education – Page 2

Dear M, (Student Letter #12)

To help me be more critical and mindful of the bonds I’m forging with individual students, I’ve decided to write letters to some of my current and former students. This is the 12th post in the series.

Dear M,

Since the day you left my class five years ago, I knew I was going to write this letter. I’ve thought about it often. I could done it back then, but it didn’t feel right. Your impact on my teaching was immediate, and that year ended rapidly. While I knew you changed me as a teacher, I also knew that only time could show me how. I needed time to process.

In the years since, you regularly cross my mind. I’ve wondered how you’re doing and in what directions life has pulled you. You were always a thoughtful and contemplative student. You served contrarian ideas to your classmates, offering them (and me) a distinct perspective on the world. You wrote poetry and loved music. You were profoundly introspective. Intellectually, you moved with grace and fortitude.

Yet, despite all these melodic character traits I recall so effortlessly, they do not stand out to me most when I think about you. Instead, what comes over me is all that you taught me.

One of the most powerful moments of my career was meeting your mom during parent-teacher conferences. After a solid start to the year, the spring brought forth many struggles for you. We needed to find a path forward, and your mom showed up to conferences that evening with a smile.

I explained what I was seeing in the classroom. She shared more about you. You sat and listened. After several minutes, we turned to you. We wanted you to join the conversation. How were you feeling? How did you see a path forward?

I will never forget what happened next. After we turned to you, you said nothing. You stayed in a hushed stillness. You couldn’t bring yourself to join our discussion. Most teenagers would nod and smile, apologize, and offer up a synthetic promise to do better. Not you. You were pure and unapologetically yourself. It wasn’t rude or standoffish, it was contemplative. Like you wanted to offer us your input but couldn’t.

I still don’t fully understand how you felt that night at parent-teacher conferences, and probably never will. But the gravity of the moment didn’t escape me.

After several deafening moments of silence, I got up and hugged your mom. I didn’t plan to—it just happened. During our embrace, I promised her to keep an eye on you until you graduate two years later, to do my best to support you.

I checked in on you regularly for the remainder of that year. I brought you back up to speed with Algebra 2. You were an excellent listener and fast learner, so it wasn’t hard. During tutoring, we made space to chat about life. We talked about the past, present, and future. You shared your poetry. I felt like I was holding up a mirror during most of our talks.

For the remainder of your time in high school, checking up on you was a priority for me. We lost touch, however, so my check-ins were of the long-distance variety. I would ask your teachers how you were doing and randomly pull up your grades. I also made an effort to watch your body language around school. You never sought me out and we never really had another genuine, in-person conversation, but I never forgot about you. I needed to live out the promise I made to your mom. Ironically, I didn’t attend your graduation because of a family obligation. This still haunts me. It’s always felt like our story went unfinished.

We teachers are tasked with helping young people understand their curriculum, the world, and—when teaching is done well—themselves. Overwhelmed by the urgency of these mounting responsibilities, teachers work at a blinding pace. The velocity of our decision-making propels us to function at 60mph. From the moment we walk into the building, there’s always an email to send, a meeting to attend, or lesson to plan. Rarely do we have time to slow down.

Without trying, you taught me to slow down. It started with that moment with your mom at conferences when you willingly or unwillingly remained silent to force me to hit the brakes. In the months afterward, our unhurried, intentional chats urged me to delay my tendency to move on. You gave me the opportunity to appreciate the depth that comes with teaching instead of getting lost in its overwhelming breadth.

This is how, though I was only getting to know you better as a student and young person that year, our talks helped me understand all my students in the ways that matter most. You prepared me to truly see the young people in front of me.

In the 14 years before teaching you, I would look at my class and see students. In the five years since, I’ve seen sons, daughters, brothers, sisters, nieces, nephews, and grandchildren. They’re all there now, every day, in plain sight, indirectly asking for guidance, support, and love. They need a teacher, yes, but they also need an adult to understand them, offer suggestions, hold up a mirror, and be their biggest fan. I am glad to be in a position to do these things in large part because of you.

Maybe one day, our paths will cross again. But if they don’t, and we never talk or meet again, that’s okay. I’m proud to have known you and taught you. We served a purpose in each other’s lives for just a brief time, but my current and future students have a more empathetic, discerning, and caring teacher because of it. I’m forever grateful to you.

Please give your mom a hug for me.

Sincerely,
Mr. P

P.S. The photo of your class hangs in my classroom. I look at it sometimes and am reminded of you.

Teaching the same students

Early in my career, I taught the same group of students for back-to-back school years. This happened a couple of times when I taught Geometry and Algebra 2. There was even one class taught back-to-back-to-back school years (Algebra 1, Geometry, and Algebra 2). That was wild.

Reflecting on those students, I think about the unique circumstances that emerged from teaching them for multiple years. Specifically, I remember how our preexisting relationship shaped the year. In September, instead of “Nice to meet you,” it was “How have you been?” A sense of continuation and familiarity filled our days. Our shared history meant we picked up where we left off, leading to a lively class dynamic.

