Things that are Good: A Problem Based Learning Approach in Mathematics

July 26, 2011
Geoff Krall

Geoff Krall

As a teacher in a Project Based Learning (PBL) school, I cherished the projects I created. I worked diligently to ensure that all PBL units I developed were rigorous and engaging. They were oftentimes a beautiful marriage between my Schoolwide Learning Outcomes and my state content standards, a labor of love that took weeks to prepare and weeks to implement. I had students usually more drawn to art or reading or athletics declare that mine was the first math class they ever enjoyed. A substantial pillar of this class they so enjoyed was a PBL approach in which students created ­amazing complex products that aligned with my project goals. In order to develop math fluency, I incorporated consistent math scaffolding into a meaty project tied to the real world that would create cognitive connections in students’ brains that would last well after the unit test was completed.

These were good things.

I am now, however, unconvinced that a solely PBL approach in mathematics is always the most effective conduit through which math and 21st Century skills are transmitted.

These are also good things:

1. Reading critically in math is good.

2. Writing for explanation in math is good.

3. Students steeped in inquiry is good.

4. Continual assessment is good.

5. Multiple entry points into a math problem are good.

6. Student conversation about math is good.

These are some of the tenants of a Problem Based Learning approach, which I am convinced is an extremely effective mode of both mathematics instruction and 21st Century skills development.

At the 2011 New Schools Training, I had the opportunity to work with math teachers new to an inquiry based model of instruction. I asked them to list the characteristics they would like their students to leave their class with. Among the characteristics that received the most audible support were Confidence, Critical Thinking, Persistence,Math experts, and great Collaborators. Upon reflection, the teachers and I came to the realization that a Problem Based Learning mode of instruction can develop these characteristics in our math students.

So what is a Problem, in the sense I am talking about a Problem Based approach in Mathematics? What does it look like?

1. Students read/view an Entry Event, which launches them into the Problem Scenario. A prescription for a solution is NOT included.

2. Students brainstorm “Knows”, “Need to knows”, and “Next steps”, all the while being guided by the facilitator to generate the intended learning outcomes.

3. Students work in pairs or groups to solve the problem, beginning with what was brainstormed in the “next steps” section of the entry document. The facilitator prepares workshops and lessons and has helpful resources at the ready, as needed.

4. Students present their solution in some form.

5. The facilitator asks guiding questions, prompts generalizations, and promotes connections.

This process is similar to the Projects of PBL, the primary difference being size and scope. A Problem generally focuses on one specific key concept or skill and lasts only 2-5 days, unlike a large swath of standards and 2-5 weeks in the former. This process allows for all the inquiry-based learning of PBL, but on a much more rapid time-frame to allow for differentiation, assessment, and possibly revisiting a concept or two. Also, by nature of their shortened scope or size, it forces the student to think deeply about the mathematics involved, rather than the final product. This final point is crucial.

Even my best Projects saw students go a couple days here and there without them being practitioners of mathematics: requiring students to narrate a voice-over to a video. Even my best Projects were contrived when I tried to fit math into the Project were it doesn’t belong, affecting the authenticity of the Project at its core: requiring parallel lines to be drawn onto an already-created light rail map for some unknown reason. And once the threads of math and authenticity begin to get pulled away from a Project, it can unravel quickly. And then you’re left with a five-week investigation that students don’t fully believe and you don’t fully believe in.

What, then, of all the Projects I created as a PBL teacher? I really liked them, and sometimes my students did too. Moreover, they were scaffolded well enough to avoid one of the great pitfalls that can sometimes plague Math PBL: students focusing solely on the product, not the process, thereby avoiding the Math content. Am I just to toss out those Projects that I worked so hard on and engaged students?

Either due to my better judgment or my educational hoarding tendencies, I have not and probably will never take the step of dragging any folders into the recycle bin on my desktop. Why? Maybe I’ll see a way I can condense those sprawling, hyper-relevant (or pseudo-relevant) projects into a concise, maybe-not-quite-as-relevant problem. Maybe I’ll use one of the scaffolding activities as the basis for a problem. Shoot, maybe I’ll use it as a project again someday.

I can’t deny that I had students buy into my class through the drug of the product-focused Project. I’m really glad I did too, because I’m just not that good of a teacher that I can get by solely on math content. If I have to bribe students every now and then with the carrot of them creating a cool animation, video, or presentation in front of community members, so be it. And if you want to do the same, and have the ability to create engaging, authentic, rigorous, and math content-rich PBL units, go for it. And while you’re at it, post it somewhere public so we can all see it and learn from you. But continually ask yourself the following questions: what are the students engaged in right now, the product or the math? When’s the last time I probed each individual student for their math knowledge? And, is this Project really that good, that I can be sure, absolutely sure, that students are becoming fluent in mathematics?

The challenge here is not to make you question the use of PBL, or to disregard it as a potential math educational tool. The challenge is to develop problems that are equally engaging as your projects. So let’s begin that work.

An array of Problems that are equally engaging as Projects, and get the student to consistently think about math: those would be things that are great.

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