Tag Archives: problem

Updates on my problem-based experiment in algebra 2

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.

 

bp

Internalizing feedback without seeing it

Feedback on exam in spanish

I’ve found that students all too often overlook, or simply ignore, the feedback I give them on assessments. For whatever reason they just don’t use it. This is a problem.

I value reassessment and see feedback as crucial in that process. If a student struggles on an exam, I need them to learn from their misconceptions. My feedback reflects this. I’ve always provided fairly detailed feedback, but this year I’ve stepped it up significantly. In fact, all I do now is give feedback. I provide no scores or grades on exams. This helps, but I still need to find ways for students to grow from the feedback they receive.

I have experimented with kids relearning concepts the day after an exam without seeing their actual exam. The day after the exam, I give a copy of the SBG results to each group. Each student uses the data to identify the specific concepts that they need to relearn or review. The groups are a mix of proficiency levels (based on the exam results) so if a student needs help with a particular standard, there’s someone in their group that understands it and can help them. I also give them blank copies of the exam to work on and discuss.

After about 15-20 minutes of peer tutoring, I give them their exams back. Based on their newfound understanding, at least some of their misconceptions should be alleviated. They now spend 15-20 minutes correcting their mistakes on a separate sheet of paper while directly responding to the feedback I’ve given them on the exam.

Ideally, this means that they are using feedback from their peers to understand and respond to the feedback I’ve given them. It serves as relearning/remediation before they retake the exam. What I’m missing, though, is a reflection piece that ties into the feedback as well.

A colleague conjured up a different spin on this. After an exam, he informs students which standards they didn’t earn proficiency on. (He doesn’t hand back their actual exam either.) He allows one week (more or less) of relearning/remediation on those standards – either on their own, or with you. He actually uses an online resource for this. Then, when they feel ready to retake, he returns their exam and asks them to self-assess and correct their original mistakes. If they can, he allows them to retake. If not, they continue relearning. It may not focus on feedback, but I like this.

Closing thoughts: what if I do get my students to internalize my feedback? Are they just going to be doing it to satisfy the requirements that I ask of them? When they leave my classroom, will they view feedback as a necessary component of success? Will my feedback really make a difference? How else could I get them to value it?

 

bp