Posted in Algebra 2, AP Calculus, Calculus, Mathematics, Precalculus

## Day 2: Learning to Fly

Math is hard. I can’t do math. I have always struggled in math. Math is not my strong suit. I’m going to fail this class. These are things I hear over and over and over again at the beginning of every school year as my students are walking through my door. Certainly they must know by now whether or not they are “good” at math – most of them are juniors and seniors in high school. They’ve never done well in a math class before, why would this one be any different?

Math teachers have the most difficult job in the building. Like all teachers, we the curators of our content and we are charged with disseminating content in a manner which allows students to grasp it. Before we can do this, however, we must slay a much larger dragon. I set out to slay the dragon on the second day of school.

First, I gave the students a copy of the lyrics for a song. I had them read the lyrics and take a few minutes to decide their meaning. I did not tell them that they were song lyrics; most students thought it was a poem. We discussed the possible meanings as a class. The responses ranged from “someone learning how to be an astronaut” to “someone who is really sad.” They had to point out specific lines that led to their conclusions.

After a few minutes of class discussion, I told them that I was going to show them another interpretation of the words. I played a video that I made years ago. The video is a montage of video clips of my baby boy set to Pink Floyd’s Learning to Fly. It starts with the baby rolling over, rolls through the crawling and standing phases, and ends with the baby’s first steps.

After the students watched the video, we discussed what they saw. What was the baby doing at the beginning? What did the baby have to do to achieve his goal? Did they think that the baby ever fell while he was learning to walk? Did he get frustrated? What did he do after he fell? Did it ever occur to the baby that his goal was impossible to achieve? Did he ever think that he would never be able to walk?

Babies and young kids are amazing. They have no inhibitions. They aren’t afraid to take risks. They are driven. It never even occurs to them that something might be impossible. And they have no baggage to carry.

As they gain experience, they begin to accumulate baggage. They learn that math is hard. They can’t do math. They always struggle in math. Math is not their strong suit. They are going to fail. I asked them why they would want to bring this baggage into my room. Why did they insist on carrying it? Wouldn’t they be interested in the possibility of getting rid of some of it? I told them that this year, they need to leave their baggage at the door, because if they don’t, then they might as well just pack another bag to add to the pile.

After a few years of experience in teaching, I know that slaying the dragon is nearly impossible. But maybe I can wound it enough to teach my students some math this year.

Posted in Algebra 2, AP Calculus, Education, Mathematics

## The Road (not) Less Traveled

High school students are on a journey. They probably don’t realize it, but they are. They travel a road that is littered with long monotone lectures that put them to sleep, mounds of homework that they ignore until five minutes before the bell, and tests that they are not prepared to take. As they navigate the tricky landscape, they encounter many roadblocks, most of which they roll right over. But there is no roadblock that is more feared than the dreaded math class.

For the last 3 years, I have taught math classes in a private high school in the metro Detroit area. Our students are “tracked,” meaning that they are placed in math classes at one of three levels; honors level, average level, or low level. During my short tenure, I have taught all three levels of students. And at all three levels, my goal as a teacher is the same – teach students how to persevere through problems by engaging in the productive struggle. Though all of my students are walking the same road, their perception of the journey is skewed by their previous experiences in math.

My AP Calculus class consists of the most accomplished (academically) students in the school. I generally have most of the top ten, including the valedictorian and the salutatorian in my class. They have been in honors math classes since middle school. They have breezed through honors level Geometry, Algebra 2, and PreCalculus. They have mastered the art of parroting back our “repeat after me” procedures on quizzes and tests with little difficulty.  Their success has made them confident, capable math students; but our failures have made them weak problem solvers.

Enter: AP Calculus. I am extremely hard on these students. On purpose. From the moment they walk in the door, they are pummeled with a big fat reality check. It starts when I give them each a packet of letters written to them at the conclusion of the school year by the previous AP Calc class. The letters usually describe horrors that these honors students have never dreamed they might experience. Last year’s students discuss their first failures, lowest grades ever, and how they might not ever understand math again. They talk about how Russo doesn’t grade (or check) homework and they fell into the trap of not doing it – even though they knew they probably should have. It is not uncommon for me to have several Calc students cry in my classroom because of their grades. They feel like they are rolling downhill with no brakes; and they have no control over where they are headed.

My low level Algebra 2 class is the exact opposite. These students took two years to complete a 9th grade Algebra 1 class. They struggled through every second of every math class they’ve ever had. Many of them are still making up credits for previously failed math classes. They are students with IEPs, behavior issues, and rock bottom self esteem. They walk into my room referring to themselves as “the dumb class.” They have allowed themselves to be defined by failure.

I spend every second of every Algebra 2 class reminding these students that they are quite capable of doing the same work as the higher level classes. We ban words like dumb, stupid, and slow. Rather than referring to their cohorts as “the smart class,” I convinced them to come up with another name – they settled on “the Romans,” since the average level class is labeled with a Roman numeral two (Algebra II) rather than the number two (Algebra 2). These students feel like they are climbing a steep hill – every step is difficult for them.

How you fail is just as important as how you succeed.

My Calc students and my Algebra 2 students are traveling the same road. They are learning how to connect seemingly unrelated mathematical concepts to solve problems that they have never seen before. My Calc students must learn how to fail – and they ultimately figure out that how you fail is just as important as how you succeed. For them, improvement is a direct result of meaningful reflection and analysis. My Algebra 2 students, on the other hand, must learn how to succeed. They begin to see small gains throughout the year that add up to their first passing grade in a high school math class. For them, improvement is a direct result of hard work, persistence, and self confidence.

If I have done my job well, then at the end of the school year, all of my students leave my class knowing that they have accomplished great things. They have learned how to proceed when they don’t know how to proceed. And when they look back at their journey, they find that what they thought was an uphill climb or an out of control drop was made level by their own hard work and dedication.

This post was written for The Virtual Conference of Mathematical Flavors.

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.