Close your eyes and imagine a place, on a planet far far away, where students relish doing challenging homework problems…on their own and smile while doing them; in fact, where they may even be inspired to do individual homework and have no compulsion to cheat. A cozy place where during most of a three hour lecture period the instructor mingles casually with students discussing the beautiful and big ideas of her discipline, while the students intensely collaborate and innovate. And where sophisticated (and correct) subject-matter language, punctuated with phrases such as “how do you know that?” or “what’s your evidence for that?” or “what if we tried it this way?” are coming from students’ mouths, not from instructors or teaching assistants.
Welcome to AP50, a new applied physics class in the School of Engineering and Applied Sciences at Harvard University, taught by Professor Eric Mazur and preceptor Carolann Koleci. Students are freshmen, sophomores and juniors and from a mix of disciplines. The course is equivalent to introductory, calculus-based physics.
I spent the good part of an afternoon this week hanging out in this alternate universe–with all the landmarks mentioned above. I spoke to 8 students about their experiences, and overwhelmingly they reported sincerely enjoying doing homework. Here are three qualities they pointed to that differentiated their experience compared to traditional courses.*
3 Qualities of Enjoyable Homework
1. Graded on effort versus correctness
The first quality of enjoyable homework has to do with the approach to grading. AP 50 problem sets are rigorous, but graded on effort versus correctness. Students are required to do problems and show their work and explain their thinking, versus arrive at a correct answer. In fact, one student told me: “First of all, there is not really a right answer to some of these questions. I don’t know if I have ever gotten a problem like that before.” On the topic of grading, another student said, “these problems are graded on effort not correctness. I felt less pressure to find the right answer and more freedom to explore.” She went on to suggest also that this strategy might minimize cheating, because the end goal is not one right answer.
Another student stated, “I liked the problem set, I could fiddle around, try stuff out. If I didn’t get it right, I could just try something else, and if it came out wrong, I could just figure it out today with my group.”
This approach emphasizes the means, as one student indicated, rather than the end, and mimics the kind of work we do as experts–lots of trial and error before arriving at a solution.
2. Autonomy is encouraged
In AP50, homework is set out in two stages: 1) students work on the problem set alone, at home and 2) they spend the first portion of the following class period going through each problem using a reflection guide and with a permanent team. Students don’t turn in their homework until after this reflection, and make marks on their individual problem sets with colored pencils so instructors can see what they did at home and what they did with their team. One student commented that this was very different from other classes where homework is almost always done (and encouraged to be done this way) in groups. “The night before a problem set is due, I would normally be going to study sessions, form study groups, work out problems with my roommates, etc. Last night, I was inspired and encouraged to do these problems on my own with the promise of collaborative work today.” (No, I am not making that up!).
Another student reflected, “in a traditional class, we would all be standing out front before class comparing and changing answers on problems before we put them in the dropbox, but none of that was going on today, knowing you’ll have the chance to collaborate.” Another student mentioned how in traditional courses when you are working with groups to do homework it is “hard to know what work is your own.” In this class, however, he knows what he’s done, and what he has gotten from others.
Another student emphasized, “I am classically trained.” He went on to explain that in more traditional approaches to problem sets, he was always given problems with explicit “variables and equations.” He went on to comment, “here, I have to think of my own variables and find an argument, not an answer, and this is really interesting.”
3. Reflection is built in, rewarded, and the opposite of boring
While accurate self assessment is a characteristic of expert thinkers, we rarely teach students how to self-assess, or provide them self-assessment practice opportunities or reward them for engagement in self-asessment. In AP 50, the problem sets are structured to provide students guided self-assessment training. Again, after working the problems on their own at home, a significant portion of class time is dedicated to going over the problems as a team. They are provided with a reflection handout, on which they write up their own reflections on how they can improve their learning and hand that in with their marked up work. Here are some of the phrases I heard while observing them do this reflection: “What assumptions did you make?” “I took a totally different approach,” and “I like your assumptions.” Part of the reflection is rating their own understanding of ideas and concepts in the problem set on a three point scale: green, yellow, and red (and they have a rubric which explains each point on this scale).Their grade on the problem set is determined, in part, by how well they rated their own understanding of the concepts.
At the end of the first problem which is displayed in Figure 1, two students summed up the process as follows: Student 1: “I got to the final number differently. Our different approaches were all plausible, even though our assumptions were different.” Student 2: “Which is OK, because that’s what would happen in the real world. It would be boring if we had all the same assumptions.”
My Own Reflections
The elegance in Mazur’s approach to problem solving is that it seems to be squarely aligned with current thinking about human motivation in the 21st century. Specifically, counter to our intuition, rewards (in this case right answers) may diminish rather than promote motivation. In AP 50 the reward appears to be the innate pleasure of problem solving and discovery (see Willingham, 2009), not the grade.
The real take home for me is two fold:
- I felt deep regret for how much energy, time, and anxiety today’s students direct toward correctness. As one student told me, “I might have put in more effort if this was for a real grade.” This perplexed me as I leafed through her many pages of beautifully written math and extensive narrative about how she arrived at her solutions. When I probed a bit, it became clear that in more traditional environments students spend a lot of time worrying about getting it right, rather than getting it. As another student described, “It was weird to adjust that this is not graded on correctness. I was working on this last night and about to check and double check my solutions, but then remembered, that didn’t matter!”
- This obsession with correctness is extremely problematic. I don’t want the creative space in my students’ minds crowded out with anxiety about correctness. I want to free up that space for them to “fiddle” with different solutions, and to be “encouraged and inspired” to do autonomous work. I invite you to consider that the focus on right answers is less the doing of students and more the doing of ourselves as educators. When you change up the emphasis with homework to hone in and cultivate what really matters, your dreams about student learning will not seem so utopian.
*Interviews with students were not recorded, but verbatim notes were attempted.