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 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.

20171019_125638Enter: 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 Precalculus

Spinning Wheels

Despite the hours of work I have done this summer, I feel like I am getting nowhere. I am not even close to feeling prepared to teach Honors PreCalc this year. It will be my first time, and I’m trying to organize my thoughts first. I spent a ridiculous amount of time creating an outline of the class, so maybe I am getting somewhere. Since I have to turn in lesson plans weekly, I also spent a ridiculous amount of time putting lessons and objectives into my online lesson plan book (commoncurriculum.com – check it out!).  Maybe by the time school starts I will feel ready…

planner2

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.

50math

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.