Posted in Mathematics

I Am A Teacher

I am a teacher. And despite what you have probably seen and heard over the last few days, I am not a hero.

When I was younger, I wanted to be Wonder Woman. I grew up watching the Super Friends cartoon on Saturday mornings, and Lynda Carter on weekdays after school. Even as I sit here, many years older and wiser, there is still something about superheroes that captures me. I’m not sure what it is…I mean, let’s face it, Lynda Carter’s Wonder Woman was not exactly a badass. But how awesome would it be to beat the crap out of 20-30 criminals at once while not breaking a sweat or messing up your hair?

Despite the fact that I manage groups of 20-30 teenage students at once for several hours a day without breaking a sweat or messing up my hair, I am not Wonder Woman. In fact, if I were a hero, it certainly wouldn’t be Wonder Woman. I’ve always thought that I’m really more like Batman – I run around with a bad attitude doing what I think is the right thing, regardless of the specific orders of those in authority, and as a result, I’m constantly being chased by people who think I am a criminal. But alas, I am definitely not a hero. I am a teacher.

I go to work every morning thinking, “I will be nicer today than I was yesterday.” But almost as soon as the day starts, I am reminded that I am expected to function in a system with which I do not agree. So I go rogue. I do what I think is the right thing. I attempt to educate my students while ignoring the newest directive from the bureaucracy. I fight off the angry emails from parents who are disgusted by my “behavior.” I listen to the whining pleas of jaded teens, who want to maximize their grades but only at the end of the quarter when it’s too late. I go home from work every afternoon thinking, “I’m a stark-raving bitch.” Rinse and repeat. This is me. This is what I do. I am not a hero; I am just a teacher.

Enter: global pandemic. The spread of “teachers are heroes” tweets and memes is outpacing the exponential growth of the coronavirus itself. And it’s not just teachers…truckers are heroes. Grocery store workers are heroes. Delivery people are heroes. Small business owners are heroes. Parents are heroes. Generation Xers are heroes. Millennials are going to save us all; wait, no…GenZ to the rescue!

In the meantime, I’m still just doing what I do. Circumstances have changed, but I still wake up every day and think “I’m going to be nice today.” I still make my best attempt to function in a system with which I do not agree, and I still ignore directives if I think they’re ridiculous. This is me, and this is what I do; whether it’s in the virtual world or the real world. I am not a hero. I am a teacher.

And all of those other people on the list? They’re doing the same thing. They’re not heroes. They’re being themselves. They are going to work so they can afford to feed their families. Or maybe they are going to work because they’ve found a profession that they love, even though it might be difficult or life threatening. Many of them are dedicated, hard working, charitable people. But they are not heroes.  There’s really nothing extraordinary about going to work every day and doing the same thing that you’ve always done, even if the circumstances happen to be extraordinary. A hero is not defined by the fact that he can adapt to a changing environment, nor is he defined by the fact that he does a job that no one else wants to do.

I am a teacher. Despite the difficulties that I face, it’s what I love to do. As much as I might aspire to be Wonder Woman, I know that I am not. Though it has taken some time, I have finally learned to let go of Wonder Woman and embrace my inner Batman…particularly given the fact that we both seem to share the same philosophy with regard to social distancing. But please stop calling me a hero. I fear that if you continue to project the image of “hero” onto someone who is merely adapting to changing circumstances, then you will be quite disappointed when the mask comes off and you see Bruce Wayne.

Posted in Algebra 1, Algebra 2, Education, Mathematics, Precalculus

Day 3: Balancing Noah’s Ark

Day three was all about work20180827_065827ing together. Whenever I have used groups in the past, there were always students who were not working, students having side conversations, and students who just did not seem to get along with those in the group. I wanted to do an activity that would model the ideals of good teamwork. Development of the skills required for effective collaboration takes practice. We are so busy trying to hit our content standards, that we don’t always recognize the value of spending time teaching “soft skills” such as communication and teamwork. As a result, these skills are often lacking in many professional working environments.

