Summer School Part 2: We give every task a try.

*For Part 1 of this summer school blog series, go here!

Norm 2: We give every task a try.

In May, I attended YouCubed's Teaching Mindset Mathematics workshop at Stanford with some colleagues with the plan to implement their summer school curriculum for our summer school program. Having a curriculum with a focus on developing positive attitudes towards math, collaboration and openness felt like a nice fit for a four-week program that wasn't focused on credit recovery. The tasks we did at the workshop gave us a chance to get messy with math, put our heads together with thoughtful group members, and made us giddy imagining how the students we'd be teaching would fall in love with math done "this way". How naive of us! As you can imagine, not every task landed exactly how we had imagined. It turns out, it's not enough to open tasks.

There's always a lot of buzz about the nature of the tasks we put in front of students, with a tendency towards (suggesting) that the more open the task is, the better. An open task is one with a low floor and high ceiling, one with entry points for theoretically all students and opportunities for multiple approaches and levels of engagement. What I don't think gets talked about enough is, how open is too open? Or, when do we close parts of the task, whether through establishing some sort of structure for collaboration or defining some success criteria, in order to support students? The open tasks that I had experienced as a learner at Stanford played out differently in a room full of 7th graders who had experienced mostly direct instruction in their previous math classes.

One of the first tasks we did was Four 4's (Sarah Carter blogged about how it went in her class awhile ago here, and I reallllllly wish I had read it before doing the task with kids!) where students are challenged to calculate to find the numbers 1-100 (we started with 1-20) using four 4's and any mathematical operation. Fun, right? Open, yes? Challenging and compelling, amiright!? Orrrr not. Students were stifled by the openness of this task, and for the first 20-30 minutes, some sat paralyzed, discontent with the direction to "try something".
The thought that this task could literally go on forever was terrifying to students who had been used to having the learning of each lesson wrapped up nicely for them in a bow. 
Convincing my students that it was ok to try something and find that it didn't work was remarkably difficult, and even coming up with a solution together didn't seem at first to move stuck students forward. Eventually, encouragement to find a thinking partner in their group helped some students as their peers started having some small successes and being more brave about making a mistake. And when I revealed that we would be revisiting this task throughout the four weeks of summer school and keep a public record  (poster with sticky notes) of the solutions we had found, most students seemed to shift from discomfort to willingness to try. Together, we paused and defined some success criteria, which was that given each period of time that we tapped into this task, they would try something, even if it didn't result in a unique solution. By the second week, two students had (voluntarily) taken on the roles of verifiers, and would stand at our poster and check that the solutions posted were correct. Throughout the two weeks, students added equations until our poster was overflowing. One student told the class that he had lost sleep over figuring out how to get an answer of 13. A happy ending if I ever heard one, but one that wasn't imminent at the launch of the task because it had initially been too open.

This has me thinking a lot about how students experience problem-solving. How do we balance encouraging students to jump in when faced with a task  (whether with an open middle or open end) with getting them to make sense of a problem and look before they leap into a solution path? It's like, we want students to try something, but not in an erratic, random way. Can we have both? I would love to hear your thoughts!


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