It takes only an instant. We turn our heads to see if a car is coming. We judge its speed and distance. In seconds, we determine if it is safe to cross even though the car has the green light. It can be a matter of life or death, yet we rarely hesitate in our decision.

If we look this up on the Internet — when and where two moving objects intersect — we see words like vector, sine, system of equations and even calculus. If I asked my 11th-grade math students to calculate the point at which the car would hit them, they would be at a loss; yet they perform these calculations all the time. As they run across the basketball court, they must determine if they should try for the basket or pass the ball. On their way to school, a local train pulls into the station and they have less than a minute to determine whether they should jump on the train or wait two minutes for an express. When they have five minutes between classes, they have to determine the fastest way from one end of the building to the other, taking into account the crowd in the hallways. Each of these decisions requires them to do complex mathematics in a single moment without a pen and paper!

When I tell my students this on the second day of class, I see their eyes light up. In a moment, they go from students who may have struggled in mathematics to geniuses! Suddenly every person in the room feels capable of doing math. It amazes me how little things we say can make such a big difference. That’s why I feel we need to have high expectations for our students, show them that they are able to achieve anything, and allow them to express themselves in a wide variety of ways.

Mathematics is a difficult subject to teach. I have students who walk into my room in June to tell me I am their teacher next year and I should be forewarned that they are “not good at math.” I have parents tell me their child “does not have the math gene.” But every one of our students is capable of jaywalking. They are capable of determining how far they should risk going into the ocean. It’s just that sometimes they don’t know how to express it or they haven’t had the opportunity to express it in a way that makes sense to them.

In my 14 years as a teacher, I’ve identified five ways in which students express themselves in mathematics. Some students can talk about math even if they can’t put it on paper. How often do you have a student who you believe mastered the material and then failed the test? Some students can write about math but don’t know how to put it into spoken words. Some can draw clear and specific schematic diagrams that explain a difficult process. Others can solve abstract problems, relishing the comfort of letters and symbols. Finally, we have students who can provide us with math examples in the world around them. When I group my students, I group them homogeneously or heterogeneously by their strengths. Regardless, every student feels he or she is best at something.

When grouped heterogeneously, they have the opportunity to see other ways of expressing themselves and, hopefully, improve upon their weaknesses while sharing their strengths. In group activities, I always vary the problem a little so students get to use their strengths, and when we bring the class back together for discussion, students get five different perspectives. This accounts for the fact that not everyone’s strongest method of communicating is the same as his strongest method of learning.

In the beginning of the year, I identify my students’ strengths through careful observation and, in some cases, a diagnostic test. Every project I assign gives students the option of expressing themselves in different ways. I often give them the choice of a YouTube video, an essay, a model, a visual representation or providing real-world examples. This element of self-choice makes them feel more in control of their own learning, and I can differentiate instruction without creating 30 separate projects.

Students will sometimes leave my class having performed better than in previous years, but they almost always leave my class with more confidence, a renewed or new appreciation for mathematics, and a greater ability to think analytically and express that thinking.