One of the newer initiatives at our school is to help students listen and tell stories. We partnered with an organization called Narrative 4 (you can see their work here) I am simplifying the mission here a bit but the idea of storytelling is on my mind for a number of reasons. Next Wednesday our sophomore and freshmen students will participate in a Narrative 4 workshop sharing songs that mean something to them and explaining why. I love the power of stories and am prone to share them myself to try to make a point. I was reminded of this in the Empowered Problem Solving (#epsworkshop) run by Robert Kaplinsky. He made reference in one of the videos in a study module to ‘the story we are telling in our math class’ and this made me think of a recent frustration with our precalculus book. It all comes together, at least in my mind! Anyway, we are starting our unit on conics and our text, as many do, suddenly changes format of how a parabola equation is presented. Our students are used to y – k = a(x – h)^2 and this format makes sense to them. We can easily adapt this to x – h = a(y – k)^2. Suddenly, we are talking about the directed distance from the vertex to the focus and we introduce this new constant p. Okay so far, right? But suddenly, my students see 4p(y – k) = (x – h)^2 and they see 4p(x – h) = (y – k)^2. Why? It is pretty simple to let them know that the a that they have grown to interpret has a side personality as 1/(4p) It is easy to find a point on the curve and show distances that are equal to each other. I do not want to ignore the examples in the text because my students use it as a reference and a resource. I also do not want to stray from a meaningful way to write equations simply because of the whims of our textbook author. I also suspect that so much of what kids learn in school feels like an arbitrary set of equations and definitions and I want to battle that. I want the story in our math class to be that this is a journey together that builds on what we’ve known before. A journey that ties ideas together. A journey that feels logically coherent and consistent to the best degree that I can possibly make it. Lofty goals, I know. I just find the weird changes like the one above undercut that sense of logic, consistency, and damage the connective tissue of ideas that I try to nurture. I am almost certainly overreacting to this weird quirk of Precalc texts, but that feeling was amplified when I thought about our storytelling exercise at school and tried to reflect on Robert Kaplinsky’s message in our workshop. I love it (LOVE IT) when my brain is agitated by these ideas, when I see connections and themes in my life. I try to share that joy (agitation sometimes!) with my friends, colleagues, students, and you, my dear readers.
I am overdue in writing about a high energy twitter exchange I was engaged in recently. I am going to include a few links here in this post that will help give some background to the conversation.
First, many thanks to those on twitter who are willing to engage and get my brain moving. In this particular story the star twitter pal is Kristie Donavan (@KristieDonavan) who went on quite a twitter tear and wrote a GREAT blog post. First, I will link the article that started the whole discussion.
A colleague shared an article from Edutopia with me. You can find the article here The article is called The Case for not Allowing Test Retakes. Now, the idea of test retakes/corrections is something that has been on my mind for awhile. Two years ago, after a wonderful PD session with Henri Picciotto (@hpicciotto or over at https://www.mathed.page ) our department adopted a policy of test corrections. You can read my original blog post about it here. Well, last year the department voted to move away from that policy based on a number of concerns that they had about how kids dealt with the policy. Many of their points were raised in the Edutopia article linked above. We have some new admins at our school in the last couple of years and there is reason to believe that we will be urged to move back to some form of test corrections or retakes. That is why my colleague sent me the link in the first place. I tweeted out a link to the article asking for insights and boy did I get some. Most vigorously from Kristie. Who sent a tweetstorm and wrote an awesome post. Here is where you can find Kristie’s post, I urge you to read it. So, what I am wrestling with is a real sense of hypocrisy that might be simply the result of a strong but unsound argument presented in the Edutopia article and in other debates/discussions about educational goals, student motivations, balancing workload, etc. When Henri was with us one of the things he said that REALLY resonated with me was this – ‘When you are grading you help one student. When you plan for a class effectively you help all of your students.’ [I admit I might be mixing his words a little, but the message here was clear, spend time and energy planning for your class do not get buried in grading] What he also urged, and I saw it in our policy, was to concentrate on learning not on grades. When we did our test corrections I saw kids dig into their work, they debated with each other why something was wrong and how to fix it. They engaged with their tests when they were returned instead of simply filing them away in their backpack or locker. I truly believe that my students, my youngest ones especially, benefited for the motivation to reflect that the policy provided. In the wake of an overwhelming feeling by my department colleagues that we needed to move on from that policy, I adopted a variation for two of my classes – the two where I was the only teacher. What I did was I wrote a reassessment for every test mirroring skills as closely as I could for each problem. Students were allowed to reassess on up to three of the problems that they originally took and I would average scores from the original and the retake. I wanted to minimize time and effort on their part so that they were not mired in looking backwards while we were still on the move. I also wanted to make it more realistic that we could find time during our day to make this happen. There are all sorts of tweaks I wish I had thought of, but it felt like a good faith way to try and hold on to the benefits of reflection while providing some motivation to do so. However, the time and energy spent on some much rewriting and regrading was exhausting. I found myself getting resentful and not enough of the kids were showing the same kind of benefits I expected. I also am actively struggling with what SBG would look like in my classroom. I admit some ignorance here, but my understanding from some reading and from a workshop I attended about four years ago makes me worry that my assessment strategy would not mesh well. I cannot regularly look at a problem on a test or quiz and put it in a nice box. I tend to write problems that pull different ideas together or put an old skill in a new context. Twitter pal Julie Reuhlbach (@jreulhbach) very kindly shared a folder of assessments that she uses in her SBG approach and I am beginning to dive in and try to figure out how I can make some form of this fit my life. She also hosted on her blog site a nice post about SBG. That post is here
So, here I am with about two weeks left before the beginning of my school year. I am trying to balance what would make sense for me as a teacher in my classroom with what would work for my department and what would work in our school context as we try to figure out the path that our new leadership wants to explore. All of this needs to be framed with our students in mind, they are the point of why we are doing any of what we are doing. I have an additional ingredient in my head that becomes more and more pronounced and that is the fact that my older child is now in our high school. Factors that I had been thinking about in terms of educational philosophy are suddenly feeling more urgent and more personal.
Where do I stand this morning? I worry that many of my students are SO driven by grades and by trying to balance their commitments that they are motivated to reflect and learn more by grades than by almost anything else. They tell me this year after year by saying things like ‘I would do more homework practice if you graded homework regularly’ They say this even after acknowledging that they would learn more and do better if they practiced more regularly. Given this fact (at least I am pretty convinced it is a fact) I want to have a set of classroom practices and policies in place that take advantage of this motivation and reinforces habits in a way that leads to better learning, less stress and, hopefully, better grades so that my students feel a tangible sense of their efforts. I want policies and practices that do not increase stress and put time pressures on me and my students. I want students to feel that there is equity across their classes, not to feel like they lucked into (or were cursed by) certain teachers. I think that some sense of uniformity of expectations is kind of important. I want a coherent set of principles to be visible to my students and their parents, a way to express what I believe is important about our work together.
This month I start my 33rd year of classroom teaching. At one point in my life I thought I would have figured all of this out already. I suppose the job would be less rich and rewarding if that were true.
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.
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 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.