Mindset and Brain Science
Written by: Dr. Christine von Renesse.
Many (most?) people believe that they are just not "math people," that they can never learn mathematics and that making mistakes is a really bad thing. Large segments of our society have internalized this view. They do currently not have agency or access to mathematics and its (implied) advantages. Given the role of mathematics as the gatekeeper for much of science, technology and engineering, this exacerbates inequality in our country. And currently we, the community of educators, are still doing too little to convince our students otherwise.
Changing the mindset of our students, helping them understand how our brains work, how we actually learn is incredibly important for any mathematics class, from Kindergarten through graduate school. Since there is a lot of wonderful material, including blogs and videos, already published about this topic, I will use this blog to just present some of the main resources. Why am I personally excited about and committed to teaching with a lens toward mindset? Because of student responses like the one below:
"This paper is supposed to be a final claim about my development as a mathematician, and the weird thing is before this class I would have said I am really good at math. Now looking back I would say before this class I should not have been able to call myself a mathematician and now I feel like a have developed into a student of math deserving maybe not mathematician, but something close. I have learned not only more formulas and processes to use because to me that's not what mathematics even is anymore. Being a mathematician is more a lifestyle or a way of thought. Learn from failures and create success, understand that learning from others besides the teacher is also important, be more open to different processes because “your way” is not always the right one. Being a mathematician is just as much about being flexible, hardworking, a good listener, and ones abilities to respond to failure, as it is about inherit smartness or affinity for mathematics. One day I definitely think I will have a good job and I will look back and be able to say that the discoveries I have made about myself in this class are the reason I am now succeeding in other parts of my life and I don’t think I can say that about another class."
The AMS Blog "On Teaching and Learning" has had wonderful contributions and I highly recommend reading all of them. Here are some of my highlights regarding mindset:
Benjamin Braun, professor at the University of Kentucky asks "The Secret Question: Are We Actually Good at Math?" to point out an invisible undercurrent of embarrassment and self-doubt that flows through American mathematical culture. He uses writing assignments and conversations based on the ideas behind Carol Dweck's research on growth mindset to help his students learn and change their beliefs about their mathematical abilities.
In the article Theory into Practice: Growth Mindset and Assessment Cody L. Patterson, professor at the University of Texas at San Antonio, describes how the recent work on growth mindset has influenced his assessment practices and adoption of specifications grading. He uses Carol Dweck's research on fixed versus growth mindset to reframe assessment and grading as a way of stimulating growth and providing guidance for learning, rather than rewarding success or punishing failure.
In an Atlantic article from August 2015, When Success leads to Failure , Jessica Lahey describes how children that are considered successful by looking at their performance and grades may actually lose their love for learning. She explains that if the system (parents and educators) praises correct results and good grades instead of diligence, persistence and effort, children may fear failure so much that they do not dare to take risks anymore.
I have found that my liberal arts students are astonished by the following video about mindset and physiology. After watching the video and discussing it they are much more open to changing their mindsets. They often reference the video weeks after we have watched it and are sharing the ideas with friends and family outside of class.
Mathematical Habits of Mind...
In her recent blog Our Responsibility - Our Opportunity Brigitte Lahme, professor at Sonoma State University, argues that it is the responsibility of higher education faculty to teach all students, including future teachers, productive mathematical habits of mind. She uses the mathematical practice standards from K-12 to frame what productive mathematical habits of mind are, and uses classroom activities and student work to showcase pedagogical ideas that provide students with experiences where they engage in mathematical practices.
Jo Boaler, a professor at Stanford University, created a website called youcubed which contains a wealth of resources on mindset and brain science for K-12 teachers. Her "weeks of inspirational math" have beautiful open tasks and video clips that are also a helpful resource for classes for future teachers. I have use Jo Boaler's Mathematical Mindsets book in my class for future elementary school teachers and loved seeing all the connections students were making.
Allison Henrich, professor at Seattle University, shares in her blog in “I Am So Glad You Made That Mistake!” how she convinces her students and the reader of the value of making mistakes. To do this, she provides explicit class structures and language to use during class and argues that
mistakes benefit deeper conceptual understanding, the development of a tight-knit classroom community, increased student self-confidence, and more engaged student participation. Here are some of my favorite examples of her classroom language:
“I am so glad you made that mistake! You’ve just made one of the most common mistakes I’ve seen on this type of problem, so it’s worth us spending some time talking about. Can anyone point out what the mistake is?”
“That was perfect! Too bad there were no mistakes in your work for us to learn more from. I’d like to hear from someone who tried a method for solving this problem that didn’t work out so well. Would anyone be willing to share something they tried with the class?”
“Any questions, comments, or compliments?”
“That took a lot of guts to get up there and make mistakes. I thought you did a great job fixing the solution and taking constructive criticism from us!”
In our blog on making mistakes you can see videos of students making mistakes in a liberal arts math class and a calculus 3 class as, as well as an instructor modeling how to "not know."
Stan Yoshinobu, director of the academy of inquiry based learning, explains in his blog how he uses "productive failure stickers" as a reward system in his class for future elementary school teachers. He also presents a list of Videos on Productive Failure, including an interview with Michael Jordan about his failures in basketball.
If you know about other great resources that we should add to this blog, please let me know. Thank you :)
Image 1: Wei-Chung Allen Lee, Hayden Huang, Guoping Feng, Joshua R. Sanes, Emery N. Brown, Peter T. So, Elly Nedivi - Dynamic Remodeling of Dendritic Arbors in GABAergic Interneurons of Adult Visual Cortex. Lee WCA, Huang H, Feng G, Sanes JR, Brown EN, et al. PLoS Biology Vol. 4, No. 2, e29. doi:10.1371/journal.pbio.0040029, Figure 6f, slightly altered