I teach several mathematics courses in the Liberal Studies Program at DePaul. For many of the students, this will be the only mathematics course that they will take during their entire college career, and many of them are apprehensive. I try to do a few things to allay their fears or at least help them see that they are in the same boat.
During the first week, I ask them to participate in a discussion forum by responding to the following prompt:
“Most children have a natural affinity for mathematics; they take pride in their counting skills and enjoy puzzles, building blocks, and computers. Unfortunately, this natural interest seems to be snuffed out in most people by the time they reach adulthood.
What is your attitude toward mathematics? If you have a negative attitude, can you identify when in your childhood that attitude developed? If you have a positive attitude, can you explain why? How might you encourage someone with a negative attitude to become more positive?”
This quarter, the students responded very well to the discussion. Those who were comfortable with mathematics encouraged those who weren’t. As the quarter progressed, the students have bonded and helped each other both in and out of class. However, every time I ask this question (and I have for more than 5 years now), I see responses similar to these:
“…I’ve always hated math. It just seems like all my thinking went to the right side of my brain so no room for numbers and logic. I cannot do math to save my life.”
“I don’t really dislike math, but by no means am I good at it! I always had to work really hard to understand it.”
One could argue that their minds seem to be made up. Math is tough and it will be painful! On the other hand, I have seen statements similar to this:
“I’d advise someone who dislikes math to think of each problem with an end goal in mind. When you work on a problem for a long time and finally figure out the answer, it is a great feeling and, eventually, the problem solving can even become fun.”
With these contrasting opinions in mind, I’d like to discuss the work of Dr. Carol Dweck, a psychologist at Stanford University (http://www.stanford.edu/dept/psychology/cgi-bin/drupalm/cdweck). Her research has led to the notion that people approach life experiences with either a fixed mindset or a growth mindset.
In the case of my students, the first two clearly express what Dr. Dweck describes as a fixed mindset—their minds are made up that they are simply not good at math. However, the third student demonstrates a growth mindset—one where the journey can become the reward.
Paraphrasing from Dr. Dweck’s work: people with fixed mindsets believe that their talents are fixed. This is the way they come, and there isn’t much you can do about it. It isn’t limited to people who say they can’t do math. How many people do you know say, “I am really smart, so I don’t have to study”? This is an example of a fixed mindset. And how often have you seen that really smart, non-studying person outdone by those who worked a little harder? This leads us to the growth mindset, which is where people believe their talents can be developed through exploration and hard work. Learning is a process, not an innate talent that you simply have.
Why is this important in the courses I teach? Well, it has to do with how you recognize a student for his/her effort in your class. While most of Dr. Dweck’s research was done with younger students, I think it is transferable to even our college-age students. As parents and teachers, we sometimes unknowingly reinforce the fixed mindset with praises such as, “You are really smart,” or, “You had an easy time of it. Well done!” But what happens when these students run into trouble and have to work a little? Dr. Dweck’s studies show that these students simply give up and assume they are not as smart as they thought. They feel less in control of their intelligence and, if they don’t understand, it is because they feel they are not smart enough.
What if students are praised for the effort and not for the end result? Dr. Dweck’s research shows that these students respond by saying that they could do better by focusing more. Their fate was in their control, and their learning was a matter of putting more effort into the task. This is engendering the growth mindset.
As I noted, the studies were done with elementary and middle school students. How do you do this at the college level? I do try to praise and reward effort, but the bottom line still continues to be performance on the midterm, final, and other assessments (formative assessment notwithstanding—but that is another topic). The good news is that I was able to introduce the concepts of fixed mindset vs. growth mindset in class. Some students started thinking about math a little differently, and a few even began examining their own overall mindsets.
There is a large body of work available regarding this subject. Rather than going through a lengthy discussion of the details, let me point you to a few websites that explain it much better.
The 10-minute version (which I showed to my class): Eduardo Briceno at TEDx
A 3-minute video on the experiment
“How Not to Talk to Your Kids”– A summary article in the New York Magazine
Mindset Works – A commercial venture based on the work of Dr. Dweck
Mindset (the book website)