Iceberg Diagram: Fixed-Mindset, Math Anxiety

When students say something like, "I don't learn this way...", it may be the tip of an iceberg. A sign that math anxiety and/or fixed mindsets about learning math lurks underneath the surface. Unless you know the student really well, you may not know the size and depth of the issue. Most people don't go around campus telling others about their math anxiety and fear of failure. Instructors often learn about these things indirectly through more subtle ways.

Here's the Iceberg Diagram

"I don't learn this way..." and "I need to be shown the steps..." are two commons ways to detect an iceberg. Some students may not verbalize these things at all, which highlights why it is important to visit with students regularly and discuss with students about how they are doing with the math task at hand. The more comfortable students are at asking you questions, the better you can hone in on this issue.

Stereotype threat, poor attitudes that do not support learning (i.e. non-availing beliefs), believing mistakes are bad, not realizing hard work is an ingredient of success, and so on. These are things that students have picked up along the way, possibly starting as early as elementary school or perhaps from their homes or elsewhere, and they bring them to your class. These beliefs lie beneath the surface, and ultimately hold some students back.

What can we do? 
There isn’t an easy fix, but we can do something to help melt the iceberg. A broad approach provides the most options and angles of attack. First, problems that are pegged at the right level are necessary, including problems that ask students to explain why things work. Second, instructors need to be ready to coach students through being stuck, pointing out the advantages of productive struggle, including spending time on student buy-in. Third, assessments should also measure process, not just getting the right answer. Fourth, active learning environments that allow all students to ask questions (not just the vocal 3 to 5 in each class), and also regular opportunities to discuss with one another rich mathematical topics. Fifth, readings and/or videos about effective thinking and growth mindset are needed to provide other expert insight, who weigh in on growth mindset. If you, the instructor, are the only one saying these things, it might seem to students like you are making things up. But if growth mindset is presented as a widely accepted emergent truth from research across disciplines, then that's a entirely different framing.

With all that you have a set of strategies that hits at the issue from multiple angles.  Let's get back to the main point. We have a model and a way to see the iceberg, and we have a set of teaching strategies that can address the core issues, which is like applying gentle heat to slowly and surely melt the cold ice.

Here's a quote at the end of the term from a first-year student. This is what melted icebergs sound like.

One big thing I learned from the... assignments was how productive failure can be. Your brain actually grows and develops when you fail. This proved to me that it is more about the process of arriving at the answer than it is about actually getting the right answer right away.