I decided to use Sara VanDerWerf’s 100 Numbers task. I put the students in groups of four, and gave them 3 minutes for the first round. When the round was finished, I asked each group to tell me how many numbers they had found. I wrote their numbers on the board and we discussed possible ways to improve their speed. I told them that for the next round, they would only have two minutes. As soon as I said it, they all immediately started moving their desks as close as possible and leaning in toward the center of the group, ready for the next challenge.

20180824_112116.jpgAfter the second round, nearly all of the groups had improved. There was even one group that found all 100 numbers! I then had them make three columns on a sheet of paper. In the first column, I wanted them to write down words that describe what an effective group looks like. In the second column, I asked them to describe what an effective group sounds like. And in the third column, they were to describe what an effective group feels like. I let them talk for a few minutes, and then as a class, we had a quick discussion of the qualities of effective group work. I projected a picture of the class that I had taken while they were working. They were quite shocked that they did not even notice me taking pictures. I asked them if the students in the picture looked focused, determined, and engaged. It was clear that they were.

Since we still had about 20 minutes left in class, I told the class that I wanted to try to apply our new group norms to a math problem. I gave each group a copy of Fawn Nguyen’s Noah’s Ark problem and gave them the remainder of the time to work on it in their groups. All of my classes were 100% engaged and focused on the problem. Effective group work looked amazing, sounded amazing, and felt amazing.

Posted in Algebra 1, Algebra 2, Mathematics, Precalculus

Day 1: Three Things…

Another first day is in the books. I do this every year and every year I wonder how I am going to make it through the year. It was so much fun, but so exhausting.

This year, I decided to use the first 3 days to establish some norms in the classroom. We really didn’t do any math; but the things we discussed were well worth the time invested. Rather than have a plain old discussion about class norms, I decided to make it a little different.

First, I told the class that there are 3 things that we will do in this math classroom that most other math classes DO NOT do. I told them that it was their job to figure this out, and the clues would come in the form of music. I told them I was looking for three action words, and to listen closely to the words in each of the 8 songs that I had prepared.

One by one, I played clips of different songs that included the words read, write, and fight. Every single person was engaged. They danced in their seats, wrote notes, and did some lip syncing. And best of all, I could “see” the active listening as they were straining to hear some of the words.

When the music was over and they had guessed the three words, we talked about reading and writing in math class. We talked about how we weren’t actually going to “fight” in class, but “debate” instead (you try finding songs with the word “debate” in them).  We discussed respectful disagreement and comfortable spaces. And I did it in all of my classes, including honors.

Did we “do” any math problems? No. Did the students hit any of the CCSS? No. Did I lose 50 minutes of “instructional time?” Probably. Was it worth spending the time? Absolutely.

Posted in Algebra 1, Education, Mathematics

A Good Student

“What characteristics do YOU think make a good student?” It was a question posed by one of my students during a class discussion this week. Their definition of a good student: someone who is smart, responsible, respectful, diligent, and helpful to others. A good student is on the honor roll. A good student avoids “bad” people and “bad” choices. That was their definition. My definition?

One of the best students that I’ve ever had was in one of my algebra classes. He was quiet at first, and rarely spoke to me. Algebra was difficult for him; he seemed to struggle through every problem. The situation was incredibly frustrating, because he demanded so much individual attention. When the term started, he would not work a single problem on his own. He asked me to help him with EVERY SINGLE PROBLEM. Knowing that I could not keep this up for the entire term, I began pushing him to do some of his work on his own.

Every day became a fight. Every time he asked me a question, I answered him with another question. Every time he told me that he couldn’t do a problem, I assured him that he could. I refused to give him straight-up answers. He would cuss and throw down his pencil.

