Mathematical Mindsets

This post is adapted from a piece I wrote for my school newsletter in the Fall of 2016.

I have borrowed the title of this article from an excellent book by Jo Boaler. A researcher in from Stanford University, Dr. Boaler draws compelling connections between her work in mathematics education and the work of Carol Dweck, another Stanford researcher, who studies the growth mindset. Dweck draws an important distinction between a growth mindset and a fixed mindset. Those with a fixed mindset believe that their intelligence is innate and cannot be expanded, whereas those with a growth mindset believe that they can increase their intelligence through effort.

125489887_124cf772c5_bA growth mindset is essential for learning in mathematics. Research has shown that students with a fixed mindset tend to avoid challenging work. Interestingly, this tendency is particularly pronounced in high-achieving students, likely because an inability solve a challenging problem is a threat to their self-concept as a smart person. Conversely, students with a growth mindset see challenging problems as an opportunity to extend their skills and develop their intelligence.

There are many elements of my approach to teaching math that are designed to cultivate growth mindsets in general, and specifically in students’ approach to learning math. As IB students, they are expected to be thinkers. As such, there is more focus on processes than products. In other words, my goal is for students to understand how to solve a problem, or why an algorithm works rather than learning it by rote or simply replicating what they have seen me demonstrate. While that is more challenging than following a procedure demonstrated by the teacher, it normalizes the effort required to reach a deeper understanding.

An important part of reaching this depth of understanding is for students and teachers to reflect on mistakes. Mistakes, like challenging work, are essential to learning. Teachers and students alike learn more about a student’s thinking when they make a mistake than when they get the right answer. For example, consider the work of these two students:

Student A Student B
2 x 2=4

2 x 3=5

2 x 2=4

2 x 3=6

Both students answered the first question correctly; however, the error that Student A made in the second question reveals a significant misunderstanding that was concealed in their answer to the first question. When students make mistakes, they are able to re-evaluate their thinking, and teachers are able to adjust their instruction to address misconceptions.

Another strategy I use to help students develop a growth mindset in math is to use unfamiliar problems. One of the IB rubrics for math in the Middle Years Program requires that students solve problems that are challenging and unfamiliar. By making such problems a regular feature of our math program, students expect the unexpected and develop courage and resiliency when faced with challenging, unfamiliar problems. Rather than responding with, “I don’t know how to do this, I’m not as smart as I thought I was”, students who expect the unexpected are more likely to respond with something like, “I don’t know how to solve this problem yet”. Such courage and resolve will help students to extend their understanding and abilities.

A willingness to tackle challenging work also contributes to a culture of effort and persistence. By attempting challenging work, students learn that math is complex and requires a variety of strategies. In such a learning environment, students learn that any progress requires effort.

As much as a growth mindset is an important part of learning math, studying math is also a great avenue though which to develop a growth mindset. Regardless of whether students continue their studies in math, the ability to persist with a challenge and learn from mistakes will contribute to their success in their other pursuits.

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