A Mathematical Conundrum

It’s Wednesday.  I’m sitting in my office with two students waiting for a third to arrive when one of them shares this epiphany.

“I couldn’t stop Dr. Podraza.  I worked on this problem the entire weekend.  I looked up articles.  I had my parents Google stuff.  I got everyone involved.”

“And I don’t think the math is actually right.  After all, it doesn’t make sense that my answer was in the billions.”He then went on to explain why he thought his answer was implausible citing relevant facts.  

There it was.  The thing educators all dream of.  A student who was so engaged in learning that he pursued it for the pure joy of it as opposed to turning it in for a good grade.  

So what caused all of this determination and excitement? 

Right before Winter Break, I was talking with these same students about how they hated the current way they had to learn math because they were given problems that were either out of context, completely fake, or that they were being forced to solve them in a way that was inefficient. 

“So what do you think we could do about it?  How would you like to learn math?”  

“We think math should be connected to the real world.  We should be able to solve problems about things that we can connect to, not some weird story about a monster at the bottom of a made-up lake or worse, Felicia’s cookies (this is an inside joke).  We get that we have to solve problems and learn the math behind it, but it’s frustrating when we are told we have to use a specific way of doing it.”

“Ok, so what might that look like?”

“Well, there’s stuff going on in the world.  Like global warming.  Stuff that’s actually a problem and math is probably related to it.  We want to solve problems like that.”

This was how the Top Secret “Tangerine” project began.  We decided at that meeting that the three of them would create their own YouTube Channel (real name forthcoming) based on real-world math problems.  It would be a weekly show where they presented a math conundrum to their viewers based on something happening in the news.  There would be opportunities for viewers to suggest problems or topics as well, but the work would always be done by the students.  They’ve even tossed around the idea of writing their own curriculum one day.  

I’ve seen this type of enthusiasm in students hundreds of times throughout my career and it’s always related to the same type of work.  Ryan & Deci would attribute it to something called, “Self-Determination Theory” which hypothesizes that any human needs competence, relatedness, and autonomy to be intrinsically motivated.  In non-theoretical terms, it’s really just offering students relevant and meaningful work that they can connect to.  Genius Hour, Passion Projects, Project-Based Learning, Inquiry-Based Learning, & Service Learning are all examples of how educators are currently harnessing the power of relevance in their classrooms.

So here’s what I’m currently grappling with.  Students would love to pursue this type of work all day every day if we let them.  The group of kids in the Tangerine project has requested to come to school as early as 7:00 a.m. to work on it and would stay until five or later if I had the time.  It’s easy to jump to the conclusion that school should be a place where everyone pursues projects all day long, but in reality, that may not be the case.  It’s made me wonder…

• What would school look like if we gave kids longer periods of time to work on big projects instead of the way we currently teach?  What are the opportunity costs of this approach?
• How do we balance teaching students’ skills with working on the projects themselves so that they can handle the cognitive load required?  What types of teaching structures might work best for this? 
• Do we teach the skills in isolation first and then give students time to explore projects or do we have them work on projects first and teach the skills as they come up? (the chicken or the egg question)
• What professional learning would educators need to successfully approach the classroom this way?  Are there any mindsets shifts that need to occur (within myself and others) related to this?

I wish I could tell you I had an even semi definitive answer to these questions, but unfortunately, I don’t.  I keep hearing that we live in a VUCA world (volatile, uncertain, complex, ambiguous), so it makes sense that we should give students experiences where the answer is not immediately obvious.  However, within this world of unpredictability, there are also constraints that we all must adhere to so it also seems relevant to provide students with structured learning experiences as well.   The only way to really know how much of each is to continually experiment in the classroom and see what works best with our students. 

 

 

 

Best Practice Isn’t Always Next Practice

I walked into a 5th-grade classroom Tuesday morning during our math block and almost walked right back out because I was sure the students were taking a test and I didn’t want to interrupt.  The students were working fervently on a worksheet, pencil to paper, pausing periodically to reflect, erasing at times, and moving on to the next problem.  Literally, a pin could have dropped and I would have heard it.  

I slowly started to tiptoe backward out of the room when I caught the eye of the teacher who was looking over the shoulders of students at a cluster of desks.

“Are they taking a test?” I whispered.

“No, just independent practice.”  

“Do you mind if I walk around and talk to the students?”

“Not at all.”  

Now normally I wouldn’t ask, “do you mind if I talk to the students,” because that’s just a regular part of what I do when I go into classrooms, but I was still mesmerized by the perseverance of these students and was afraid if I talked I’d somehow break the magical spell and ruin the determined working the students were doing. 

As I moved in closer (still slowly) and started looking over students’ shoulders I was even more impressed.  Not only were they highly engaged, they were working on multiplying decimals, a concept that can be tricky, causing some students to shut down and give up without even trying.  Not in this room though.  The air was thick with intellectual engagement. 

Each student I spoke with could articulate not only what they were doing, but why they were doing it.  They had a process for checking whether their work was accurate and did this without prompting.  There was a palpable feeling of this work is important and I want to do it well.  When I think about Danielson Domain 2B, “Establishing a Culture for Learning,” this was it personified.

Deep Learning Doesn’t Have to Always Involve a Big Production

When thinking about student engagement, many educators (myself included) tend to think of having to create elaborate lessons that incorporate exciting content and usually require a lot of time and materials.  Words like collaboration and creativity are hallmarks of next practice that deepen learning and motivate students to be engaged in the work they are doing.

The work that I observed that day incorporated pretty much none of these things and yet the students were unquestionably deeply engaged in the work.  It was a good reminder that as wonderful and effective as collaboration creative projects can be, kids need time to process concepts and develop understanding on their own.  When they work independently, they get to work at their own pace, choose strategies that work best for them and develop their own conceptual understanding.  This leads to self-confidence in any subject area.  

It also reminded me that as much as innovation is important in our classrooms, we also have to make sure we don’t just dismiss everything we did before just because we have learned something new.  Sometimes we simply need to tweak what we know has worked in the past layering in new ideas.  The work students were doing in this lesson was essentially a worksheet of math problems.  Many would dismiss this as an ineffective old school practice.  However, because the teacher had communicated clear expectations with success criteria to students, in addition to having a classroom culture that values learning and rising to challenges, the worksheet became a powerful learning tool for all.