He ended up struggling through the term, earning a C in the class. At the beginning of the next term, he came to see me and showed me his new schedule. He was no longer in my class. He told me that there was no way he would make it through the next term. I looked him in the eye, shook my head in disbelief, Photo10160701and said,

“You will be fine. You don’t need me. Look – your name is on the hero board. You probably didn’t even notice it. Do you know why your name is on that board? It’s because you fought. You came here every day, and you fought. You got frustrated, but you fought. You failed, but you continued to fight. You got angry at me, but you didn’t run. You stayed in the fight. And because you stayed in the fight, you won. And now you will do whatever you have to do to win the next fight. I know that you will not need me. But if you ever think that you do, you know where to find me.”

A good student may not be on the honor roll. He might not always be respectful or helpful. He may be confrontational, rude, and short-tempered. He has serious academic deficiencies. He’s been in jail multiple times, and has a one-year-old baby at the age of 18. He missed an entire term after being shot. He failed. He struggled. But he fought. And despite the circumstances, he won. As I watched him walk across the stage at his graduation, I remember thinking that I would certainly miss such a good student.

Post submitted to the Virtual Conference of Mathematical Flavors.

Posted in Education, Math

So Many Ideas, So Little Time…

It’s already mid-July, and I am desperately trying to accomplish some planning for the coming school year. I will have 5 preps; Algebra I, Algebra II, Honors Algebra II, Honors Pre-Calculus, and AP Calculus. I’m the senior class moderator, and I was also asked to be the Math Department Chair. I know I have to get something done this summer, or I will be in way over my head this fall. So, to help myself synthesize some of the ideas that I want to incorporate into my classroom, I have decided to pick the best of the best and put them all in one place. Here is the short list of goals that I have for this year.

1. Incorporate more reading.


About a million years ago, I was in a bookstore and I found a book called 50 Mathematical Ideas You Really Need to Know by Tony Crilly. The book does exactly what the title suggests: lists 50 different mathematical ideas that are integral to mathematics. Everything from the concept of zero to game theory is described in detail. This is a great resource to help me do pre and post assessments on student understanding. For example, before taking on the study of complex numbers, I can have students read about imaginary numbers. I like to use Tweet the Text to assess students’ understanding of the concept from the text. I have students “tweet” the main idea in their own words. Once we finish our work on complex numbers, I give the students the same text, and ask them to do the same thing. Comparing the two tweets shows how much the students learned and how giving them context can help them better comprehend what they read.

2. Take more risks.

chefThe first book I read this summer was The Classroom Chef by John Stevens and Matt Vaudrey. There were so many great ideas in this book, but the biggest takeaway for me was the fact that I need to take more risks in the classroom. Reading great books, following rock star math teachers on twitter (thanks #MTBoS!), and keeping up with the best blogs in math education has given me an infinite number of fabulous ideas; what I usually lack is the fortitude to implement them. The fear is real – fear of failure, fear of looking like a fool in front of students, fear of the repercussions for doing something “unconventional” in a very traditional environment, fear of not covering enough material (the ACT is right around the corner!)…the list goes on and on. One of the first things that Stevens & Vaudrey address in their book is the fact that if we become risk-takers, our students will follow. Aren’t we always telling our students that failure is a sign of learning? That they must be willing to be wrong if they want to accomplish something? That solving difficult problems requires them to take a risk? It’s time for me to start modeling the behavior that I expect from my students.

3. Music!

Thlearningtoflyis one is easy – bring some music into the classroom. I’ve always wanted to do this, but it’s been pretty low on my list of priorities. This summer, I bought myself a bluetooth wireless speaker and compiled a list of really great motivational music as well as some stuff that just makes you want to dance. When I first started teaching, I used Pink Floyd’s “Learning to Fly” to introduce a particularly difficult project. I began by passing out a copy of the lyrics and asking students to read them. As most of these students were unfamiliar with the song, we had a short discussion about what the words meant. As expected, the students stuck to the literal interpretation of the lyrics, someone is learning how to fly an airplane. After the short discussion, I played a video that I had made of my firstborn son learning how to walk. We then revisited some of their earlier conclusions about the meaning of the song, and they were able to connect the song to the difficulty of learning something new. It was a quick lesson that was not math related, but so much more important than anything in the textbook.

