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.

Seeking Better Feedback From Students

At this school and my last one there is a formal process for students to voice their opinions/concerns/suggestions through a course evaluation form. At both schools I have noticed that not enough students take this process as seriously as we want them to. The forms are well-intentioned and detailed in their questions, but they are all Likert-scale questions (with some blank space for expanding answers) and they are hand written forms. I suspect that many students are self-conscious about their handwriting being identified. I think that one of the results of this is that the only handwritten extensions we tend to see are from students who are happy and want to share nice words in depth (we love it when we see these!) or when they are especially unhappy and want to share unkind words in depth (happily, these are much less common.) However, I always walk away feeling that these could be better and more useful. I would love to have a process where these are done online anonymously as I suspect that we will get more willingness to expand on answers. I also want questions that are aimed a little more directly at the concerns of our math classrooms rather than well meaning general feedback forms.

I am convinced that the process is a meaningful one. Letting our students know that their voices and opinions matter is a powerful thing. Letting them know that the adults who have been evaluating them need to hear back on how we are doing levels the playing field (at least a little bit) and this tells our students that they can be part of an honest feedback loop where we can grow based on their experiences/opinions/successes/failures. But I also know that the process can be better than the one we have.

I know I have read a few posts along these lines and I am off to the MTBoS search engine this morning to see what I can find. I would love to hear from anyone reading this about their successes, and failures, in elucidating meaningful feedback from their students.

As always, feel free to drop a comment here or pick up the conversation over on twitter where I remain @mrdardy

Thanks in advance for any wisdom.

Collaborative Classrooms

When I moved up north from sunny FLA in 2007 I made a big decision about the geography of my classroom. In my last school I had seats arranged in groups of 3 or four, I referred to them as pods and my students selected their pod mates. They usually stayed with the same group all year long and built up some real team identities centered around their pod. When I moved to my new school in 2010 I had two large conference style tables brought to my room and had students sitting in big groups of 10 each. Typically, students stayed at one of the two tables all year long, but there was a little bit of movement at times. In 2015 I moved those tables out and got moveable desks and I am back to my sets of 4 seats. However, this year I am using visibly random grouping (using Flippity and happy with it) to shake things up and encourage more of a sense of collaboration across a larger group of their classmates. I begin each week with a new seating arrangement. I have been pretty happy with most of this evolution and I am convinced that these arrangements have increased student communication over the years. However, I saw Susan Cain’s TED Talk not too long ago where she talked about introverts and the impact of all of this collaborative time on their learning and their comfort. Since seeing that talk I have had a bit of an internal struggle about how to try to compensate for the fact that not everyone wants to talk as they learn. Not everyone is comfortable thinking out loud before they have come to some sort of a clean conclusion. Not everyone thinks at the same pace. Luckily for me, Brian Miller (@TheMillerMath) wrote a blog post that has come to the rescue for me with ideas about how to address some of these fears. Brian wrote about a great idea for balancing the principles at hand that seem to be in competition with each other. His post is over at and I strongly encourage you to read it if you have been thinking about some of these conflicts.

Our school is moving to a new schedule next year where we will have five class meetings in each seven school day stretch with one class at 90 minutes and the other four meeting for 50 minutes. I think that these longer spans of time together (currently, the majority of our class times are 45 with a handful of 40 and a handful of 50 based on assembly schedules, etc.) will work beautifully with the ideas that Brian laid out. I am on the fence about the nature of how I want to deal with the earbud/headphone question. I like the idea that Brian has but I am not sure about endorsing any type of paid music services explicitly with my students. I know that almost all of my students come equipped with earbuds and mobile devices everyday (probably a higher percentage than those that come equipped with a writing device to class each day!) so that is not a hurdle at all. I have announced a group quiz for next Wednesday and I know that I want to have at least one day before then where I explicitly have ‘alone time’ for thoughts before reconvening our pod conversations. I am debating whether I need to physically separate seats for this alone time or whether that is too much time and interruption. I’ll be writing about how it goes.

Communication Breakdown (Rethinking Assessment Ideas)

My first post of 2017, good golly where did January go?!?

Our school uses an LMS through FinalSite, a company that manages our school home pages. It is a pretty typical looking LMS. I populate each class with my students so that when they log on to their student portal they see each class they are in (as long as their teacher uses the LMS) and they can see calendars, they can download assignments, they see their HW and upcoming responsibilities, etc. My hope is that students check in pretty regularly (daily is a pipe dream, I fear) at least on Sunday night to scope out their upcoming week. In addition to populating this calendar – usually about a week in advance, but I sometimes lag a touch, I keep a spot on one of my side chalkboards where i highlight upcoming highlights. I lagged on that recently as well. As I hinted earlier, January has been a bit of a blur for reasons I cannot pinpoint. Anyway, last Monday I had a rare Monday test scheduled for my AP Calculus BC gang. Their class met right after lunch and a couple of students came in during lunch and asked if the rumor that they heard was true. The rumor they were referring to was a rumor that they had a test that day. I mentioned that this had been on their calendar for well over a week and confirmed that, yes, this ‘rumor’ was true. Kids got on their phones to notify classmates and they frantically started flipping through their text book.

