First Day Plans

This school year I will be teaching four different courses – Geometry (2 sections), Discrete Math, Calculus Honors, AP Calculus BC. My Twitter feed is being bombed with first day plan posts, so I will jump in here as well. Sitting by a pool, so this I’ll not be lengthy.

Note that our first day has 25 minute classes and a long community gathering.

In Geometry I have started the past three years with a dramatic introduction to the handshake problem. It generates some fun guessing and conversations right off the bat. We are also able to revisit this problem in various forms during the year. I think it is a winning first day activity.

In our Calc Honors class I will take students out in the hallway with some wheels chairs. I will have a segment of hallway measured for length and we will have some races pushing these chairs down the hall. This, I hope, will generate some conversations about average speed tat we CAN calculate and all sorts of instantaneous information that we cannot. This should be a basis for distinguishing between secant and tangents over the first days/weeks of the course. Plus, it is fun to run down the hall!

In Discrete I am going to use a fantastic quote that I read this summer (you can find it here )  I think that this might generate some fun research and some fun conversations about magnitude.

In Calculus BC I want to start with a deep dive into a conversation about linearization and approximations. I have gathered some fun ideas on twitter about how this conversation can unfold. I hope it leads to quite a bit of noticing and wondering about accuracy and when/why that accuracy falls apart.

TMC17 Reflection Addendum

I am kind of embarrassed that I forgot one of the best highlights of the TMC17 conference. A while ago I received a tweet from John Golden (@mathhombre) asking if we could have a video chat about calculus. He was putting together an idea about a resource for his calculus students and wanted a variety of perspectives. Well, after a series of attempts we finally settled on a group chat on Saturday night. It was pretty loud everywhere on the lobby level so I offered my room as a quiet refuge. I had the joy of chatting about calculus with John, Jasmine Walker (@jaz_math), Edmund Harriss (@gelada), and David Butler (@DavidKButlerUofA) You can find our conversation here

 

I was SO flattered to be asked to do this and it was such a blast to chat with these four lovely and brilliant people. I told John on Sunday that I was jealous of his students. My apologies for having this wonderful experience slip my mind when I posted earlier today.

TMC17 Reflections

Beginning my reflections on the latest TMC experience (I am fortunate enough to have been for the past four years) I find myself focusing more on the personal experiences in ATL than the mathematical ones. That being said, I LOVED the presentation on base-8 math by Kent Haines (@kenthaines) and I am beginning to shift away from my strict aversion to multiple-choice questions based on Nik Doran’s (@nik_d_maths) advice in his morning session.

 

Last year in Minneapolis I allowed myself to dwell on the fact that there were social happenings that I was not part of. I KNOW that this is an inevitable fact when any large group of people gather together. It was especially true since we were housed in different places AND I was not equipped with technology that allowed me to tune in to everything going on around me. It was not until November of this past school year that I had a smart phone. Looking back, I KNOW how foolish this was. I had lovely dinners and chats with folks. I went out within hours of arrival to a lovely pub with Brian Miller, his school colleague Wilson, and Henri Picciotto. I had an amazing talk at dinner one night with Dave Sabol, who is kind enough (or crazy enough) to be one of the hosts for TMC18. I had fantastic math conversations and life conversations and came home a richer person than I arrived. However, I have allowed myself to dwell on what did not happen.

 

This year, armed with a smart phone (that I did not end up using much at all, really), going to a hotel where (almost) everyone was staying, and being in a city I knew, I went in with an agenda for myself. I knew I would be away on Friday night visiting an old high school buddy who was also my first college roommate. I made a commitment to myself. I was not going to hang around and see what happened about lunches or dinners. I sent out a tweet on Wednesday night inviting folks to join me at a restaurant I found called Smoke and Duck Sauce. Wednesday night ended up with a large gathering at Rose and Crown that was a great deal of fun. I sent out a call on the #tmcplans for Thursday night and had a great dinner with a fun group. On Friday night I had a lovely meal with my old friend and his family and returned to the hotel to stumble in on a deeply meaningful conversation with a fantastic group of friends. I was drawn over by seeing Brian Miller and Jasmine Walker (a couple of my favorite TMC pals) and ended up awake far later than I intended to be as a sprawling group of folks in a corner of the lobby bar really dug down deep on some personal and professional issues in a sensitive and vulnerable way. My had was spinning as I went to be. On Saturday night, I sent out another call on #tmcplans and ended up at Cowfish with a dozen folks. A LOVELY meal, great conversation, laughs as we celebrated a fake birthday, and a great sense of belonging and satisfaction as people piled into my rental car there and back on each evening. I went along to a breakfast at Waffle House based on an open invite. I had lunch with different folks every day at the campus of Holy Innocents. I had a quiet breakfast by myself the first morning of the conference enjoying southern grits and getting my head focused for the upcoming adventure.

