Rough Draft Thinking
My push towards teaching math through rich tasks revealed a problem in my classroom--students didn’t want to dive into the math, they wanted to get the right answers. I had to work on creating a classroom culture which valued risk-taking more than correct answers. This shift has been central to my professional work for years. In order for the whole process to work, students needed to feel safe in our classroom community. Normally, it took a couple of months to get students to believe I actually wanted to know more about their thinking than whether their answer was ‘correct’. In years past, most students were willing to present their partial solutions by about November. This past year, that happened late August. For real. The change: I started the year with ‘Rough Draft Thinking’ paired with ‘No hands up, except to ask a question’.
It started with a PD session over the summer. I don’t remember if it was the end of the year or the beginning of the year. I do remember not having classes to teach that week. Anyway, I was sitting with a group of Humanities teachers and they were talking about how in a semester they only get a couple of essays or projects done. Instead of asking students to turn in lots of different essays, they ask the students to perform multiple rough drafts on every essay. The conversation went around the table about how these different teachers deal with the various problems they encounter with the process. I can’t think of a word that was said after that. I was fixated solely on the sheer amount of revisions. These students are putting down initial ideas and then reworking them over and over and over again. Really, that’s what life is like. We try something and it doesn’t work and then we try it a different way. Repeat the process for 80 years. But in my classroom, we didn’t revise anything.
As I mulled over the revision process in life, I decided to steal the “rough draft” concept from the humanities and apply it to math class. When I asked students to present their thoughts, I would ask for their rough draft thinking. For the first month of class I’m sure I sounded like a broken record.
- “I’m looking for your rough draft thinking on this not a final solution method.”
- “When you present, you’re giving us a place to start the solution process; you’re giving us a rough draft. Then, the rest of us get to be good editors and start the revision process.”
- “If you get it right the first time that means I’m not giving you challenging enough problems.”
- “Mistakes are evidence that the work I gave you was tough enough to make you smarter” (Wiliam and Leahy, 81). I even made a poster out of this one.
All of my comments before and after students presented initial solution strategies were about lowering the stakes of failure in my classroom. I wanted to make it so getting something wrong the first time was completely expected (Wiliam and Leahy, 172). That’s how life works--even in math class.
No Hands Up, Except to Ask a Question
What this idea doesn’t do is solve the problem of only 4 or 5 kids raising their hands to answer questions in each class. For pretty much all of my professional career I’ve asked a question to the class and then called on students that raise their hands. With some well positioned think-pair-share opportunities and group-work I had it workable. Mostly. After reading multiple authors talk about the benefits of cold-calling I decided to give it a try. I cut up index cards into fourths and put students’ names on them. Rather than calling on students with hands up, I pulled a card from the top of the deck. Wiliam and Leahy call this: “No hands up, except to ask a question” (Wiliam and Leahy, 65).
I tried this way back when I was a new teacher. It went horrible. No, I don’t think you understand--words cannot express how much I disliked the process. It caused unnecessary disciplinary issues when students would get defiant and refuse to participate. The students fought me tooth and nail to go back to just raising their hands. I hated it. This time, thankfully, things went differently. There was zero push back on me calling on students who didn’t know the answers! None. I can’t believe it. When a student didn’t know what was going on I asked them to give a starting point for the conversation: How might they approach the problem? What information do they see that might be relevant? ‘IDK’ isn’t an option if you’re called on--you have to help the class move forward somehow. By lowering the cost to participate in class most students were no longer fearful of getting called on and every student was willing to participate. They knew they were only being asked for their rough draft thinking. Getting it wrong was expected. They only needed to give the class a place to start the revision process.
We had another mantra in class: Be kind. Be brave. I stole this from another math teacher. If memory serves me correctly, she got it from the new Cinderella remake. Whatever. To help create the culture of low risk participation we talked about ‘Be kind. Be brave.’ as students walked up to the front of the classroom to present. We did this at least once a week for the entire year. It’s probably excessive but I wanted to keep it as a norm in our classroom. No matter how the outside world treats people, in my classroom kindness is king.
Okay, here’s how it works. Students who are presenting need to be brave. It’s nerve wracking to present a solution process which you know is probably wrong. It takes guts no matter how low the risk bar is set. Be brave.
Students who are listening need to be kind. We have no clue how the person presenting feels. Whether they look nervous or not, we don’t know what they’re thinking. Even if they are people who normally don’t mind talking in front of groups, they could be having a bad day. We need to be kind because we want to be a safe community for sharing ideas. If you make an unkind remark about someone’s presentation, I’ll ask you to leave immediately. There can be no laughing, or snickering, or giggling. At all. It doesn’t really matter whether it’s directed at the presenter or not. The presenter will feel like it is. No questions asked. No warnings. We will honor each other’s ideas and critique them with care. Be kind.
Unexpected survey results
At the end of the year I gave a 5-minute survey about my classroom culture. Here are the results from the survey. When asked about using “No hands up except to ask a question” students were quite positive with 85% saying they liked it. I asked several questions about whether students felt safe contributing to the classroom discussion and whether or not students felt like I valued their thought process more than the “correct” answer. Though both questions came out to about 94% in favor of what I was trying to do in my class, only one student responded ‘no’ to both of those questions... and he was angry at me for recommending he repeat the class. So, take that with a grain of salt. That means the students who didn’t feel safe contributing to whole class discussions did believe I valued their thought process more than whether they were right. The students who didn’t believe I valued their thought process still felt safe contributing to group discussions. Weird and unexpected.
When asked about whether this class helped them become more confident math students, about 64% said yes, 31% said there was no change, and 5% said they were less confident. I so wish that 5% didn’t exist in my classrooms but that’s the reality. Some students did worse in my classes than in previous classes. What’s interesting here is that the breakdown between my Algebra and Geometry students was about the same.
Okay, let’s give a little background for why this blew my mind. I teach middle school. My Geometry students are spectacular math students--they are all at least 2 years advanced (some of them 3). I expected them to be very confident in their math abilities. As it turns out, they weren’t. That the introduction of rough draft thinking helped them just as much as it did my Algebra students was completely unexpected.
After sitting with the results for a couple of days it started to make sense. These students are the ones who are excellent at memorization and abstraction. They have no difficulty moving symbols around like musical chairs until someone says ‘stop’. Having a math class which intentionally put sticks in the spokes of the memorization bicycle is super frustrating for them at the beginning. It calls into question what being “good” at math looks like.
Rough draft thinking decreased the stress of needing to understand content the first time through or getting all the answers right the first time in order to be ‘smart’. Slowly, my wicked smart kiddos began to disassociate speed and correctness from intelligence. It took time but it happened. That’s a win in any teacher’s book.
P.S. - If you're interested in learning more about rough draft thinking in math class, I know Amanda Jansen is doing research in this area. Give her a follow on Twitter (@MandyMathEd).
P.S.S - It’s crazy to me that my classroom played out the research of Jo Boaler and Carol Dweck this year.