Do students need to finish every problem?
When I have asked this of colleagues, everyone has responding with a resounding no!
- Definitely not!
- Not every student needs that much practice.
- It’s okay if not everyone gets to the challenge work!
- As long as they give it their best effort!
- I just want them to get the ‘big idea!’
After asking this a bunch of times, I realized that people were envisioning different assignments, and I think many of them may have imagined a worksheet with many computational problems, even if that’s not something that factors into practice with great frequency. Sure, if there are 20 practice problems on a page, doing 15 is just as good as 20, right?
The Problem of Problem-Based Learning
But what if these problems aren’t for practice? In problem-based learning, students are given time to wrestle with a problem before the class discussion, and the learning has been made explicit. In problem-based learning, students often work with a series of problems within an activity that each contribute to deeper understandings. Missing a problem might mean missing exposure to a particular idea. It’s not truncating an assignment, it’s truncating learning!
It can feel tempting to slowwwwwwww down. As the class waits for students who are still processing the activity, ‘quick finishers’ are fed a steady diet of more (and more) work.
This looks different in every class. I’ve seen it work beautifully. Also: sometimes, a task is open enough that students can continue to engage with it in different, meaningful ways. I love these days! (e.g. No More Mathematical Matchmaking: The Return of the Inaba Place Value Puzzles; and The Striped Barbeque Snake Puzzle: Exploring ‘Challenge’ in 3rd Grade.) Unfortunately, I’ve never figured out a way for this to be our daily experience, while also offering a coherent pathway through the curriculum frameworks/standards. And that’s okay. Many days, we offer closed tasks and focus on the discourse.
So: for closed tasks, how much do students need to do?
Do students need to finish every problem?
I taught sixth grade math in my district’s Remote Learning Academy this past school year. It was the only option for middle school students to stay remote. Thus, we had students transfer into (and occasionally out of) our program over the course of the year. We had a lot of students transfer in as COVID case numbers rose in the fall and winter.
Every time a student transferred into my classroom, their first question was: “what’s the minimum number of problems I have to do?”
At one school, all students were required to finish 13 slides.
At another school, students’ homework was to finish however many slides they hadn’t finished in class. Students that had completed everything had no homework. Students that had only finished a few problems had a lot of homework to do.
I’ve never seen these teachers in action, so I can’t really speak to their decisions. I don’t know their context. I can explain my context, though.
This is the structure I used within each activity. We began with an invitational, discourse-heavy warm-up, before launching the activity (on Desmos). Students worked in breakout rooms, either individually or with classmates. After a few minutes, I would pull students back into the main room to examine student work and discuss ideas (activity synthesis).
So did students need to finish every problem before engaging in the discussion? I decided: no.
Where does the learning happen?
I thought back to this blog post from Max Ray Riek: “Explicit Classroom Norms to Teach Kids How to Learn From Solving Problems” (Illustrative Mathematics blog, July 29, 2019). Max advises that “most of the learning in a problem-based classroom happens when students compare their ideas to one another.” Students don’t need to uniformly finish every problem before the discussion because they “had opportunities during the launch and work time to develop a better understanding of the problem. The teacher can set a goal of everyone being ready to make connections between their ideas and their classmates’ ideas, even if they struggled with the problem.”
Then, instead of asking students to finish problems they didn’t complete before this synthesizing discussion, I asked them to work on separate homework practice problems. Because the practice problems were designed to be worked on after the discussion, the problems were generally ‘harder’ than the ones from the class activity. For example, the numbers may be less ‘pretty,’ or the context slightly more complicated. I wanted students to work on applying their understandings, not filling in answers to problems we’d already discussed.
I worried that some students would feel frustrated that they never ‘finished’ an assignment. There were some students that took longer every single day, for a variety of reasons, like processing speed and distractibility, and how deeply they engaged with the problem.
I tried to assures students that the assignments may be incomplete, but that didn’t mean that the learning was. This seemed to reassure a few students.
Most students didn’t seem to need this assurance. They already felt some freedom that they didn’t need to complete the assignment. They seemed confused about why I asked, so I stopped asking. I wondered: did they see me as less rigorous than the other teachers?
Eliciting Feedback from Students
In the last week of the school year, I asked students to anonymously complete a teacher report card. I used the one from Matt Vaudrey (@MrVaudrey) which was immortalized beautifully in a blog post by Martin Joyce (@martinsean). I used the google form from @MrVaudrey.
Finding this was a saving grace at 11pm on a Thursday, so a million thank yous to Matt and Martin. I made almost no edits.
There were a few questions that helped address this dilemma I had: were students okay with leaving assignments incomplete?
So it looks like most of the students felt like the classwork, homework, and assessments were reasonable and fair. That’s a good start…
This prompt was a little vague. I wondered why more students didn’t give lower scores for pacing, since I frequently let them out of class a minute or two (or three? hahahaha) late. They were still able to make it to their next class on time, but I cut into their break between classes. I think some students did interpret this as pacing within the lesson, which was often fairly tight.
This response really got at the heart of the matter: did students have enough time to finish assignments? 63.6% of my students gave the highest “strongly agree” rating for this! From there, I think it’s fair to say that students did not worry about not finishing as much as I worried, although I’d love to hear from those students that gave scores of 3.
Very few students finished all of the slides on Desmos activity builder. We closed the year with only 51 students, but at the Remote Learning Academy’s peak we had roughly 75 sixth graders, and only 4 or 5 would finish everything. That means that lots of kids are okay with not finishing.
I wonder if the fact that the problems appeared as individual screens on Desmos contributed to the general acceptance of not finishing. Students looked at one screen at a time. They could navigate to other slides that I had opened with the pacing feature, but it doesn’t have the same feeling as seeing all of the unfinished problems on a printed page.
More than half of all students gave the highest rating of agreement for ‘leads good class discussions,’ too. Of course, I’d love to hear more about what students thought, but for the crude data this is, I feel encouraged. Students seemed mostly okay with not finishing assignments, and that they benefited from the class discussions, as a key leverage point for learning.
“What do you like BEST about this class?”
Students wrote a variety of responses. Here are a few that related to this dilemma about whether students are okay about not completing assignments:
- Talking and comparing ideas
- We learn in a fun and interactive way
- How we can be fun and casual but also do the assigned work
- It’s fun and creative
- When we all joke around and work together
- There is a mix of class discussions and doing independent work
- She’s very kind and doesn’t shut down ideas even when they are rong. (sic)
- Class discussions.
- The teacher is encouraging and open.
Another prompt was “how can Ms. Laib’s class be improved?” Not a single person wrote “give me more time to finish,” but maybe they were thinking that and didn’t know to write it. I don’t know. (Two kids wrote about ending on time so that they could have their full five minute break. Oops. Sorry, everyone.)
Where do I go from here?
I feel more empowered to talk with teachers about this data. Yes, it’s data from one grade level at one moment in time, and perhaps not fully generalizable. I think it’s also encouraging: maybe we really can focus on the learning and not on the task completion? Without harming student work habits?
It’s something to think about.