 

I am not going to dip my feet into the mini controversies that came up during the week about hashtags and inclusion. I just want to say that I know that when I took it upon myself to be responsible and engaged in the community I enjoyed myself far more than when I was passive about it. Even though I also enjoyed myself then!

 

Of course, the social aspect and the connections are only part of the reason to come to TMC. There is also some sweet math to be experienced. My morning session with Nik thinking about hinge questions has me seriously re-thinking my bias against multiple-choice questions and recognizing their value if they are thoughtfully constructed and are treated as important data points in understanding what my students understand. His energy, intelligence, and good cheer made the morning sessions well worthwhile. I had two moments of mathematical epiphany during the week. On one of David Butler’s afternoon sessions he introduced us to some of his puzzles from 100 Factorial. I worked in a group with Jasmine, Joe Schwartz, and a new pal Mo Ferger on a fantastic problem called skyscrapers (you can find a link here!) We worked doggedly, and successfully, on this problem. On an afternoon session with Kent Haines I worked on some problems and pattern finding in base eight arithmetic. Again, working with some folks in the room (I wish I could remember who!) we poked around and noticed and wondered and fought the frustration that many of our students must routinely feel as we tried to find a comfort level in this realm of mathematics.

 

After a busy, happy, and rewarding three days with my #mtbos family in Atlanta, I am now relaxing with my (much smaller) family on vacation counting down the days to the new school year. I know I will still have some of this energy fresh in my mind in a few weeks. The challenge is to keep it fresh in my mind all year.

How Important is the Silence?

At our church this past Sunday one of the members of the congregation gave a thoughtful sermon about what it means to keep the sabbath. At least that was the primary framework of her conversation. Much of the time was spent talking about learning to take care of herself and what that looks like. Is it listening to a sermon at church? Is it staying home to garden instead? Is it taking a long walk? Is it listening to an inspiring TED talk? Naturally, there is no universal answer for this, but it sure got my mind spinning thinking about what it means for me to take care of myself.

I have engaged in a number of twitter exchanges recently sharing podcast tips. I have become hooked on a number of them and I listen while walking/jogging outside. I listen while I am on my Airdyne in the basement or on the treadmill in the basement. I was listening to Marc Maron and Randy Newman talking to each other just half an hour ago while eating my breakfast here in the airport (I am heading to TMC17 today!) Last month I was visiting my last hometown in New jersey and I went for a long stroll in a park where my wife and I used to walk as a pit stop on the way to pick up our son from day care. At the urging of an old friend – again, through a twitter conversation – I unplugged for that walk. For about 30 minutes I was strolling through this park, remembering cool fall days walking with my wife, listening to the sounds of the park and the neighborhood. It felt energizing. However, I have to admit I have not unplugged like that for another walk or run since. As energizing as that silence felt, I also recognize that I draw a great deal of energy from taking in ideas/content/entertainment through my podcasts. I tend to have music on in my house most of the time I am there. My wife and kids bought me a hammock for Father’s Day. I always bring a book with me to the hammock. I wonder (worry?) if I am just hiding from silence and from being with myself this way. I justify it by recognizing how much I enjoy being tapped into a number of conversation. By recognizing the joy I find when something I hear about that seems brand new suddenly starts popping up all around me. I am excited that I have been spending more time and energy listening to new music again due to my summer DJ gig (which I hope will turn into a fall one as well!) However, I also worry that this is making my time and mind feel even more crowded. I worry that I should put that aside and be quiet. I worry that I should be goofing around with my daughter at home more often instead of curling up with a book while she plays in her room or watches a show on TV. I justify this by thinking that I am ‘taking care of me’ by indulging in books, music, podcasts, exercise so that I can be better at helping others – wife, kiddos, students in the fall, etc.

I am in the last few weeks of summer here and I have taken on a teaching overload for the upcoming year. I’ll be teaching five classes with four different preps. This is on top of being a department chair. I think that the looming concern about what this will feel like has also made this past Sunday’s sermon more meaningful. I mentioned earlier that I know that there are no universal answers to this question, what I am worried about is that I am not clear about what the answer is in my particular situation.

