Habits of a Mathematician


One of the things I try to instill in students is that there’s no such thing as “math people.” I can’t tell you how many times I’ve heard “I’ve never been a math person.” And it’s not just students that say this– it’s parents, administrators, and even other teachers. It’s as if people think that there are some individuals that were born with the ability to think mathematically and others are just out of luck.

Instead, I’d like to propose the idea that mathematical thinking can be developed just like you’d develop athletic skill or musical talent. You practice. And you actively cultivate habits over time that contribute to better mathematical thinking.

Bryan Meyer has come up with a list he calls the “Habits of a Mathematician.” I really loved these when I came across them a few years ago and decided to make some signs of the main habits and hang them on the front wall of my classroom. I reference them as often as I can while I’m teaching. I also like to think that by seeing them on a daily basis, we all (myself included) are reminded that our capacity for mathematical thinking is not fixed, but rather can increase as we seek out ways to develop it.

Would you like a free copy of these signs for your classroom? If so, click here to download.

The Beauty of Mathematics

I’ve decided to start sharing some of the things that I’m doing in my classroom. I’ve been heavily influenced by other classroom teachers over the years and, since finding a robust teacher community on twitter (#MTBoS rocks!), I’ve been even more inspired to flex my creative muscles when it comes to classroom activities. Plus, when I take the time to reflect on my practice I find that I continue to grow as a teacher.

By way of a small introduction, I have been teaching since 2003. I taught for five years in public schools in North Carolina, then transitioned to online education for another five years before moving to Long Island, NY where I presently teach at a private boarding school. I’ve taught everything from Algebra 1 to Calculus, but my true love is Geometry.

A few years ago, I stumbled upon Dan Meyer via his blog and was intrigued with his Three Act Math concept. This led me down the path of reading other like-minded folks and I eventually found Paul Lockhart’s Mathematician’s Lament. Lockhart’s writing had a profound effect on me and my philosophy around mathematics education. I am convinced that my primary purpose as a math teacher is to instill wonder and curiosity in students as they interact with the beauty that is mathematics.

I strongly believe in the idea that mathematics is beautiful and that this is why we as a society should spend so much time and effort educating students in the fundamentals of mathematics. I am thankful to have the chance to go into my classroom each day and try out new ideas and methods with students that are motivated, talented, and most of all patient with their teacher.

The digits of pi are used the create this "skyline"

The digits of pi are used the create this “skyline”

A few days ago I had the opportunity to create and teach the first part in a mini-course called The Beauty of Mathematics that will take place over three weeks. It will take place for four hours on the first three Wednesdays of November. For the first class, we explored different mathematical patterns like tessellations, the Golden Ratio, and the Fibonacci series. We also investigated why the number pi is so significant and how it could be used as inspiration for art. I wasn’t sure how students would react to the activities we had planned, but I was blown away by the focus and creativity that they brought to the task. I am so proud of them!

A student works on a tessellation project

A student works on a tessellation project

Pink elephants emerge from this tessellation project

Pink elephants emerge from this tessellation project


A student creates a unique tiling of triangles, hexagons, and rhombi to produce this “set of keys.”

Next week we are taking a trip to NYC to visit the National Museum of Mathematics (MoMath.) I am beyond excited to take my students there and have them interact with the mathematical concepts they have on exhibit. Seriously, I cannot wait.

A Teacher’s Thoughts on the Spring Valley High Video

I awoke early on my first day, nervous but excited. After driving an hour through the beautiful rural North Carolina landscape dotted with countless tobacco fields and dilapidated old barns, I walked into one of the most intimidating situations I’ve ever been in. I was a fresh-faced, twenty-three year old white woman, determined to do something meaningful with my life. I was going to do more than strive for money and success. I was going to inspire young people.

I was going to teach high school mathematics.

To say that my students were unimpressed with their new teacher would be an understatement. I tried to make up for my inexperience by having loads of enthusiasm for my subject, but after several weeks of begging students to quiet down and give me their attention, I was starting to regret my decision. I have countless stories from that first year and almost all of them involve some variation of a student misbehaving in a small way, me asking him or her to stop, and the situation escalating to a full blown confrontation. I couldn’t maintain control of my classroom and the students knew it.

Twelve years later, I sit alone in my living room and watch the video of the young girl from Spring Valley High in Columbia, SC, being pulled out of her desk by a school police officer. I watch it over and over and over. I can’t get the image out of my mind. I don’t know what to say. It’s brutal. It’s inhuman. It’s indefensible.

While the massacre in Charleston earlier this year affected me deeply, this video has shaken me to the core.

As a high school teacher, I spend a ton of time with teenagers. I have the privilege of seeing them at their best and at their worst. I see the kid with ADHD who can barely sit still after lunch and I see the girl who just had a fight with her best friend. Teenagers are complex—they can be happy, frustrated, bored, sad, lonely, hyper, angry, insecure, and on and on. It’s no wonder that tempers flare at times, but what we can never forget is that they are children. They may look fully-grown, and heaven knows many of them think they are, but they are not.

