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Higher Maths and PBL: oil/water or peanutbutter/chocolate?

Higher Maths and PBL: oil/water or peanutbutter/chocolate?

I often receive questions on my website here or over on my LifePractice PBL site and sometimes the questions are really worth taking a moment to think about. Often, they’re questions I also get in my face-to-face workshops. So after reading and responding, I consider whether someone else might benefit from hearing the answers. And when the answers aren’t just easy responses, it’s important to capture that thought right away.

Here’s a question I received yesterday from Julie:

Hi Ginger,

PBL sounds great, and I want to expand beyond my first small attempts.

Two important questions:

1. When a course is externally examined, like an AP math (Statistics or Calculus), how would a teacher go about making sure students are well prepared for the exam within a PBL framework?

2. How much do we let go of teaching specific content to favor the PBL organic learning process that isn’t as quick as teaching skill-based lessons? Again, knowing that advanced mathematics skills are built on foundations of problem solving strategies learned over a number of years.

Thanks for any direction you can provide!

Good stuff, right?

Math PBL is a bit different from “other” PBL only because we feel so rigid and tied to the linear way we’ve been taught by math theorists. So I tried to answer her question from a chained-to-traditional approach, as well as from a let’s-do-better approach. If you think I missed the mark, please do gently chime in!

Hi Julie, Thanks for reaching out. There are people who say that PBL can’t be done in math classes for similar reasons that you state: advanced math skills are build on foundations of previous teachings. And that math can’t be “just discovered.” And to some point, that might be true. But I’m going to try shift that lens a bit. Let’s start with question 1:

1. When a course is externally examined, like an AP math (Statistics or Calculus), how would a teacher go about making sure students are well prepared for the exam within a PBL framework?


While the big-gun gurus may say differently, I am a big believer in making sure that students are learning what we need them to learn for life. And if life includes college and those entrance exams, we want to be sure they’re ready. Additionally, even if we’re not looking at that college path specifically, we do have a moral obligation, as educators, to be sure our students are learning solid content as well as skills in school. And I believe this is true with all levels of education. 

I’ve worked with educators, but upper level maths classes specifically, who have told me that in discussion and daily work, it was obvious their students understood the concepts and mechanics of what was needing learned. And with the guru-level PBL, they say this is enough. I disagree. We want to be sure to include end-of-unit pencil paper tests, at least until we as PBL educators know that what they’re doing is actually translating to all areas of application. 

 

Example: Mr. B is a higher-maths teacher. He told me his kids totally were understanding the math and the deeper concepts. But on my recommendation (and because the kids do need to know how to take tests, whether or not we agree this is the best way to measure learning) he gave them an end of unit test, which every single kid promptly bombed. And he was disappointed, rightly so. In our reflection conversation afterward, he recognized that he would need to give them explicit examples during their learning. “Yes, kids! You’ve got it. Now what will this look like on a test? Here. Let’s take a look.” 

 Some teachers will eventually be able to step away from explicit connections to tests during the learning process, but some might not. And it’s ok. According to the gurus, it’s not ok, but to me, it’s a need for too many of us to be SURE we’re prepping our babies for ALL situations. And for many, that includes tests. So while I would never advocate using the test as the hook on which we hang all the learning (which some AP classes actually do advocate), I would keep it on our map as we navigate through more relevant PBL challenges to the next level of math life. 

2. How much do we let go of teaching specific content to favor the PBL organic learning process that isn’t as quick as teaching skill-based lessons? Again, knowing that advanced mathematics skills are built on foundations of problem solving strategies learned over a number of years.

Great question and I have a varied answer. Again, some will say that in math, we can’t go full 100% PBL. And I’m not sure that’s true. I’ve not taught upper level math before in a PBL style, but I think that a teacher who understands math (and not just the application of algorithms) can find a way to get real close to 100% PBL, year-round. This course will probably not follow the traditional linear approach to learning math; eg, defining and knowing how trigonometric ratios work with triangles before we move to circles and coordinate planes. The pacing guide might jump around a bit more, based on the real-world problems being solved and we learn the math we need for that right now — aka, just in time learning. And that just in time learning may be several layers deep that’s totally out of traditional sequence. **Here’s where I’ll admit I’m not a person who understands math. I was able to get through the algorithms, barely, as a student up through trigonometry and know that if I could have a math class where I can see it happening in the world, it would make so much more sense. Like it did in Geometry for me. 

So with that being said, in any math PBL unit, there will likely still need to be side-workshops to take 10-15 minutes to explicitly teach an algorithm in the problem-solving process. Allow the students to dive into the problem, get to thinking, questioning, trying, and then get stuck. And then ask for help. And you take a moment to teach that skill they need to know to solve that problem. Then let them back at it. Yeah, that’s still PBL. 

Will a teacher be able to make a leap to full PBL in one year? I’m thinking probably not. It might take several years as we add 2-3 units a year, taking our time to refine and figure out the PBL process with math (because it IS different than in say a Social Studies class). Where can we get these trig/calc concepts rolled into science? Demonstrated in Physics? Art? 

And which of these concepts are we teaching simply because they’ll see them in college? To what end? At what point is the system asking us to teach specific concepts to create little college-professor mathematicians, working in pure mathematical theory? I wonder how many of our kids actually end up doing that theory work vs the number who actually take their math learning and use it in application.

My guess is we (as a system) might be a little stuck in the trap that college has created for us because they, who define what kids need to know for their classes (and therefore the entrance exams), really love their theoretical math. Which is cool! But not practical for most kids’ lives. And, I’d venture to say, is chasing kids in droves away from the joy of math. And it’s not something that one teacher can solve alone. But if we don’t question what we teach, why we teach it, and how we teach it, who will?

So after all that, I wonder if the question of “how much do we let go” is best answered by the individual teacher, department, and community in which one teaches. I don’t feel comfortable defining that for anyone, ESPECIALLY since I’ve not taught higher-level PBL math. And I fully recognize that’s likely dissatisfactory for you.

What I will recommend is finding a couple of units that tie nicely/obviously into kids’ daily lives and starting there. And seeing where your comfort zone is. And then adding another unit next year. And maybe only doing it with one class at first. 

Does this help? Where am I missing the bigger point? Do I need to take another stab at it? Let’s talk. 

If you want to know more about bringing PBL to your school and community, let me know

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Written by GingerLewman

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