I work better when I set specific goals. Last fall I was waking up early three or four times a week and going for long walks before coming home to wake up my wife for coffee in the morning. I think that I want to commit this fall to picking one day each week, Monday feels like a good choice, to making sure that I go out on this walk with no earbuds. Take a long walk or jog with the silence of an early morning in my ear. Keep my mind clear thinking about what the upcoming week holds. By putting this in writing, I am convinced that I am more likely to carry through with this plan. At the very least, I will feel vaguely guilty or embarrassed if I cannot carry through on this commitment. Not a BIG game changer, but at least this feels like a start. I will check back in on this after the school year is in gear.

As always, feel free to join in the conversation through comments here or by poking at me over on twitter @mrdardy

 

Back in the Saddle

I gave myself the month of June off after a busy year. On July 2 I sat down and started a project that I was stewing about all year long. I am happy about the problem sets I wrote for Geometry, I think that they are a nice set of interesting problems. Many of them have been borrowed from sources all over the internet and I think that my students who took them seriously are more persistent in their problem – solving than they were when the year began. However, I also learned a couple of important things along the way. Not all of my students gained in persistence through these problem sets. In part, I think that the students found them a bit intimidating at times. I also think that they skewed a little long on time needed for thoughtful reflection. I have two solution ideas for the upcoming year. We purchased a license to Kuta’s Infinite Geometry (and their other course options) and I did not use this as often as I should have last year. I do not think that these are terribly thoughtful exercises, but I do know that they are flexible (for me) and supportive (for my students) and I need to use them more often. Since all of our classes in our new schedule are at least 50 minutes, I will be able to carve out comfortable space for in-class practice on basic skills as we are developing them. I also made a commitment to reviewing my problem sets and working on two improvements. I wanted to clean up the language and make sure that problems are a bit clearer in what I want my students to focus on. I got engaged in a great twitter conversation about how important it might be to have students answer y-intercept questions as ordered pairs rather than as a number and how important it is to talk about the graph of a line as an object that is distinct from the equation of a line. I tried to make sure I talked about points on the graph of the line whose equation is 2x + 3y = 12 instead of asking for a point on the line 2x + 3y = 12. Just one example of how I tried to clean up the language I was using. More importantly, I trimmed many of the problem sets by eliminating some questions. I have posted all of my HW problem sets on my dropbox and I am happy to share them with anyone who wants to borrow (or just outright steal!) from them. You can find those problem sets here.

I would love to hear any advice/questions/concerns about these HW assignments. Please reach out by commenting here or through twitter where I am @mrdardy

 

So, What Kinds of Change?

In my last post I wrote about our department’s terrific two day workshop with Henri Picciotto. One of the major decisions we made based on the time we spent together is that we have decided, as a whole department team, is that we will allow test corrections on all tests in our department. Before I dive into the format of the decision we made, I want to include a couple of important links here with other points of view about assessment policies. The first comes from a new twitter contact Steve Gnagni (@Steve_Gnagni) who shared this interesting document written by Rick Wormeli (@rickwormeli AND @rickwormeli2 for reasons I am not sure I understand!) called Redos and Retakes Done Right and the second is a link Henri shared gathering together some of his ideas about assessments.

So, a little history here about where I am as a teacher and where I, and my team, hope to move. In the past three years I have had a policy in some of my classes. In any class where I have been the only teacher I have allowed test retakes. If you are unhappy with your test score, make an appointment to sit with me and look at what went wrong on your test and sometime within the week that your test was returned, you can take a new version of this test. Originally, I averaged the two test scores but this year I weighted the retest so that the score that stayed int he grade book was two parts retest and one part original test.  I also told students that anyone who scored below a 70% on the assessment were expected to take the retest. I did not do this in classes where I was part of a team teaching the course since not everyone agreed with this policy. The advantages of this policy were that students who were struggling to master material and perform on tests felt that they still had a lifeline. Those students were more likely to follow up with me and try to figure out what went wrong with their original attempt. Students were willing to take the extra time and energy to try and improve and I had reason to believe that material was sticking a bit better for many of my students. The primary disadvantages? This created quite a bit of extra work for me writing and grading reassessments. Some students seemed stuck on a perpetual hamster wheel of assessments and a handful of students were very honest about the fact that they sometimes pushed my assessments down their list of priorities since they knew this lifeline existed. This was a small group of students but enough that I was questioning the wisdom of this policy.

