About six months after completing my master’s degree, I went to a holiday party thrown by one of my former classmates. In my particular program, master’s students take many classes with first-year Ph.D. students. The attendees at the party were a mix of the Ph.D. students I knew — now in their second year of study — and new master’s students that I had not met before that night. At some point, one of the Ph.D. students, who was my officemate the year before, made a comment to one of the master’s students that I still remember.
“We have ten weeks to finish the work of a quarter, right? Katie was always done in seven.”
While finishing three weeks ahead was an exaggeration of my general pattern, I couldn’t deny that I was usually ahead of the pack in terms of finishing course requirements. It wasn’t that I was faster than everyone else when it came to reading or writing. I may be a bit above average on writing speed, but I would bet that I’m below average on reading speed, and usually slow to organize my thoughts, as well. Speed wasn’t the issue. And I really struggled with a lot of the coursework in grad school. Ease versus difficulty wasn’t the issue, either.
The reason that I tended to finish early, and still tend to do this, is this: I live in perpetual fear of running out of time.
While I do have isolated bouts of procrastination, it definitely isn’t my biggest vice. I start projects the day they are assigned just in case I end up making a false start and need more time than I anticipate. If I happen to have extra time during one week, I tend to read ahead in my courses just in case something big comes up the next week. I love to be done early. That’s the only time I feel like I can be justified in not working on something.
I have long known this about myself, but I started to think about it in a bit of a different way after revisiting the work of Carol Dweck (1999) and Jo Boaler (2012).
Dweck’s (1999) work focuses on the idea of fixed versus malleable conceptions of intelligence. Student who believe that intelligence is malleable and they can become more intelligent over time are more likely to choose and persist at challenging tasks. Student who believe that intelligence is a fixed tend to avoid challenging tasks. Among Dweck’s more prominent findings is the fact that the kind of praise given to students when they succeed can have a strong effect on their conceptions of their own ability and their reactions to failure. Students who are praised for being smart develop a fixed theory of intelligence, and tend to react to failure by starting to believe they are not smart after all. Students who are praised for their effort develop a malleable theory of intelligence, and tend to persist in the face of challenge and try again upon failure. Building on Dweck’s theory and findings, Boaler (2012) has conducted studies of interventions aimed at helping students develop a malleable view of intelligence, or a growth mindset.
Dweck and Boaler are among my academic heroes. A big part of my reason for starting a career in education research is my desire to help put an end to the prevalent I’m just not a math person narrative, and hopefully help to prevent a similar I’m just not a computer science person narrative from becoming as common. Growth mindset interventions have a lot of promise in this regard.
At the prompting of one of my instructors earlier this year, I took some time to think about whether I have a growth mindset. I was pleased to come to the conclusion that I think I do. There isn’t much that I don’t think I could learn, if I took the initiative to do so. What I found interesting about this reflection, though, was the caveat I felt I had to add:
I could learn just about anything…. as long as I had enough time. Some things might take me a very, very long time.
This was interesting to me from both personal and professional perspectives. On a personal level, it helped me to explain my perpetual anxiety about running out of time and how that coexists with a solid sense of my own academic ability. I think I’m perfectly able. I just think that there’s always a risk of things being slow and difficult. Not impossible, but slow and difficult. I’ve never articulated that belief before. It’s helped me to reconcile my belief in malleable intelligence with the existence of sports stars, musical prodigies, and the like. Everyone can learn anything they like, with sufficient time, resources, and motivation — but this does not mean that each person will have to do the same amount of work to get there. There is such a thing as a natural proclivity. The power of growth mindset is that it shifts this idea of natural proclivity from separating the world into cans and cannots — something that is false — to identifying the those who have a quicker path to being highly skilled among a huge population of capable people.
From a professional perspective, this realization helped me to think more carefully about the problems that growth mindset work does and does not help to solve. I think many students carry around a belief that they are not good — and cannot be good — at mathematics, and that particular issue can be addressed with growth mindset work. Even so, the interventions won’t remove all potential anxieties about mathematics. Even if a student comes to believe he or she can indeed learn mathematics, that won’t necessarily lead to the belief that it will be easy, enjoyable, or worthwhile.
On one hand, perhaps this is ok. The goal has never been for all students to become mathematicians — just to help them attain a certain level of mathematical fluency and efficacy. One can hope that any overpowering anxieties about slowness and difficulty could be kept at bay through K-12 education. At that point, perhaps a greater number of students will pursue mathematics-related careers, and the rest will have reached a point of mathematical literacy that makes them effectively able to interpret and use mathematics to understand day-to-day issues.
On the other hand, there’s something about this line of thinking that bothers me. Is it a slippery slope? Is “Everyone can do math, but some people can do it more easily and faster than others” really a better narrative than “Some people just aren’t good at math”? I’m not so sure. My perpetual assumption that I need to plan for things to be difficult and time consuming isn’t something I want all kids to be carrying around.
The simplistic solution is to just change the narrative to “Everyone can do math,” and leave it at that. The decision of whether or not to pursue mathematics is then up to the student, and hopefully any decisions made won’t be based on worries about fixed intelligence. I just worry that the second part, “but some are better than others,” will be carried around after it, implicitly, if we don’t address it head on. Then we won’t really have fixed the problem — just shifted the barrier a bit.
I am sure you can tell by my rough writing here that I have not worked out all of my thoughts on this. But it’s something I’ve been thinking about, particularly when considering how I can use lessons learned from mathematics education to help to prevent a not a CS person narrative from taking hold as CS is introduced into K-12 schools.
Boaler, J. (2013). Ability and mathematics: the mindset revolution that is reshaping education. FORUM, 55(3), 143-152.
Dweck, C. S. (1999). Caution—Praise Can Be Dangerous. American Educator, 23(1), 4–9.