The Perseverance Problem (and one solution)
A joint blog post by coach Joanna and high school math teacher Leah, introducing one community-created solution to building perseverance…. 8Q5
Joanna: There are so many open-sourced resources for great tasks available to us online. We love Dan Meyer, Robert Kaplinsky, Geoff Krall’s maps, MARS, Open Middle, just for starters. We have been thrilled over the last 6 years to learn about and through these tasks. In fact, a small group of math teachers across WV have collaborated to organize our favorite OERs by units inside integrated courses – check out WV Math Tree, if you’d like to stop googling!
Leah: Here’s the thing… as a dedicated math teacher, I go through the process of selecting the perfect low-threshold, high-ceiling task for my students, I write a thoughtful lesson plan, but then it can turn out to be a huge flop upon implementation. Here’s what was happening to me… students try for about 30 seconds, then slam their pencil on their desk, put their heads down and declare that they are done.
What am I supposed to do? How can you get students to continue to work once they are stuck? Can you really teach persistence, or is it an inherent, fixed aspect of character by the time someone enters high school? Maybe this is a skill they should have learned long before high school. Maybe this is out of my control.
Joanna: So what would you do?
Leah: I would teach the task. I would ask guiding questions, and a few students would lead the way to help me through it. The class was fine, we explored some math together, we made some connections, but I wasn’t doing what I wanted to do. As math teachers, we are not just accountable for teaching the content standards, but also the process standards. I want all students to “Make sense of problems and persevere in solving them.” I knew that, without the perseverance to dig in, hit a roadblock, and then try something else, students would never realize this standard.
Joanna: This is most definitely a common problem of practice. It was bugging teachers at all levels, at all 6 schools I work regularly in. So we talked about how we could assess what we value. In the same vein as our process to dream up CRAVE, I came up with a first draft of how we might structure a class where the primary purpose was to develop perseverance. 8Q5 was born, tweaked, refined, and grown through a collaborative effort of all middle and high school math teachers in the district.
Leah: So let me tell you how it works! We take a problem we like from one of our favorite sources and place it on an 8Q5 template. The front just has room to work the problem. The back has a self-assessment and room for a question.
The assessment piece is a rubric that makes explicit what our idea of productive struggle looked like. It came to measure politeness, effort, relevant and specific questioning, creating models, and persisting. Before implementing the first 8Q5 task, it is important to go over the rubric with students so that they are aware of the grading criteria. It is worth noting that a student could get only half of the solution correct and still receive a 90% on the task!
Note: To implement 8Q5, students must be sitting in teams of 3-4 students. If your class does not already use cooperative teams, have heterogeneous teams assigned ahead of time to use for the task.
Students are to work for 8 minutes alone, without talking. It is not necessary to have students move away from their team, but it is important that students work completely alone during these 8 minutes. The teacher is also unavailable to help them during this time. It can be helpful to remind students that they will have an opportunity to receive help from their team and from the teacher – but not during this time.
**Note: we start with 8 minutes each year, and grow the initial time as students acclimate.
Students are also to be thinking of a question they have during this time.
At the end of the 8 minutes, students have 2 minutes to craft a question that is both relevant and specific, and this will count for part of their grade on the task. Direct students to the portion of the rubric page that has space for them to write their relevant, specific question.
It might be helpful to give examples of questions that meet one criteria but not the other. For instance, “Why is grass green?” is a specific question, but not relevant to reaching the solution to the task. “How do you solve this?” is a relevant question, but is not specific.
If a task referenced intercepts, a relevant, specific question could be, “Can someone remind me how to find an x-intercept?”
It is also important that students write only one question.
The Question Process
Teams are then given 5 minutes (can be adjusted as the teacher gauges class progress) to ask their question to their team. Rules: Student A asks a question. Going round the circle, students B, C, and D start their response one of three ways. “I think that…”, “I’m sure that…” “I disagree because…” or “I’m not sure either. I have the same question”. Student A must thank each of their teammates who respond to their question. This is not a team collaboration time (we do plenty of that daily); this time is only question and answer. Students are not allowed to debate during this process.
For the first implementation, it is helpful to select a team to model the process:
Student A: How do I find an x-intercept?
Student B: I think you plug in 0 for x and solve for y.
Student A: Thank you.
Student C: I disagree. I think you plug 0 in for y and solve for x to find an x-intercept.
Student A: Thank you.
Student D: Sorry. I’m not sure either.
Student A: Thank you.
It is important to note that student A is not allowed to say, “Oh yeah, because an x-intercept lives on the x-axis, so it makes sense that y would be 0. You’re right, Student C.” This is not discussion and collaboration time; it is just question and answer time. Remember, we are trying to build individual persistence. We speculate that learning to ask the right question of others, together with the discipline to answer and listen carefully, may be central to the process of working yourself through being stuck when solving problems on your own.
The team repeats the process until each student has had a chance to ask his or her question.
FAQs for the Question Process
What if a student understands the task and doesn’t have a question?
Students are required to ask a relevant and specific question as part of their grade. Students may use the sentence starter, “Does anyone agree that…” to ask their question without giving away the whole solution to the task.
What if a team is not able to answer a question?
After the question round, and before moving on to The 5, the teacher will address any questions that the team was not able to answer for a student in their team. Students are to hold up the paper where they wrote their question, and the teacher will read off the question and answer it to the whole class.
After the question round, students are given 5 more minutes to work independently without talking to revise their answer. Encourage students to add on and amend their work rather than erase their work.
At the end of 5 minutes, students are to fill out the self-assessment portion of the rubric.
After students submit their rubric and task, discuss the solution as a class and see if there could be other approaches to the task.
Leah: With at least monthly implementation of the 8Q5 process, my class culture changes to value persistence. This has happened at all levels, in all four years that I’ve been implementing this approach. Students are encouraged by good scores on a task even when their solution was not completely correct. Students got better at answering one another’s questions, more willing to speak up, and habits in my class changed even when we weren’t doing an “8Q5” task.
Joanna: Leah’s not alone. Across three schools who have been regularly implementing 8Q5 tasks, all teachers report similar outcomes. We think that we removed some of the social pressures of being ‘dorky’ or the temptation to pick fun by making the conversation part of the grade. We think we removed some of the anxiety about being wrong, and replaced it with incentive to keep going when you’re not sure.
We’d love to have folks in other settings give 8Q5 a try. We plan to devote a second blog post to answering questions you might have, and talking about how iterating on this approach over time with explicit focus on one sticky piece at a time has really improved our learning and teaching. We’ve attached a sample lesson template and student self-assessment template, which would be the back side of a one-page student task. We’d love to have teachers in other settings try your favorite tasks in an 8q5 frame, and join us in conversation and in tinkering towards better math teaching and deeper math learning.
-Joanna and Leah