When Henri was with us he spoke passionately about the advantages of students correcting their own work. He talked about a cycle of student reflection and about the burden of careful written feedback on assessments. A sad fact is that most students (we probably know this about ourselves from when we were students) simply look to the grade. While many of us take careful time to highlight problems and write notes or to write congratulatory notes for work done especially well, much of this probably falls into the cracks. I know that I have read research – and I wish I could find it quickly – about the tension between writing comments on papers and writing grades on papers. These two forms of information for our students do not work in support of each other. So, after some conversation with Henri and then a long, productive final faculty meeting in the week after Henri left, we came up with a policy that we feel pretty good about. On unit tests when we grade them the first time we will assign one of three options to each problem. If the problem is done well, clear work and a correct answer (or a minute problem like some minor arithmetic error) that problem will receive full credit. If a problem shows no sign of clear explanation and no clear sign of understanding that problem will receive a zero. The vast world of problems in between these two poles will receive half credit. We will not highlight or circle errors in solutions. We will not write notes about the problem-solving process. We will simply return the paper with an initial grade. We will be able to do so quickly under these circumstances. The students will then have time to take this assessment and rework any problem that received less than full credit. They can earn back half the points that they missed by submitting corrections. The resubmission will have the original paper and two requirements for earning back points. They will need to submit correct solutions AND they will need to submit a written reflection/explanation of what went wrong and how it was corrected. Students can meet with each other, they can ask their teacher for guidance in our extra help sessions, they can look at their notes and their text, in general they can seek any kind of help. Some will inevitably just take the word of someone or something (like Wolfram Alpha) but ALL will be encouraged to take some time to reflect. ALL will be allowed to earn back some part of the points that they missed. ALL will know that test day is not such a high stakes day where it is do or die. There will be some bumps along the way as we train ourselves and our students to take this process seriously. We will have to be very conscious early in the year about establishing standards for what these written explanations need to look like. The student who earned a 60% the first time has a meaningful lifeline. The student who earned an 85% the first time still has motivation to rework and rethink the material. We will need to think about timelines, especially near the end of a grading term, but these are good problems to have and good conversations to make public. Teachers will be talking to each other about this process as we unpack it. Students will be encouraged to talk to each other about math and to seek guidance from each other. This will feel like a serious sea change for our department, I am totally excited about it.

Or, I should say I was totally excited about it. I know that there are different ways to view this process and the meaning of it. I know that we decided that events that we call tests are subject to this correction policy. We decided (for a number of reasons, some more ideologically defensible than others) that short quizzes were not subject to this policy. I know that I will be balancing this with graded take-home problem sets and on these problem sets I always encourage collaboration. So, when Steve Gnagni shared the article above, I found myself doubting some of the decisions we made. I found old reactions about grades being really seriously challenged and I began to doubt whether our decision on process is ideologically pure enough. I also know that this is progress. I will be sharing Rick Wormeli’s article with my team in the fall and we will be checking in with each other on how we feel about the impact of this new process.

I want to thank Henri again and to thank my new twitter pal Steve Gnagni for sharing their ideas. As long as we are all willing to keep questioning ourselves we can continue to help our students grow.

A Change is Gonna Come

A little background info to the story I am about to relay.

Our school has operated for quite some time with a static schedule of 7 classes that meet every day and in the same order. Our class times vary a bit based on assemblies and special events with the primary class times being 40 minutes, 45 minutes, or 50 minutes. There is certainly a comfort level with having a steady rhythm. As a teacher, I am pretty sure what my 8 AM class will be like after a few weeks. I know who is sleepy in the morning, I know who is a bit frisky right after lunch. Unfortunately, I also know who will be late to first period and who plays a sport each season so they will be missing my last class pretty frequently.

