Category: Math

Posted in Education, Math, Mathematics

Why?

Posted on by Denise Russo

Everything I learned about teaching I learned from gangsters. I say that with the utmost respect and affection – I loved my students, even though they were probably the most unlovable humans on the face of the earth. But I learned to love them. They taught me.

In November of 2012, I applied for a job at an alternative high school in the metro Detroit area. I was called for an interview, and when I showed up at the school I was more than a little tentative. I sat in the car and texted my mom, “It’s a shithole. I don’t even want to go in for the interview.” In her usual up front manner, she texted back, “Don’t go in then.” I don’t know why, but I collected myself and went into the building.

When I walked in, all I could think about was the opening scene of the movie “Lean on Me.” I told myself that I would sit through the interview, but I didn’t have to take the job – if they even offered it to me.

I didn’t even make it home before they called me to offer me the job.

My students used to ask me all the time why I would want to work there. To be honest, I don’t know if I really knew why I wanted to work there. I had decided to change careers after working as an engineer for nearly eight years, and it was my first job as a newly certified teacher. When I left my engineering job, all I knew was that I wanted to stay home with my kids in the summer. I had always enjoyed coaching softball, so I thought teaching would be a good fit. Of course, I had to find a really fancy way of saying it when I was required to draft a philosophy statement to earn my certification.

As a teacher, I will be committed to making sure that every student has the opportunity to choose his or her own destiny.  I believe that everyone is capable of learning, and I never allow students to utter the statement, “I’m not a math person.”  I believe that the most valuable lessons learned in school are not always academic.  No matter what classes I end up teaching, my highest goal is to teach my students how to think.  Students who know how to think are prepared to interact intelligently with the world around them.  This is, after all, the purpose of education.  It’s not about math, it’s about life.

Philosophy of Teaching – November, 2012

During my tenure there, every time someone asked me “why?” I would respond, “Someone has to.” It was a lame response, but my philosophy just didn’t fit. It was pie in the sky. And I knew I couldn’t save them. I couldn’t be a hero. I always wished I could be one of those teachers that had the power to inspire students to greatness – like the teachers that are always portrayed in the movies. But I was too acquainted with their reality. At the end of every day, my gangsters were going back to a hopeless, empty existence no matter what I said or did.

And then, something changed. Someone asked me “why?” And I knew. I’m not sure how I knew, I just knew. I looked at my class and said, “I have no idea why I took this job; but I know without a doubt why I stayed.” It was them. I was there for them. I couldn’t save them. I couldn’t inspire them. But I could love them. And maybe even teach them a little math along the way.

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

Day 3: Balancing Noah’s Ark

Posted on by Denise Russo

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

Posted on by Denise Russo

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…

Posted on by Denise Russo

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 2

Going Off The Rails

Posted on by Denise Russo

I am a planner. I spend hours upon hours planning lessons. Oddly enough, after all the planning, the lessons almost never go as planned. After a few years of stressing over this, I have learned to roll with it. And I have found that some of my best lessons were not planned at all.

One such lesson occurred last fall. Every year, our entire school does two service days. I happened that we were serving in a soup kitchen, and I was peeling potatoes alongside my students. For some crazy reason, they were in awe of my potato peeling prowess. They claimed that they had never seen anyone peel potatoes so fast.

A legend had somehow been born. I don’t remember exactly how it happened, but there was a group of students who swore that they could beat me in a potato peeling contest. Knowing how competitive some of them were, I took every opportunity to trash-talk right along with them.contest

Then one day, I found a note on my whiteboard. They wanted a contest. Though I knew I would be losing at least two instructional days, I thought it was worth doing. I decided that we would take the two days right before Thanksgiving (instead of their suggested date in December) – it was perfect timing.

I brought in a 5 lb. bag of potatoes, and set everything up before school. In each class, we picked two students to compete. We talked about the variables involved in the contest – time and potato size. Each student was given 5 potatoes, and they weighed each one. Our data keeper recorded the weights on the whiteboard and the rest of the class had a data sheet where they recorded their data. The students took turns peeling one potato at a time while another student timed them with a stopwatch. Times were recorded for each run.

ninja

The next day, we had to decide who had won each competition. Looking at crowded data sheets, it was unclear how to do this. We talked extensively about what to do with the data and decided that graphing it would show us a picture. What followed was a discussion of independent vs. dependent variables, linear vs. non-linear relationships, correlation, and variability. We discussed the slope of the fitted line and what it meant. We talked about whether or not Benen was the winner because he had the fastest time and why two of Joe’s data points seemed to be outliers.

It was a good way to spend the three days before Thanksgiving break. It was non-stressful, fun, and the students were engaged. And it was not planned.

Posted in Algebra 1, Education, Mathematics

A Good Student

Posted on by Denise Russo

“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

Posted on by Denise Russo

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

Posted on by Denise Russo

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…

Posted on by Denise Russo

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.

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

The Power of Reflection

Posted on by Denise Russo

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.