Posted in Algebra 2, AP Calculus, Education, Math, Writing

The Power of Reflection

When I went back to school to get my certification, I was required to take a class called Technology in the Classroom. Oddly enough, the most important thing I learned from this class really had nothing to do with technology. We were required to publish an online portfolio detailing our philosophy of teaching. My online portfolio was composed of several different written reflections that demonstrated key aspects of my philosophy. At the time, it was agonizing work. I hate talking about myself, and it had to be about me. It was torture.

Fast forward a few months, and with a brand new certification in my hand, it was now time to find a teaching job. The pool of candidates in the system was HUGE, and I was a total newbie. I knew I had to do something to set myself apart from the rest of the candidates. I decided to expand my portfolio.

After doing some research, I divided my portfolio into four sections; the first section contained my philosophy of education, The second section contained personal data – transcripts, resume, and letters of recommendation. The next section showcased carefully selected artifacts from my work as a graduate student, as well as my student teaching experience. I organized the artifacts around the ten principles of teaching developed by the Interstate New Teacher Assessment and Support Consortium (INTASC). Associated with each artifact was a rationale page, explaining why the artifact was chosen to support a particular standard. The last section contained a final reflection on my previous experience and my goals for the future. I chose an attractive theme, and peppered the document with quotes that reflected the themes. It took hours, but when I finished, I had it printed and bound and I took it with me for every interview that I had. It was gold.

“I’ve failed over and over and over again in my life…and that is why I succeed.”

-Michael Jordan

Reflecting on my experiences in writing allowed me to connect my attitudes, values, and beliefs to the work that I had done in grad school. Making these connections gave me a clearer view of my own philosophy, which ultimately translated directly into my classroom instruction. Realizing the value of this experience, I knew I had to figure out how to incorporate the same process into my math classroom.

During the summer of 2015, I began to do some research on incorporating portfolios into the classroom. I decided that my students would have to do one submission per quarter, for a total of four submissions. The format of the final portfolio submission was modeled after my own teaching portfolio. At the beginning of the school year, I handed out a project overview, found here.  I talked about the portfolio process and introduced the project.

I knew that I had to provide some instruction to help the students create their portfolios. So, over the first 2 weeks of school, I did a few in-class activities to introduce the process of reflective writing and the eight mathematical practices. The students were now ready to begin.

The portfolios were required to contain four samples of student work (called artifacts) – one from each quarter. After the first two weeks of work, I assigned the first artifact. I was careful to give lots of detailed feedback when I graded the artifacts, so that students had the opportunity to improve for the next submission.  I also peppered in several activities over the course of the year to help students improve their writing. Each quarter, I assigned a new artifact. Part of the beauty of this project is the ease with which I can change the theme for each artifact. For example, during the third quarter we were studying exponential functions. I decided to have the students use an in-class activity for their third quarter artifact.  During the fourth quarter, I have students write an introduction and conclusion for the overall project along with their fourth artifact. The result of this year-long process is a project that documents the students’ journey through the class.

For the last two years, I have done this project in my Algebra 2 and AP Calculus classes. Students have a love/hate relationship with the project; though it takes a lot of time, they do ultimately learn the value of analyzing their own work. Throughout the year, I try to highlight the importance of making mistakes in the learning process. Students learn that the analysis of their mistakes is where the learning happens. I often tell them that if they get A’s all the time in my class, then I probably haven’t taught them anything.

The biggest challenge that I have encountered is keeping students from repeating the same paper four times throughout the year. One way to help alleviate this situation is to have students think of one word to describe themselves, tell a personal story that illustrates that description, and then select an artifact to discuss. This will allow them to better connect their problem solving skills to their personal lives – something that math teachers always strive to do.


Posted in Education, Math

Hello, World!

Welcome to my new blog, where I hope to share some of my experiences in the classroom. My goal is to post something at least once per week throughout the coming school year, even if it contains only a sentence or two. This blog is my attempt to become more involved with math teachers from around the country (and world) as part of the #MTBoS online community. Send lots of questions or comments!