A couple of years ago some momentum was (finally) building to look at alternatives to our daily schedule. I was one of the people agitating for this change. My current school is the fourth one where I have taught and each of my last two schools had rotating schedules. Each of them also combined some class drops and one noticeably longer class than others in the day. While the planning for a long class sometimes felt like a bit of a burden, the benefits of minimizing class misses due to sports and tardiness related to time of day were pretty big. I also noticed a benefit that surprised me. Different kids step up as class leaders at different times of day. The personality of my class never seemed as set as it has in the two schools I worked with static schedules. After many meetings and discussions, we hired a consultant to come in and learn about our school, talk to us about our goals, and suggest a working schedule. We settled on a  seven day rotating schedule. Each of our seven periods takes the starting block once during this rotation. Each of our seven periods gets a 90 minute block once during this rotation. Each of our classes meets five times during this seven day rotation. We get a two day back-to-back, a day off, then a three day back-to-back-to-back before another day off. Obviously weekends and school days off work in as well here. When a class does not meet for 90 minutes it meets for 50 minutes. So, what used to be our long class becomes our short class. We get the benefit of a 90 minute block with each of our classes once during a seven day rotation. There are all sorts of things about the schedule that makes me happy. But, there area also quite a few of my colleagues who have not taught in a rotating schedule, they have not planned around class drop days, they have not taught a 90 minute class. This leads to some anxiety, naturally. So, when we adopted the schedule in the spring of 2016 we set the fall of 2017 for the beginning of our life this way. We also announced that we would run a test trial sometime during the academic year that just ended. As a department chair, I started poking around for ways to help my team out in easing their concerns about this transition. I found a nearby school that had made a similar change and I arranged for a team of three teachers to visit that school. I was convinced that seeing this in action and talking directly to people who had lived through such a change would help build enthusiasm. I was right on that front. I also spoke directly to an administrator at that school and asked for advice about how to build support structure in my department for this change. He told me that the best thing his school had done for the math department was to hire a consultant specifically for math who came in and talked about long-term planning for rotating schedules, he talked about utilizing the 90 minute block, and he helped them start some important conversations about curriculum. With fewer contact days, some things we hold dear have to go.  This admin remembered that the consultant came from the Bay area of California and that his first name was Henri. I guessed who he was talking about just from the first clue. After the second clue, I knew I guessed correctly. He was recommending that we seek guidance from Henri Picciotto. My guess is that anyone reading this knows of Henri. If not, fix that quickly. Find him on twitter @hpicciotto. Go to his web home http://www.mathedpage.org  You’ll be happy you did. If your school is considering such a change, or if you simply need motivation and inspiration to really examine your practice as a department and to start serious conversations about curriculum, you should consider reaching out to Henri. I sought approval from my bosses and made arrangements for Henri to spend two days with my department during our final exam week. My Dean of Faculty arranged final exams so that we would have two days with no supervising responsibility so that we could spend two workdays as a team together. Let me tell you a bit about those two days and publicly thank Henri for helping to spur some serious conversations among my team, conversations that have been hard to start otherwise.

I reached out to Henri and shared the praise I had heard. I was excited about arranging this for a number of reasons. I had been reading Henri’s web page for some time and was excited when he dipped his toes into twitter. I had reached out to him for guidance about lagging HW (more on that later) and was happy to have met him in person last summer at twittermathcamp in Minneapolis. I also knew that we had already batted around a number of ideas together as a team here at my school and I felt that we needed to hear a new voice to prompt us to make some tough decisions. We also were looking at a brand new way of living in school that made these decisions feel much more urgent. We ran schedule trials twice in the winter/spring. Once, we ran a seven day cycle one time. The second time, we ran two full cycles. This prompted a combination of optimism about some of the structural advantages of the day under these new circumstances, but it also prompted some real concerns about pacing and curricular pressures. We were primed to have serious conversations and we needed guidance/wisdom/structure for these meetings. Once we agreed that the dates would work, Henri started peppering me with some questions via email and he sent me a set of files to run off for our meeting days. He sent me a broad outline of goals and times and we established that we would spend two days together from 8:15 – 3:15 with a lunch break and a few small breaks built in. I was excited for a number of reasons. First, Henri clearly had a vision for our time together and some rich activities were being sent my way. Second, we never have this much time together focused as a math team. Whenever we are together as a faculty for big pieces of time, we are together as a full faculty or broken into smaller non-departmental groups. I was so excited to spend this kind of time just talking about math and about teaching math. As the days got closer I was increasingly happy about this time together. I was appreciative of my team for being so open minded about this. Normally, during exam week if you do not have proctoring responsibility, your time is your own. I was able to get serious buy-in from six teachers who were trading in time off to grade for two eight hour workshop days. I cannot thank them enough for this.

