I used to think teaching math successfully came down to guiding students through the numerical algorithms or procedures, delivering tons of examples, and supplying plenty of extra practice. I was wrong.
The first year I taught Algebra 1, I was not confident in my ability to deliver the curriculum. My background was in science, and I was unfamiliar with math pedagogy. So I did what most teachers do, I relied on the textbook to guide my instructions and assessments. Regrettably, covering the book meant racing through the curriculum at breakneck speed. My math lessons were on a rinse-repeat cycle: review yesterday’s problem, demonstrate a new concept, assign a page from the textbook for independent practice, and move on to the following topic the next day. Suffice to say, my students didn’t get it.
Many were confused because they had no time to master the math concept, and some just stopped paying attention to my lessons. When it came to tests, very few of my students passed. As a result, I struggled to understand how I went wrong that year. After all, this method was how my teachers taught me math.
But today, I realize there was a crucial ingredient missing in how I approached teaching math. And that component is perseverance. Boaler from Stanford University proposed that students learn math best when they have failed and persevered through complex problems. She points to neuro research positing that neurons create new synapses when one recognizes mistakes and struggles to overcome wrongs. Moreover, Carol Dweck’s studies indicate that the growth mindset attitude is essential for student success. The key is to adopt the perspective of optimism in solving difficult problems as a way to help our brains make meaning. When a person is always right, that person has no room to grow.
This concept reminds me of myself as a math learner. During my final high school year in the late eighties, I had my heart set on entering the University of Waterloo. One of the requirements for admission to the faculty of science was a calculus credit. Unfortunately, I came from a small town in Saskatchewan, and calculus was just not offered at my school. So I taught myself calculus through distance learning.
Learning this way was hard. During the pre-Internet era, remote education consisted of textbooks and lectures recorded onto cassette tapes. It was frustrating not to understand the lecturer, constantly rewinding the cassette tapes, and finding my answers did not match the answer key. But I was undeterred. I kept redoing the questions until I discovered where I went wrong. Eventually, I passed the exams and earned a B, enough to qualify me for acceptance into the university. In short, my struggles and perseverance were essential for me to understand calculus. It is this perseverance that is lacking in many math classrooms today.
One of the US Math Common Core State Standards articulates that students need to make sense of problems and persevere in solving them. This expectation implies that we cannot just feed our students with answers. They need to understand the problem, adjust their mental models, and articulate their thinking. Also, we should provide puzzles and challenges requiring them to customize their math procedures and thinking processes. We should purposely give time for students to struggle. Such a strategy may mean we sacrifice the superficial breadth of the curriculum for depth. And most importantly, let’s make math not always about getting the correct answers. It’s okay to make mistakes; that’s how we learn.
Perseverance is an enduring trait. The apostle Paul wrote, “…we know that suffering produces perseverance, perseverance, character, and character, hope.” (Romans 5:3-4) We do injustice to our students when everything comes easy. Instead, we should embrace difficulties in mathematics as a way to foster the next generation’s character. And that gives me hope.
Boaler, J. (2022). Mathematical mindsets: Unleashing students’ potential through creative mathematics, inspiring messages, and innovative teaching. John Wiley & Sons.
Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.