By Deanna Haunsperger, Carleton College and MAA President
Every fall I teach a differential calculus course at Carleton College that is five days a week instead of our usual three-days-per-week format. This course is designed to give students a review of algebra and pre-calculus and trigonometry skills just-in-time as I�m teaching the calculus material. It�s the lowest entry point we have for students who want or need to learn calculus, and it is where I introduce students to the idea of a growth mindset.
On their mathematical autobiography cards that students write for me the first day of class, they often admit to feeling unsuccessful in their previous math class, being nervous about the material, and worried they�re not smart enough to succeed this time. What I enjoy most about these students is that they are in my class on the first day, regardless of background or perceived ability, ready to learn.
I know from day one that one of my biggest responsibilities as a mathematician is to give my students the confidence to be successful. They need to come at this material with a fresh start, open their notebooks to a fresh page, and use a new mindset: a growth mindset.
Growth mindset, as defined by psychologist Carol Dweck, is the belief that mathematical (or any) ability is not something you�re born with, but something that can be developed through dedication, hard work, and good strategies. She and her colleagues have shown that students who believe in a fixed mindset � that you�re either born with a certain ability or intelligence or you�re not � are defeated by mistakes because they don�t think they are capable of improving. Growth mindset students, however, take mistakes as a challenge to work harder or dig in more deeply. They believe they can grow their brains to understand more.
Of course we want our math students to have a growth mindset so that when they face problems they don�t know how to solve, they engage with the problem and persevere. But how do we teach growth mindset? Here are my three ways:
- Tell them. I was talking to the director of our Learning and Teaching Center a few years ago over coffee. I wasn�t seeking advice at the time, I was just kvetching about my students and the things I thought they should know about being a successful student. �How can they not know that being in class is important? How can they not know that getting enough sleep and eating well helps? How can they not know that if they work at something long and hard and try different strategies they�ll get better at it?� He looked at me and said, �Well, have you told them?� No, I had to admit, I hadn�t. I don�t know why, but it had never occurred to me than in addition to teaching math, I needed to teach my students how to learn math.
So now on day one I tell them that showing up to class well-rested and well-nourished is important. I tell my students that finding study buddies is important and that keeping up with their homework is important. I also tell them all about growth mindset and how they can be successful if they engage the material and persevere. In fact, I have a handout I give them on �How to be Successful in a College Math Classroom� that contains these and other suggestions.
- Remind them. Before the first exam, I bring up these tips for success again. Not everyone is fully listening the first day of class, so it is important to continue to remind students of the expectations I have of them. This time, I tell them a personal story; this is not difficult for me because having a growth mindset helped me survive graduate school. My first year of graduate school, I took graduate abstract algebra without having had undergraduate abstract algebra. It turns out this was not a good idea. I felt defeated after one term, redoubled my efforts the second term, dug in even deeper the third term, and I ended up passing my algebra prelim at the end of the year on my first attempt. The material in that course did not come to me through divine intervention. I worked very hard to learn it, and I put in the hours and the focus to develop a growth mindset.
- Use growth mindset-appropriate words throughout the term. I am, sincerely, very proud of the efforts that the students put in throughout the term, and I love being their cheerleader. I don�t commend their talent or intelligence, though. Instead, I write �Great improvement; I can see you studied a long time for this exam!� �Excellent work!� on their exams. I acknowledge the hard work their brains are doing during class and over time, they are building new stronger connections between the neurons in their brains, and that�s why they need adequate rest and nutrition. Exams are not meant to judge students. Exams assess how much students have learned and indicate whether students have put in enough work to master the material.
Of course, not all students are successful in this class that meets every day; it�s a lot of hard work. But a couple years ago, a student who had dropped the course one fall, signed up for it again the next fall. He went from failing one year to earning A�s the next year. �What�s different?,� I asked him. �I learned how to work hard and focus,� he replied. Now I make sure to slip that story into the class each year as well.
Once they understand the growth mindset, students also feel slightly more in control of their own grades in the class, since they are seeing a more direct correlation between their time on task and their grade in the class.
This made such a positive change in my calculus class, that I brought it into all the classes I teach now. I see a difference in my classes, especially in the attitude of some women. If this change in frame of mind improves the classroom experience for even a few students each term, it�s well worth the extra few minutes in class.
Editor�s note: For more on the Growth Mindset in the math classroom, please see the MAA Instructional Practices Guide sections on classroom practices as well as the equity in practice section.