We met on a Tuesday and a Wednesday in the middle of exam grading week. Within the first 45 minutes of our time together on Tuesday, I was pretty sure that I had made the right decision in inviting Henri to come. We started with a math exploration looking at the relationship between area and perimeter of polyominoes that had us talking in small groups, had someone on the board drawing and explaining a pattern, had me guessing (incorrectly) that some fancy combinatoric idea was hiding in the wings, and just generally energized the minds in the room. When we meet as a department we are usually wrapped up in talking work, in looking at schedules, in discussing policy. It is a shame that we rarely talk math when we are together. This activity immediately engaged everyone in the room and had us thinking out loud and working together. I won’t go through every activity we did together, but I will say that everyone in my department either thanked me for having Henri come to visit or told someone else on our staff about what a great experience that the workshop was for them. I have already heard second hand a number of lunch table stories where my department members were talking about the positive experience that the workshop was. Most importantly, conversations are flowing right now. Conversations that did not seem urgent without a schedule change looming. Conversations that are hard to have in small bursts between classes or through emails. Conversations that are hard to fit in on a crowded agenda for a monthly department meeting. Most importantly, these are conversations that are better started when a coherent, clear agenda for the conversation has been established. This is one of the places where Henri far exceeded my already high expectations and where Henri was just better suited to be a conversation starter than I am. Within fifteen minutes of our meeting on Wednesday ending, I had two teams of teachers discussing the curriculum for their courses. Debating sequencing of curriculum, debating what topics or chapters can be entirely eliminated from a course. Debating how we can offload some responsibility from earlier courses with younger kids to later courses where the students are more sophisticated and see more clearly the need for learning. Remember, my team had already sat through two eight hour workdays on days where they would normally be at home on their own time grading exams. After all of this, they were sitting excitedly debating their courses for the fall. Henri created such an energetic and focused atmosphere to tackle these big questions that my team did not want to leave. I had my children arriving on their bus while my team was still in my room talking. Conversations that I had been trying to have for about five years were happening. The combination of the impending schedule, the valuable structured time together, and Henri’s wisdom and enthusiasm kick started these conversations. I cannot overstate how valuable our time was together and how important these conversations are for our school and our students. After exams, we had another professional development opportunity to look at teaching in a 90 minute block and one of my department colleagues was there as our representative. She talked about how enthusiastic the members of other departments were about this activity, but she remarked that she was spoiled by the two days we spent together with Henri. Pretty nice praise there.

Is your school is looking at structural changes to your schedule? Are you  wrestling with structural conversations about curriculum? Are you looking for high quality, focused professional development time with your math department? If you answered yes to any of these questions, I cannot recommend Henri Picciotto highly enough. I am not his agent, I am not a paid actor here, I am simply a happy happy teacher who has benefited greatly from the time my department spent with Henri two weeks ago. My team seems much less anxious about the changes in our life and they seem clearer on curriculum and instructional goals. I am convinced that our students will benefit greatly from this time we spent together.

Brief thoughts on Graduation Weekend

Yesterday was graduation day here at my school. I am pretty sure that this was my 31st high school graduation ceremony – mine and 30 years as a teacher. I think that I did not attend my little brother’s graduation for some reason or other. At least, I do not remember it if I was there.

There are always waves of joy/sadness/pride/regret that run through me on graduation days. I saw some alums and had lovely conversations with them that made me happy. One joked that his Calc 3 class at McGill was easier than his BC Calc class with me. I think that this is probably a compliment in the end. Some students went out their way to find me to express gratitude while others certainly showed no inclination that I was on their list of people that they wanted to talk to on graduation day. Every year ends with the good feeling that there are students who I have made connections with in or out of the classroom. Young people who appreciate that I was part of their lives here. Every year also ends with the disappointment that there are some students I was not able to connect with. Students who were frustrated by my class, did not connect with my goals or my classroom strategies. Students who will not remember me fondly – if/when they remember me at all. This is both a cause for sadness/frustration and motivation to recharge soon when I think about next year and plan for how to reach a broader set of students where they are.

I had a conversation with a colleague recently that made me reflect on graduation feelings and helped me make sense of them. My family moved in the middle of August 2016 from the boys’ dorm where we lived for six years and into a house on campus that the school owns. Since school was already looming when we moved, we did very little in the way of yard work to make the place feel like our own. This past week, my wife and I were able to spend a notable amount of time working outside and trying to make the place feel like ours. I was talking to a colleague at brunch and mentioned that I felt satisfied about the work we had done that morning. While I do not find any zen-like sense of peace and serenity while doing yard work, I do find a sense of satisfaction in looking back after two hours of work and seeing a recognizable change in our flower bed. When talking at brunch about this I contrasted the work in our flower bed with the work we do int he classroom. It feels pretty rare that we see noticeable change in just an hour or two in the classroom. The sense of satisfaction and pride I felt on graduation day when reflecting on the successes I have had is certainly deeper than my satisfaction about the flower bed, but it takes a great deal more patience to get to that graduation day feeling.

