Math is Everywhere!

What does it mean to be good at math?

I ask my fifth grade students this question during our first math class of the year. When I first posed this question, over 20 years ago, many responses involved “being fast” and “knowing your facts” and “getting the right answers.” I understand why students responded this way–traditional math education has valued speed, memorization, and getting the (one) right answer. While there is some value in these skills, centering them in the definition of what it means to be a good math student omits the essential problem-solving skills of creativity, flexibility, connection, communication, and collaboration. I explain to my students that math is a growth mindset subject; when you practice a skill and learn from your mistakes, synapses fire and your brain grows. Many students apply a growth mindset toward activities such as playing a sport or a musical instrument, going over and over different steps; they don’t expect to master new skills right away. These same students, however, might hold a more fixed mindset when it comes to math, feeling like if they don’t “get it” right away, they must be bad at math. 

The research of Jo Boaler, Professor of Mathematics at Stanford University, has worked to shift peoples’ understanding away from viewing math as a performance subject (with a narrow value on speed and finding single, right answers on tests) toward a focus on learning, valuing questions and mistakes, and applying concepts to authentic situations. I agree with Boaler that when math education values the process of problem-solving (and not just the answers), the experience becomes more meaningful and more accessible to a variety of learners. I explicitly share Boaler’s guiding messages with my students (“Setting Up Positive Norms in Math Class”). Her work has greatly influenced my teaching, and I have seen increased confidence and engagement in fifth grade math students over the years. 

This September, when I posed the question, “What does it mean to be good at math?” students responded with “to work really hard on your skills,” “to learn from your mistakes,” “to apply what you learn outside the classroom,” “to be able to solve problems in different ways,” and “to understand how other people solve problems.” (I applaud my students’ former teachers who must have shared a more nuanced view of math competence!) Holding these beliefs about math does not diminish the importance of accuracy and careful work; it does allow more students to view themselves as competent, creative mathematicians, and this positive mindset has been linked with higher levels of skill acquisition in students. 

After discussing the importance of a growth mindset, I ask students to list activities they enjoy and/or feel they are good at; I encourage them to think of hobbies and everyday tasks. We examine their lists and highlight ways mathematical thinking is involved in their activities. For example, if they enjoy art, this involves using symmetry, measurements, angles, and proportions. Enjoying sports can involve analyzing statistics and looking for successful patterns in game play. Reading involves identifying sequences and patterns in words, sentences, and chapters, and critically analyzing characters, settings, and conflicts. Math is so much more than numbers. It’s using spatial reasoning, logical thinking, data analysis and representation, making connections and generalizations in the world around us, and estimating resources such as time, money, and materials. Math is everywhere. You can’t be bad at math if you view math as a broad, rich, ubiquitous subject. I make the following distinction with students: you might not have mastered decimals yet, but that doesn’t mean you are bad at all math. I take this reasoning one step further, explaining to students that they can’t dislike math. They can dislike working with fractions, for example, (and in that case, we will work to increase engagement in that area). But if they look back to their list of enjoyable activities, and most of them involve some sort of mathematical thinking, then how can they dislike all of math? 

What about students who enter my fifth grade classroom loving math, feeling confident in their skills, and eager for challenge? Laying the groundwork with Boaler’s encouraging messages equally benefits these students. We emphasize working with multiple strategies, as opposed to having memorized algorithms. We focus on why different strategies work and how assessing the problem at hand impacts which strategy might work best. Practicing a growth mindset helps students take risks, especially when we do activities that involve productive struggle and may push students outside their comfort zone, even if they view math as a strength. We spend time in the fifth grade identifying authentic problems and collaborating to solve them. I encourage parents to engage their children in this effort—notice when you are using mathematical thinking and invite your child to share in the learning. Math is everywhere, and everyone has the potential to improve their math skills.