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 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 stubaggage (1)dents 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 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 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.