 

Seeking Wisdom and Guidance from my Students

In my last post I was reflecting on some of the important differences between students based, in part, on their age and experience. Thinking about that since the post, I also realize two other important differences between my Geometry classroom and my AP Calculus BC classroom. In our school, Geometry is the last class in our curriculum where there is not a distinction available for Honors credit. Starting in Algebra II, kids get sorted out and those students who don’t see math as ‘their thing’ or simply want to back off a bit in my subject area can. This creates rooms, in both the honors track and the non-honors track, where there is more homogeneity in interest level. In my Geometry class there is a wide divide in interest/background/ability/age in the same classroom. In my Calculus class there is a more level playing field. I think that this goes a long way to explaining some of the data I received this week. The second major difference is that, due in part to the fact that new students enter our school at every grade level, there is a more noticeable age difference in my Geometry class than in either of my other classes. I have students from grades 9 – 12 in Geometry. In my other classes I have only juniors and seniors. I think that this leads to a real difference in the social environment in these classes.

Our school asks each teacher to administer course evaluation forms to all students. The format that the school developed asks many questions, almost all of them Likert scale questions with space included for short answer explanations. I appreciate the emphasis our school places on seeking student input but I have developed the feeling that too many students just glide down the page circling essentially the same answer to questions and they are reluctant to write much down. Some have stated that they are concerned that their teachers recognize their handwriting, but I suspect that most just aren’t that terribly invested in the process. We spoke about this extensively in our last department meeting and one of the conclusions we reached was that we will administer some form of course evaluation at the end of each of our trimesters next year. After all, if the goal of the feedback is to improve the students’ experience, then telling me what to change in May does not have much weight to students who are leaving my classroom in another week. I am kind of embarrassed that I have not come to this conclusion by myself, but at least I am learning, right? I did do two things differently this year. I wrote my own surveys for each of my three classes and I administered them electronically in the hopes that I would get a little more detail from my students. If you are interested, you can see my surveys here for Geometry , here for my Discrete Math elective , and here for my AP Calculus BC class . There are not many differences between them, but I did tailor a bit for differences in the classes.

Here are screenshots of the pie-charts generated on the Google forms. First the response of the Geometry students to the group seating decisions I made this year.

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Here is the response of the Discrete Math Students. One of my sections was small enough that we stayed in one group together all year. The other section had rotating groups for two of the three terms of the year.

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Finally, here is the image for my Calculus team

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I think that there are some interesting things happening here. I had the chance to talk to my Discrete class and they were willing to share some interesting insights. I think that the comfort level with rotating groups is closely tied to a combination of comfort level with the material and with each other. My BC kids all came from AB the year before and many of them were in the same AB sections. They know each other and they are confident with math. My Geometry kids are a wide blend of ages (grades 9 – 12) and backgrounds (a good number are new to our school this year) so there is not as much cohesion. My Discrete kids come from all over the place. Some just finished Algebra II, some had a year of Precalculus. Some had part of a year of Precalculus before switching over. Some are brand new to our school. There is a good degree of camaraderie in the classroom, but there is not a consistent feeling that everyone is on the same page. This is something I need to be more aware of and a piece of classroom culture that I think I can help improve next year. During my conversation with them yesterday, we focused on two topics. The first was group assessment – I have some group quizzes and we have a group final each term. We had all eleven people working together and they seemed to appreciate that, but felt that I needed to trim the number of questions since debate/discussion took some time. Duly noted. They also seemed to largely feel that rotations are okay, but maybe they should change after more than a week. I am thinking that they may change at the beginning of each new chapter. With our new schedule at school next year, this might work well.

I feel good looking back at this year. I took the plunge and moved from static seating in small groups to dynamic seating that created broader networks of communication among my students. I personalized the feedback I ask for and I feel that my students took these questions seriously and shared some remarks with me in a pretty honest way. I have a lot to think about this summer (as always!) but I feel that I am moving toward becoming the teacher I want to be.