works best when everything compliments the other dishes. 

I enjoyed the alignment between the goals of project-based learning and idea that students should learn through rather than for problem solving. High quality PBL allows students to build understanding through their sustained engagement in meaningful problems or issues. This approach does not sacrifice learning or rigor, though it’s important to note that their early work might be clumsy or less refined than we might like. Working through some of that initial clumsiness will be the most enriching part of the meal. Better yet, it allows for the potential that one of the students spontaneously pulls out a side dish that you never considered and it improves the meal ten-fold. Okay, I may have stretched the analogy too far, but still, it’s really cool when students surprise you.

Issues I’m Tackling

So why did Cathie’s video get me thinking about this learning for vs learning through problem solving idea? Well, when applied to any particular course, a learning through problem solving looks a lot like PBL. In fact, I find PBL gives some specific structure to ensure that learning through problem solving remains productive. Though I’ve found that approach to be powerful in my courses, I’m wrestling with a couple of things right now related to either PBL specifically, or learning through problem solving more generally.

The first issue I’m wrestling with is how I can some of the general principles of PBL to an entire program. Ever since programs were given the option of moving to 4 credits, our elementary education program has been digging into program revision. In doing so I couldn’t help but notice that our entire program was structured in a learning for problem solving type of way. Students take foundational courses, learning the basics, progressing toward their final semester, when they spend the entire time in the field, doing the truly meaningful work. It felt odd that I was applying principles to my courses that I was completely ignoring when it came to the structure of our program. As I discussed these ideas with my team, we recognized that a more field-centric program would give students the chance to jump right into the real issues and work that epitomizes our field.  

This is exciting work, of course, but it’s introduced the issue I’m now wrestling with. When I was teaching elementary school and used a learning through problem solving approach, all of the inefficient, error-prone strategies could be performed in a fairly safe environment. Low stakes errors are so powerful for learning. If we apply some PBL principles to broad program design, we run the risk of higher stakes errors. Working directly with children is not exactly the space in which we want our elementary education students learning through making mistakes. Don’t get me wrong, mistakes are going to happen, but some mistakes are perceived as learning experiences, others damage our relationships with schools and mentor teachers. So, I want students to engage in the main course right off the back, but we need to make sure we do so in a way that students can make mistakes, refine their thinking, and develop deep and interconnected knowledge without those mistakes creating harm for them, for the children they work with, or for the relationships we rely on in the community.

The second issue, clearly related to the first, is that I am recognizing the need to more fully center social justice issues in my courses. When I teach students how to teach math to children, I know that there are powerful ways in which we can explore the impacts of bias and structural racism in education. I have modules to address those. The problem is, those are the modules that don’t get reached when I run short on time. Unintentionally, I have been treating those modules as supplements, or luxuries, tangential to the main focus of the course, but not critical. I can’t do that. So, in preparing for this next semester and thinking about the main course I want students to jump right in to, I know that we have to acknowledge the role of race right from the start. Here’s the challenge. I try as much as possible to work in the open and make sure that assignments have a way of generating meaning outside of any individual course. This is really important, but it also makes our mistakes a little more visible. Again, that’s not a big deal with low stakes mistakes. Exploring issues of race and power, trying to make sense of individual bias, is already a very vulnerable exercise. It’s hard enough to allow ourselves to make mistakes in this area. I have to be very careful how I merge my desire to open up work to broader critique and create PBL experiences that may involve error and refinement. My key pedagogies could create an unsafe learning environment if I’m not careful.

In sum, I love the clumsiness and error-ridden strategies that infuse early learning in a PBL approach. I think those experiences build some deep understanding. I am wary of anything that could make those early experiences more high stakes. This is not an indictment of PBL, but rather a challenge that I am eager to explore.

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