Core Beliefs of a High School Math Teacher
By Jon Davis
Teaching math requires more than just knowing the subject. You also have to understand how students learn. Over the years, I have developed a few strong core beliefs that ground me as I get all kinds of learners engaged in high school math. Here they are:
1. Anyone can learn math.
There’s no such thing as someone who’s not a math person. In fact, every student — every person — can learn math to extremely high levels.
It might not be easy at first. It might take some time, some patience, and some persistence. But that’s where we come in, not only as teachers, but also as coaches. We’re trying to get students to believe that despite their past struggles, there is a way that they can be really strong mathematicians and to improve. Yes, it will take some work and some energy. But that’s what we’re here for, and that’s the help that we’re going to offer them.
When teachers and math departments believe that every student can learn high-level concepts, that translates into students’ developing a positive math mindset. A positive math mindset helps students learn from mistakes, share their learning, and practice what they’ve learned.
Jo Boaler at Stanford University has published a great book called Mathematical Mindsets, building off her colleague Carol Dweck’s work on mindsets. At Forman, we draw on Boaler’s ideas and resources, which inform how we structure math classes and make math more engaging. Because we make a point of applying proven research to our teaching, we have looked at Boaler’s work quite a bit. We really like her message that math is for everyone.
2. There is no one type of learner.
Students learn differently. Each works at his or her own pace and responds differently to different approaches. So being able to adjust to a wide variety of learners is key.
At Forman School, where we teach a traditional, college prep, high school math curriculum to students with identified learning differences, we have learned not to apply one method for everyone. We tried it, and it didn’t work. For example, we used to use Brad Witzel’s “multisensory algebra” in all our geometry classes. But what we found was that not every student needed it. For some students, it was extremely beneficial. Actual, physical representations — say, using cups and popsicle sticks to try to solve algebraic equations — can really help deepen connections. But for others, it seemed a little bit rudimentary. It didn’t keep everyone engaged. So now we’re trying to target that method as opposed to making it a broad, sweeping part of what we do.
For our students who are really struggling or students with dyscalculia, we use more manipulatives. Being able to tie abstract concepts to something concrete is one of the best strategies we have for helping those students who have a very hard time understanding what the numbers or symbols of mathematics represent. Concrete supports can help.
A student with ADHD may have every ability to learn math at the same level and the same pace as any student without ADHD. For the teacher, it’s just a matter of keeping them engaged. We don’t want students with ADHD to just be present in the classroom — not engaged and not taking things in. If that situation is allowed to persist in a schooling environment, the student may really fall far behind. That’s not because of an inability to learn math, but just because of their lack of engagement and the lack of a teacher helping them continue to progress at the rate they’re able to. Teachers have to present the material in a way that will enable the student to continue working and progressing. That’s true not only for students with ADHD, but for all learners.
3. Students and teachers both learn the most when students are active and engaged.
What we pride ourselves on at Forman School is being able to individualize what we’re doing and to really figure out what’s going to work for each individual student. So our number one goal at Forman in how we structure our classes is to prioritize students doing as opposed to students observing. Certainly, teachers will need time to model how to solve certain types of equations or to grasp certain functions. But we never want modeling to take up the majority of our class time. Students need to do math in class, not just watch how it’s done and apply it in their homework later.
We want to make sure that students are doing math, practicing math, and getting individualized feedback from their teacher, as opposed to spending the whole class watching, listening, and trying to take things in. We will often pose an interesting problem at the beginning and let students explore it. We like to have students collaborating with each other and collaborating on problems in small groups. I love to get all of the students up working at the whiteboards at the same time. Other teachers will use individual whiteboards. As much as we can, we design our classes to be about discovery.
Observing students when they are active, engaged, and doing things in the classroom is also crucial for the teacher, who takes in what’s working and what’s not working. We use that information to adjust our strategies. If we’re not seeing that work — if students are trying to do it on their own outside the classroom, even if it’s with a tutor — we don’t know how to adjust and how to tailor what we’re offering to that individual student.
We can’t just hope that when our students leave the classroom, they fully understood what they thought they understood. Because that’s not the best approach for our students. Honestly, I don’t think it’s the best approach for any student. But more discussion and more doing and more engagement from the students — that lets us help them in the moment, and it gives us the information we need to be able to tailor what we’re doing to help these learners.
4. A highly effective teacher is a highly adaptable one.
The number one thing parents ought to be looking for in their child’s teachers, even before knowledge, is just patience, persistence, and a willingness to adapt. What makes for an effective teacher is a willingness to adapt what we are doing to meet each student’s needs as opposed to saying this is how we teach and you’re going to have to adapt to how we teach. There’s not going to be any one magic bullet for one student or a group of students. But, there are all kinds of strategies and resources and different ways to tailor instruction.
Jon Davis is a math teacher at Forman School. After graduating from Bucknell University with a degree in Computer Science, Jon starting teaching math as an intern at his alma mater, Vermont Academy, where he taught for four years. He then taught at Williams School in New London, Conn., and Boys’ Latin School in Baltimore, Md. He has taught at Forman School for the past six years.
