## What are our Goals in Class?

I have spent the past 25 years teaching at schools that go all the way from kindergarten through high school. I often tell my students that I have a crazy dream that it would be great experience to work with a group of them starting in kindergarten and move up together all the way to high school graduation. We’d REALLY get to know each other and be able to reference ideas/habits/experiences together. I am in no way equipped to teach younger children and I know this is a crazy mental exercise anyway but I do think often about habits and language that my students arrive at my classroom with that I wish they did not have. For example, when faced with the distributive property I always hear what I refer to as ‘that four letter F word’, when faced with a fraction on both sides of the equation I always reflexively hear ‘cross multiply’ [even when there are other factors in a problem] These are just two silly examples of fights that I am too often willing to wage in the classroom. A more interesting one, and one that has deeper implications, popped up in my class last week.

I often have a problem projected on the board when class starts. It is rarely a problem directly linked to the day’s tasks, I just want to get the brains moving and, hopefully, get some conversations started. This year in my Calculus Honors class I have noticed a discomfort with some of the classic word problems of the sort that pop up in Algebra II regularly. This is not a big surprise, these kind of word problems don’t get practiced regularly and there are all sorts of gut feelings that don’t always yield correct solutions. When I throw up a class opener problem I usually make a quick reminder of ‘Hey, look, there is an interesting question on the board!’ On the day I am thinking of, the question I posed was this one:

The first minute or two of each class involves a couple of gentle reminders to attend to the question that is posted and this day was no different. Another minute or so later I heard two remarks almost simultaneously that caught my attention. One student, a boy named Parker, said ‘I know the answer’. He did, by the way, know the answer correctly. Another student, a girl named Maya, said ‘I know how to do this.’ She did, in fact, know how to do the problem but had not arrived at the solution as quickly as Parker did. These remarks instantly caught my attention and I said to the class ‘Did you hear the difference between those two remarks?’ I repeated them both but did not follow down a conversation because I was not sure yet what I really wanted to say. This blog post is an attempt to unpack what I want to say.

This particular problem is not a deep one but it does remind my students of some system of equations strategies that I know are valuable in their study of Calculus. I also think it is just a good idea to brush off some of those skills every once in a while. Mya had equations written down for this, as did a few other students. Some used three variables. Some expressed the mother’s weight AND the nurse’s weight in terms of the baby therefore only having one variable. I reminded them that matrix operations sometimes help with three by three systems but they (wisely) rejected that memory here. I posted this question on my twitter account (@mrdardy) and had a nice conversations over there with some folks. My favorite conversation was this one:

I think I want to follow up with that class later this week to try and unpack the conversation and try to probe a little on where they land, and where they want to land, when faced with problems in this class. While the goal, understandably, is often ‘I know the answer’, I hope that there is at least some recognition that ‘I know how to do this’ is a pretty good place to be.

## Appreciating Appreciation

One of the nice traditions we have at our school is that we host alum at our school early in January and they work together to run what we call College Panel. Our College Guidance Office toss some question their way and then we open up the floor for students to ask questions. These alum discuss the whole college application process and how to adjust to life at college. This is a nice tradition, but the part I appreciate best is getting to talk to some graduates after the assembly.

This year we had two different assemblies, one for our current juniors and seniors and the other for our freshmen and sophomores. In the second assembly, one where I was not present, my name came up in response to a question about which high school class was most challenging. I heard a couple of different versions, but basically a couple of kids said my class (both referring to AP Calculus BC) was one of their most challenging classes in high school but that it was also a great preparation for college coursework. It is, of course, gratifying to hear that but what I want to write about here is the follow up. I saw each of these two students during lunch and had lovely conversations and they each sent me an email today. I am going to pat myself on the back here in public on a Friday afternoon. I hope you don’t mind.

The first student I am thinking of majors in English and Philosophy at an Ivy. Why did an English/Philosophy major choose AP Calculus BC? This is a natural question and, in fact, this student was challenged with this question by a classmate last year. This girl was also taking AP Physics and when she mentioned that she intended to major in Philosophy she was challenged. Why take these classes? She calmly replied that she had had high aspirations for her college admission and felt that she needed to present herself as a student capable of excelling in a number of arenas. This makes all the sense in the world and the fact that I know that she has no deep love for math makes the following remark from her email even more meaningful to me.

While you know that I am not a math person, your class really was the academic highlight of my senior year, and the way you taught us to think creatively about problems has helped me tremendously in college. Two teachers here have fundamentally changed the way that I think about the world — you and Ms. _____ ( I don’t know that it is smart to name the other teacher, but I am sharing this fact with that teacher) and I’m so grateful that I was fortunate enough to be taught by you both. I never thought that I would be excited to go to a math class each day, but your passion for teaching and your encouragement for us to think for ourselves made the Calc BC an incredible experience that I cannot even express how grateful I am to have had.

I have a story about a student from my first school (I left there in 2001) who I am still in touch with off and on. He paid me what I think is the greatest compliment I received in my career. He was talking about a boss of his and he said that this boss reminded him of me. He said his boss would ask him questions that he had not thought of on his own when faced with a problem to untangle. He said that reminded him of me. The compliment above and one I am going to mention next rank pretty close in my heart.

The second student I am thinking of wrote to me this morning. She references another one of our great traditions at our school. Every fall we host alums to come and talk about their experiences in STEM related fields.

I think quite often 0f a moment during my sophomore year where we had a conversation at my locker in your hallway. The STEM alumni panel had been the night before, and after our discussion on the content, you commented “how does it feel to know you will be back here doing that in a few years?” This unwavering belief and confidence in me before you even had me as a student helped me beyond words, so once again, just thank you.

What is striking to me about this email is that I do not really remember this conversation but she certainly did. Those of us who have been in the business for a while know how important these kind of interactions are and it is an important reminder to be present and to be attentive to our students. I need to remind myself of this more regularly and this is one way to do so.

This has been a tough couple of years teaching high school. Virtual teaching in the spring of 2020. Hybrid teaching for 2020 – 2021 (the year that the second student was in my BC class) and we are still feeling the sting of all those experiences. Hearing such gratitude from students who went through these years is especially gratifying.

This post is going on both of my websites, my math teacher site and my music fan site. Although it is not a piece of writing about math teaching or about being a music fan, my thoughts on what friendship means/looks like have been deeply influenced by my community of math teachers and of music fans/musicians. I am hoping that 2023 will see me writing more and this might be the trigger that starts this up.

I’ve been thinking about friendship for some time. Although it is a thread throughout my life, my current thinking kind of started this summer. This summer my family spent time in Florida where my in-laws host family at a gulf shore condo every July. Two of the four friends I still have from my high school days both live in Florida and they came to spend the day with us at the coast. While we were debating music and movies and sharing anecdotes about the current state of our lives we got into a conversation about the origin story of our friendship one of my friends thought out loud about his wife and how/when they met. He had graduated from UF where we all went to school and we were roommates at the time. He was already committed to head to Orlando to work for Disney, amazingly he STILL works for them, and he mentioned what a small window of time there was where he and his wife could have even met each other much less had time to fall for each other and make the move to Orlando together. That sent me down this long tangled rabbit hole of thoughts and reflections for the past few months as I have tried to sort out what I think/how I feel/how fortunate I have been with regards to friends.

This will be a bit rambly but I need to just get these thoughts out of my head. I have a number of thoughts/experiences/stories I want to share here. I’m not sure how meaningful it will be to anyone else, but this feels like an important exercise for me. [Author’s Note – I have been writing this over a couple of weeks when I have the time and energy to devote to it so some of the time references (like the beginning of the next paragraph) are not accurate anymore]