I didn’t appreciate those students and the gift we inherited from the Scheduling Gods. Unlike the waves of new students I teach every year, we already had a foundation. We weren’t laying bricks each day to build our castle in the sky. We already had our castle. Reuniting for a second (or third) year meant we could forge an empire. I didn’t take advantage of this, but the opportunity was there. In my defense, that was 15 years ago, and I was in my third year of teaching. I was treading water — I wasn’t prepared to serve them in a way that honored and built upon our past.

As this school year gets underway, I am recalling those early years a lot. For the first time since then, I am teaching an entire class for the second time. Scheduling changes dropped this opportunity in my lap on day 1, which I never expected.

I must say, I am excited. My ability to build community with students has sharpened through the years, and teaching has slowed down. We have so many rich memories and experiences to fall back on, which will only enhance the new ones we make. Our reunion as teacher and student this year is a gift I never knew I always wanted.

This class is mainly filled with seniors, adding another layer to my anticipation. Their maturity will carry us further than my other classes, but I was candid with them about my fears about the plague known as Senioritis. Although it won’t be personal, I envision most of them leaving me high and dry at some this year as they taste life after high school. The kids are wonderful and reassured me, but I have been down this road before.

Time will tell how this unique opportunity unfolds. Will we build an empire, or will it simply be a dream that never was?

Math Stories

In the land of Mathmatica, there are two happily married variables named Xara and Yesod. They lived happily, and they deeply enjoyed each other’s company. One peaceful day, however, the widely-feared gang of Arithmetic Operations suddenly took Xara within their clutches.

That was how one of my students started their Math Story, an assignment I gave students last week. The assignment tasked them with writing a piece of fiction that weaves an Algebra 2 problem into the plot. Students had a choice between eight problems my cogen helped me select, all of which we discussed as a class during the last several weeks. The only other restrictions for the assignment were:

The story has a clear beginning, middle, and end
The story has a problem or challenge that is resolved by the characters
The solution to the chosen math problem is included in the story, with work
The story is at least one page, double-spaced (not including the solution)

I gave students the option to work together, even if it was with students from another class period.

Students write regularly in my class throughout the year. However, asking them to write a short story offers them something entirely different than what I have previously done. With it, I aimed to tap into their creativity and let their imaginations run free, using math as the driving force. I’m truly horrible at unlocking this side of their brains within the context of problem solving. Practically all of what we do daily is grounded in algorithms and procedures. The Math Story was a break from that.

The assignment came as a recommendation from an English teacher at my school. We were at one of our monthly professional cycles discussing literacy across disciplines, and he suggested I try it. I always find myself telling stories at home with kids. It seems natural to bring the idea to school. Why not?

I drafted a version of the assignment and took it to my cogen students. They were into the idea and offered a few pointers to tighten it, like how long it needed to me and when it should be due. They thought it could be fun. I wrote two exemplar stories for the class to accompany the guidelines. Students had one day in class to work on it to help kickstart their writing. Everything else had to be done on their own.

The result was some awesome stories! Sometimes I forget how creative teenagers can be! Here are a few excerpts that do not do the students justice, but will have to suffice for the purpose of this post:

Once upon a time in the realm of Mathlandia, there ruled a king of mathematics known as “King Palacios.” King Palacios wasn’t your ordinary ruler. He didn’t just wear a crown; he wore an oversized calculator as a hat. Also, instead of having royal duties, he had math duties, where people had to pay him $2,000 of gold to get a chance to talk and solve their math problems. People from all over the kingdom came to him with their problems.

There was once a quiet city on the edge of the earth. In this small city, there was a mathematician that people had huge expectations for. You might ask, why? This mathematician was supposed to save the city from a nuclear beam by solving this one equation. The solution would disarm the beam.

Evil Mr. Palacios and Mr. Palacios have a math fight. This was one of the most insane math battles of all time. Their auras grew stronger as the battle continued, improving their math knowledge by a factor of seven. They both expanded their math domains, one of their most powerful techniques. This meant that whoever was stronger would win the battle since being in another’s domain meant being completely vulnerable to any attacks and having no way of fighting back.

Mrs. Yasin had a really hard time solving this problem. First, she replaced p(x) with c(x), but that didn’t work. Then she remembered what her amazing Algebra 2 teacher Mr. Palacios taught her way back when she was in 11^th grade, which is the equation p(x) = r(x) – c(x). This equation shows the relationship between profit, revenue, and cost of owning a business.

There was a trend of students using me (or at least my name) in their stories. As students wrote, they asked for extra credit if they used my name in their story. I don’t give many extra credit opportunities, so why not? It was a fun twist that proved to be worth it. Very memorable!

The cherry on top is that, at the end of the year, I hope that some of my students’ math stories will be included in our class book, Mathematical Voices Volume 5. It’s been a few years since the book welcomed a new writing task, so I look forward to adding it to the compilation.