Empowered Problem Solving Workshop: My Takeaways

My takeaways from #epsworkshop (April Soo)

I love it when professional development is purposeful and practical.  I’ve been following Robert Kaplinsky for some time now and finally decided to enrol in his Empowered Problem Solving Workshop.

My reflection post in the last module of the empowered problem solving workshop.
My reflection post in the last module of the workshop. Sad it’s over…

I don’t have time for problem solving in my classroom.”

TRUST me, I’ve been there. The first time I ever taught Calculus, my talk time during an 80-minute block was probably at 50-80%. It was awful, I was so dehydrated. It also didn’t help that I did not have a strong enough grasp of the material that I could deliver problem-based lessons with any sort of confidence. I was simultaneously teaching and relearning the material myself so how could I expect my students to develop these deep understandings when I was barely keeping my head above water?

No bueno…

Looking back, I realize that trying something is always better than nothing.  Problem solving isn’t something you do “if you have time for it,” like at the end of a unit. Because you know what? You’re never going to have time for it. You’ll always feel like the time could be better used for review, a project, to reinforce a skill…etc. Problem solving is not something you should “make time for”, it needs to be integrated into the content we teach. I would argue that the heart of mathematics is problem solving. The sooner we realize that math isn’t just about getting the right answer, passing a test, or even getting into university, the sooner we can teach in a way that honours what doing mathematics is truly about.

Why Problem Solving?

My students lack the basic skills and understanding to do these types of problems.”

If that is what you’re thinking, know that I too, have had this same thought. Herein lies the beauty of problem-based lessons: students don’t need to be pre-taught skills or content, they can learn them along the way.

“I’ve tried problem solving before and it doesn’t work. Students just want to be told what to do.”

Guilty. I’ve been there too. It’s not going to be perfect the first time you do this. Students WILL resist, and you need to persist. If you don’t genuinely believe that problem solving is worth the time and effort, your students won’t buy into it either.

When I first tried problem-based lessons, I did not spend enough time anticipating student responses and was taken off guard by solutions or strategies I hadn’t thought of. I tried to lead meaningful discussions about student work, but because I wasn’t getting the engagement I wanted, sometimes ended up making the connections for the students (I’m still working on scaling back my “rescue the student” instincts). Success, however, comes in small doses, like getting a student who normally never raised their hand to try a problem on the board, or maybe just seeing a decrease in off task behaviour.

Teaching problem-based lessons takes effort, from the student AND the teacher, but that is precisely why its so awesome. Students aren’t just passive recipients of knowledge, and teachers don’t need to spoon feed their students.

My Biggest Takeaways

  1. Problem-solving: Just DO IT!

2. Be deliberate about how to facilitate meaningful discussions in math. Often, we get to an answer and that’s it. Full stop. Getting to the last act of a 3-Act Math Task doesn’t mean that the learning stops there. Here is a wonderful opportunity to discuss various approaches to the problem, potential sources of error, limitations of our mathematical models, and to make connections between different solutions. This is an area where I feel I need the most practice, and it is also most difficult to implement during this time of online learning due to COVID-19. I’m limited by the fact that I cannot circulate the classroom or peep over students’ shoulders to see where they are at, but I am trying to find alternative ways to connect.

5 Practices for Orchestrating Discussion

Here’s a snapshot of me working out a selection strategy for sharing student work, and anticipating questions that might be helpful to ask:

My rough notes as I thought about how I might lead a discussion about student work.
Which responses would you pick to share? In what order would you share them?

3. You can always add information, but you can’t take it back. Dan Meyer refers to this as turning up the Math Dial. Robert Kaplinsky talks about “undercooking” our students (like you would a steak). Ask questions in a way that ranges from least helpful to most helpful to give your students a chance to make connections for themselves.

4. Ask yourself “Why” more often. Why am I doing this problem? To introduce a new concept? Get my students used to productive struggle? Problem completion?  Be intentional about the purpose of your lesson and what can be realistically achieved.

5. Ask better questions. Shallow questions tend to lead to false positives. A student may appear to have procedural knowledge, fluency, and conceptual understanding, when in reality they are just good at replicating the work that you do (me in school…). You might be asking, “How do I really know if my students have the components of mathematical rigor?” Check out Robert Kaplinsky’s Open Middle problems and Depth of Knowledge Matrices.

Depth of knowledge matrix (credit to Robert Kaplinsky)

What do you do when students submit low quality/low effort work?

I’ve been taking an online workshop to learn more about practical ways we can implement problem-based lessons in our math classrooms called Empowered Problem Solving by Robert Kaplinsky (#mathhero #teachercrush). In one of the workshop modules we troubleshoot various issues that may arise throughout the process of teaching a problem based lesson, for instance:

  • What happens if students don’t ask for information that they need to solve the problem?
  • What do you do if a student shares a strategy that you don’t understand or did not anticipate?
  • What do you do when students submit low quality or low effort work?

That last question really had me thinking a lot about assessment. When students submit low quality work it is often because they don’t know what the expectations are. Something I do quite often in my classes is share student work samples after an assignment or test to address common errors or mathematical practices. Here’s a brief overview of my journey in providing feedback for my students:

“What Should My Answer Look Like” Posters from MathEqualsLove,
Examples are from my class 🙂

I don’t make enough time for level 3 work, and I should. Within a single semester, my goal is to give students at least two opportunities to do meaningful peer assessment. Of course, I anticipate this to be a gradual process, and it might take some time to get to a point where students can comfortably and confidently do peer assessment.

Assessment is difficult; even with a simplified assessment scheme one two teachers may assess the same student work slightly differently depending on their interpretation of what is “correct” or what qualifies as “sufficient reasoning.” Unfortunately these discrepancies will arise no matter what, but I think there is a lot of value in putting the students in our shoes and giving them opportunities to assess each other’s work.

Inspired by the Empowered Problem Solving Workshop, I’ve created a Mathematical Peer Editing Checklist and Feedback Form with practices I value and that I think is general enough to be used with most and/or all problem-based lessons. I’ve also incorporated an “overall feedback” section in the form based on Kaplinsky’s Levels of Convincing (originally inspired by Jo Boaler #mathhero #teachercrush) that asks students to rate each other’s mathematical writing based on how convincing they think their argument/work is.

  • Do you think this framework would work with your students?
  • How would you modify it to make it better?
  • Anyone have suggestions for a more concise title, as opposed to “Mathematical Peer Editing Checklist and Feedback Form”?
  • Thoughts on my use of the word “writer” to describe the student who’s work is being critiqued?
  • Other thoughts?