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Teaching is a messy business. Contrary to what most people think, teaching isn’t really about the content. It’s not about equations, or verbs, or parts of a cell. Teaching, or better yet, learning is about the exchange that happens between teacher and student. In order for that exchange to happen, there needs to be a relationship between teacher and student. Each needs to trust and respect the other. I didn’t understand that my first year (or three) and was constantly surprised at the behavior of my students. I expected them to sit quietly in their seats, obediently raise their hand when they had a question, and generally play the role of model students. Instead, my students were rowdy, unprepared for class, and wholly uninterested in algebra and geometry.

Around year four of my career, something clicked for me. I realized that my job—teaching mathematics to a room full of teenagers—isn’t actually about me. It isn’t about my wonderful lesson plans or my overall pass rate for end-of-course tests. Instead, my job is actually about my students. These incredibly complex teenagers who I spend so many of my waking hours with, are souls that have infinite value. They are not actors playing a scripted part, but instead are individuals with fears and dreams, insecurities and interests. They come into my classroom with a backstory that inevitably effects how they perceive and understand what happens inside that classroom. It is a privilege and a joy to cultivate a relationship with them that will allow us to go about the business of learning algebra and geometry.

I don’t know everything that happened in that classroom at Spring Valley High. There will no doubt be much speculation over the days and weeks to come about what the young girl did or didn’t do, what the teacher should have done, etc. I do know that there have been moments in my own teaching career that I would like a chance to do over. There have been times, while feeling frustrated, angry, and disrespected by a student, that I allowed my own response to escalate a situation. I know there was a better way to handle those moments and, thankfully, I have learned from those experiences. I hope and pray that all of us who work in education will remember that the students we stand in front of day in and day out are someone’s sons and daughters. They deserve our very best. Surely we can treat them with the respect and dignity we would want for our own children.

Twinkle, twinkle

When I first started teaching way back in 2003, I would give students that made an A on a test a “smartie” (a rather unappetizing piece of candy.) It seemed to work pretty well, as students were really happy to get their smartie and some would even hold on to the wrapper and put it in their binder as a sort of trophy. A few years into my career, I switched from smarties to offering students stars if they made an A on a test. These were simple stars cut out of construction paper and laminated. I would give them a star and a Sharpie to write their name on the star, and then I would staple their star to my bulletin board. Over the course of the semester, I would fill the bulletin board with stars, each representing good effort and mastery of content by my students.

When I started teaching at Stony Brook this year, I decided to again use the stars to recognize mastery and hopefully encourage students to care about Geometry.


Man… did it ever work!

These students have blown me away. Seriously, I cannot say how much fun it is to teach these kids. I look forward to going to class every day, and it’s largely because of the way my students respond and interact with me. I cannot imagine doing anything else at this point.

I bought five packs of stars back in August (each pack has 48 stars, so I thought ~250 would be enough for the year.) By the sixth unit, I had bought all the stars I could find locally and ended up ordering more online. I have probably spent upwards of $50 on paper stars… next year I will figure out a more cost effective solution! Ha!

One of the incredibly fun things that has happened as a result of implementing the stars in my classroom is that my students use the stars as mini-billboards. It’s actually HI-LARIOUS.


They use the stars to call each other out. They use the stars to brag. They use the stars to show off their artistic talent.

And, as if all of that wasn’t enough, there is this star. The one that prompted this entire post.


“All Hail, The Queen!
Her Royal Highness, Mrs N. Holm
The Geometric Queen and Royal Ruler of The Stony Brook School
Rest Under the Lord’s Grace”

This star was created a few weeks ago by a student that cracks me up all the time. After receiving his star, I saw him hastily pull a couple of pre-cut paper figures from under his book. Apparently he had come prepared with different sizes of Queen Holm figures because he didn’t know which one would fit on the star better. I honestly don’t think I have ever laughed so much in class before. OH. MY. GOODNESS.


I’m actually quite humbled by how eagerly my students have embraced the stars. It makes me realize how much they long for recognition… how much we all do. I see in so many of them that same hunger I feel to measure up and to feel like I’m “okay.” I love each and every one of my students so much and I wish I had more than a paper star to give them.

As adults, the stars we collect are not necessarily made out of paper, but we nevertheless spend time and effort gathering around us little trophies to show the world and ourselves that we measure up. This world is so, so hard and we often hear the message that we must achieve and accomplish to know that we are okay. But sadly, the harsh truth is that we aren’t okay. But the even better Truth is that if we are in Christ, we are made glorious by the One that has accomplished our salvation! It is something that I still have to remind myself of daily, sometimes minute-by-minute.

I am thankful to have the opportunity to love on these kids and to share life with them. I hope they are having as much fun as I am.