A Problem Based Learning Starter Kit

You’ve seen the tasks. You’ve read the research. You’re basically bought in. But how do you begin? More importantly, how do you introduce students to inquiry driven learning?

Or maybe you’re not convinced. Perhaps you maintain that the teacher is the primary knowledge constructor. Perhaps you’ve been burned in the past by inquiry driven instruction. You tried it and didn’t see kids learning much and you feel like you wasted some amount of class time when you could have been actually teaching. I can speak from experience: if I wasn’t part of a cohesive team (all subjects, as part of an entire school effort) I quite possibly would have tossed inquiry, Problem Based Learning, groupwork and everything else in the trash after my first miserable experience with it.

Or maybe your students are burned out and beaten down on math. They’ve been labeled “remedial” and by golly, they’re living up to that stamp that your district has placed on them. To them, math is an arbitrary bunch of rules to follow and steps to regurgitate. Their test scores stink and they have difficulty applying math in new and novel situations. Applying math in new and novel situations is probably an entirely foreign concept. Up until now they’ve had example problems or math instructional software to guide them through their problem packet.

It’s always tough to be the first. In many cases, you might be the first teacher to actually ask students to solve complex math problems without pre-instruction. Students might look at you cross-eyed the first time you ask them to work in groups collaboratively on a problem that may not look like the stuff they see in their textbook. There isn’t an example problem for them to look at. Yes, you are the first line on the shores of Normandy.

Not all problems are created equally and some may be more easily acquired and delved-into by students. If you’re not careful with your first exposure of kids into a new way of mathematical task-posing, you and the students could easily frustrated with the process (if you even have one yet). As Dan states perfectly in one of my favorite posts this year on first-steps toward inquiry, “The Unengagables“, “you’ll be hearing from their attorney.” Dan poses three quick methods of introducing kids to mathematical inquisitiveness, be sure to check those out, and follow the comments. I’ll follow with a few tasks here that I think make for good first-foray’s into Problem Based Learning (PrBL).

I like these tasks as first-forays for a few reasons, pointing two directions.

For the teacher:

• The problems kind of “implement themselves.” That is, there isn’t a whole lot to do to massage the task to make it implementable. While I don’t necessarily advocate a plug-n-play curriculum, it’s ready to toss in the oven.
• It doesn’t take too long. Maybe a day, maybe two at most. I’m not sure any first-foray into PrBL should last more than a couple days.
• The task includes facilitation notes and/or other supporting resources.
• The task naturally fosters student and peer-to-peer dialogue. Obviously any good task should do just that, but these tasks especially do that with minimal teacher-prompting.

For the student:

• It’s naturally engaging or intuitively interesting. Real-world is nice, mathematically perplexing is better. 
• The problem allows for multiple ways of being mathematically smart. Hopefully some of these tasks will spur the conversation about being smart in math in multiple ways. Habits of a Mathematician type stuff.
• The task at hand is clear. And gets to the point.

Here are a few problems that I’d consider starting with. Or, if you’ve been burned or you’re skeptical, problems to try and experiment with.

• Shell Centre: Security Camera Task

Why it’s a good starter problem:

It ties together a visual and number sense. There are several ways to prove or demonstrate a solution. It gets to the point.

• Shell Centre: Gold Rush

Why it’s a good starter problem:

The task allows for guess and check. The task is intuitive and understandable. The scaffolding task involves analysis of samples of student work, a non-threatening way of fostering dialogue.

• Shell Centre: Interpreting Distance vs. Time Graphs

Why it’s a good starter problem:

The scaffolding involves manipulatives. The math naturally folds into multiple representations and modeling.

• Dan’s Taco Cart Problem

Why it’s a good starter problem:

The task prompts students to ask the question. There is an “either-or” possibility for initial guessing and estimating. The task allows for easy differentiated instruction (don’t know how to find the diagonal of a right triangle? how ’bout a workshop on Pythagorean’s Theorem?).

• File Cabinet and Stacking Cups from Andrew

Why these are good starter problems:

You probably have a file cabinet in your room.You probably have a door through which students enter your room. Students have seen and interacted with post-it notes. Students have seen and interacted with styrofoam cups. And with a phone, you could recreate this exact Act 1 video. The task may incorporate multiple ways toward mathematical smartness. Kinesthetic learners might engage via experimentation with post-it-ing the file cabinet themselves.

• Always/Sometimes/Never from Fawn and Friends

Dialogue is an inevitability with Always/Sometimes/Never. It can be tailored to your specific classroom. The notion of finding counter-examples is one of the most mathematical ways of thinking I can come up with, and one that kids intuitively understand (it’s a shame we rarely bridge that). If you incorporate some Geometry-type Always/Sometimes/Never cards (like these), kids will be begging you for scratch paper.

• Do the Best Movies Make the Most Money from Yummymath

Why it’s a good starter problem:

This task, like all of Yummymath’s, include well thought out worksheets with questions that allow for deep conceptual understanding. If you’re not comfortable with driving the car, let the questions that Bryan provides steer for a while.

• Coffee Spills and Sales Sheets from Jeff

Why it’s a good starter problem:

For teachers, I think this models nicely how to modify a textbook problem to something more interesting. For students, they have specific math-like things to do. It gives them exposure to modeling from an authentic scenario.

• Any of the stuff freely available from Mathalicious, specifically:
  • Three Shots
  • Domino Effect
  • The Fall of Javert
  • Xbox Xponential

Why they’re good starter problems:

It’s got the presentation – usually with video – ready to roll. The Mathalicious team is adept at both humor and conceptual understanding. Like Yummymath, they can steer the ship for a while until you’re more comfortable with less lesson plan structure and organizing groupwork. The lessons are all aligned to CCSS.

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So, there are a few problems to experiment with.

“But they don’t address my particular standards.” you say (For the record, all of these tasks do address specific content standards, see?, but possibly not yours). To that I’d say don’t worry about “coverage” for a day or two. Teachers lose teaching days all the time due to pep-rally schedules, fire-drills, or whatever. And (this is a whole other post waiting to happen but) coverage is overrated. If you can get kids buying into math – possibly for the first time ever – that’ll go a lot farther than coverage.

What are some of your favorite “starter problems”? What other advice would you give teachers that are starting out? Or maybe, better yet: what was your first experience with any kind of inquiry-based instruction like? What was it like for your students? Feel free to share in the comments.

Update 11/22/2013: Andrew, as always, doing great work. I feel like weekly POPs might be another way to dip you and your students’ toes into non-routine problem solving.