As a means of tracking the progress I make in my newfound problem-centered classroom, I’m posting some recent developments and thoughts. These notes are incredibly informal and far from polished.
- I’ve settled on assigning 5-6 problems for homework. When they come to class, I give the groups 20-25 minutes to peer review and make sense of the problems. They show their work on the large whiteboards around the room so everyone can see. As a class we then spend the last 10-15 minutes of the period in a whole group discussion with students presenting their solutions on the large whiteboards.
- I’m now thinking…why can’t I use visibly-random groups as they peer review the problems??
- I need to do a better job of establishing coherence within the problems. For the first 20 problems or so, students feel like they were doing random problems covering unconnected concepts. In some ways, they were since I was trying to establish some norms and routines through the problems.
- Admittedly, the first 20 problems lacked coherence (and therefore meaning). It’s ok to intersperse concepts, but I should have a focus (or foci) for each problem string we go through.
- It seems around 20 problems is a fair amount for each exam to assess.
- Duh: class size matters! Periods 1 and 8 both downsized and it made a world of difference. I now have groups of around 5-6 discussing the problems. It’s only been a few days, but this has been so much more effective than the whole-class discussions we had at the onset. As I visit groups, small group instruction is the norm. I’m doing my best to simply ask questions and avoid direct instruction on the problems. I think I need a develop a simple protocol to follow when I approach a group.
- One thing I should get back into is asking for “group questions” only. There are too many students doing their own thing and not all students in the groups are actively discussing the same problems each day. I need to push this more.
- After emphasizing problem-solving and group discussion ahead of answers, I started providing correct answers on the board halfway through the period. Students were uncomfortable because there was too much ambiguity in final answers (thank you high-stakes exams), especially since sometimes I can’t get around to everyone’s work.
- I am worried about the more introverted students in the class, those not openly engaging in group discussions. At times they seem to not be engaged.
- How should my exit slip or “closing” to each day look? Note: I need to make time for this.
- I haven’t been surfacing problem-solving strategies as students work through problems. Related: there hasn’t been a lot of focus on the various ways and perspectives to solve these problems.
- I need to organize a day/lesson where students purposely make connections between problems and establish big ideas for the course.
- Makes me think of Dan Meyer’s co-authoring the class post. I’m thinking we, as a class, can create a large concept map on the wall with paper and string making connections between key concepts and problems. In this way, instead of me saying, “all these problems belong to unit 7, exponential functions,” students can surface these sorts mathematical connections for themselves and own the content. That’s the dream, anyhow.
- Maybe start with a table with columns for problems, big ideas, key vocabulary?
- I’m allowing for students to create a 3×5 index card for use on the exams. I don’t do review days before exams so this is my way of getting them to prepare. It also forces me to think creatively about the problems I include on exams!
- To break up the monotony of this structure, I need to begin planning lessons that don’t revolve the same sort of group discussions. I also want students to see that class won’t always look the same.
- I have seen whiteboards being used very effectively. Student thinking is public. At times, students are moving freely around the room to independently seek out methods and strategies.
- With these 12 whiteboards being actively used in every part of the room, I think I have successfully defronted the room. That’s a win.
- Because the boardwork students are doing is so important, and since students can’t use their phones in my school, at the end of the period I want a student to take photos of the boards using an iPad. They would then email it the class. This would alleviate students’ feverishly copying correct work into their notes during the whole class discussion.
- Another thing so far that I love is that the class has been focusing on doing and actively engaging with mathematics. Plus, there’s been lots and lots of struggle with the problems. That’s great, but now I just my students to be comfortable with being uncomfortable. Hopefully in time.
- I managed to set up a spreadsheet aligning the problems to the standards-based grading “concepts” that I used last year. Although I don’t share this with students, I’m using it to guide the problem strings that I write.
- I’m still far away of student buy-in — which I desperately need. This is due in part because of the rough start I had in sequencing the first series of problems.