I kept my calm and I assured them that they would be fine. they had been doing their work (I said optimistically) and that last minute cramming rarely has much positive impact. Most of the class performed reasonably well – one perfect score and one student who only missed one point out of a group of fourteen – but the average was lower than usual and one student in particular was way off of his usual mark. The frustration got me thinking about a number of things and I want to use this space to think out loud about these issues.

First, I worry about communication in this increasingly digital environment. I used to print off weekly calendars and hand them out at the beginning of each week. Some kids would lose them, some would carefully put them in their folders, some would cram them in their backpack never to be seen again. Mostly, kids seemed to know what was coming up or at least kept it a bit of a secret when they were surprised by an assignment or an assessment. Now, I print almost nothing. I post on the LMS. I keep the reminder chalkboard. I send out email reminders through the LMS. I send some occasional emails from my school account with attachments for notes or suggested extra work. I hear repeatedly from students who did not know I had sent an email or that I had posted to the LMS. This makes me wonder how much of the blame lies on me for moving away from printed reminders. I mean, if 14 out of 14 students did not know that there was a test on Monday then part of the blame falls on my shoulders. But, and this is important, something is odd in the student culture around my class if 14 out of 14 students failed to register this fact in a planner or take a look ahead at their upcoming week before reporting to school on Monday. I do want to take a moment here to compliment my students in their reaction to this event. Not a single one complained about unfairness, not a single one said to me that this was my fault, and when they received their grades back not a single student voiced their unhappiness about the situation. It would have been so so easy to point the finger at me and none of them did. This is a credit to their character and willingness to take responsibility. A number of them did ask to take advantage of my policy for reassessing, but no more than usual really.

So, I am questioning my role in communication and the avenues I choose to take advantage of. The other question this raises for me is my attitude about announcements for assessment. I know that many of my colleagues, both in my building and out in the world, have as part of their practice unannounced assessments. I have never done this and it is mostly because I find myself overly sensitive to charges of increasing/causing student stress. I always make sure that there are at least three school days between announcing and administering an assessment. In the case of major unit tests, I want to have at least one weekend between announcing and administering the test. But this incident has me questioning this commitment. Am I seeing a more true reading of student mastery of material if I check in periodically when they do not know that I will do so? Am I bypassing the stress of test and quiz preparation if I just drop a quiz or test in their lap when they show up for class? How do I setup a situation where an unannounced assessment is not such a big deal for the student?

As always, I am seeking wisdom here. If you have made a practice of unannounced assessments, how do you handle that? How do the students respond? If not, is your reasoning similar to mine? How do you communicate calendars to your students? Teachers here use either our school LMS, Google Classroom, Facebook, or old fashioned paper. What are the habits at your school? What really works? Drop me a line here or over one twitter where I remain @mrdardy

A Delightful Conversation

Last week in my Geometry class we had a fantastic conversation about a homework problem. Here is the problem in question –



I wish that I could take credit for having written this, but I am certain that I ‘borrowed’ it from somewhere. Likely from the fantastic resources shared with me by Carmel Schettino (@SchettinoPBL)

So, this is the kind of problem that I expect only a minority of my students to navigate successfully on their own, but I am convinced that almost all of them will benefit from thinking about a problem like this one, from a little active struggle along the way. I KNEW that this would be asked in class if anyone took the time to do the HW I assigned, so I was pleased that it came up. I started by telling my students that I LOVE this problem and asked them if they could guess why. One student said ‘Because it’s so hard’. I laughed that off and said, yes it is hard but I love it because it ties together a bunch of important ideas. Off we went on solving this. I started by asking a couple of questions that probably seemed a bit irrelevant at first. I asked why they knew that the y-intercept was (0, 3) and that the x-intercept was (4, 0). Before they could answer I made sure to mention that they knew this without looking at the graph. We eventually arrived at the realization that we know whether a point is on the line or not by looking at the equation itself. If a point makes the equation true, then that point is on the line. If not, then not. This is the kind of thing that I think my students know but being reminded regularly sure does help reinforce it. I hope! So, I thought I had set the hook here for the rest of the problem. We talked about what we know about squares and we talked about how to identify points on the square without knowing their real coordinates. We got a little lazy, and I was okay with that,by calling the bottom right corner (x, 0) and the top left corner (0, y). This gave us no choice but to call the top right corner of the box (x, y). At this point I paused and asked them to remind me what needs to be true about points on a line. Then I asked them to remind me of what we know about a square, therefore what we know about x and y for that mystery point (x, y). It wasn’t easy to get everyone to agree with our conclusions, but I think we got there. We agreed that the x and the y had to equal each other. We agreed that the y coordinate had a definition based on x. We agreed that this was an equation we could solve even though it was not a bunch of fun to solve it. After all of this work it felt like the problem should be done, students were pretty sad to realize it wasn’t. We still had a conclusion to make about the triangles created. One of my students was pretty insistent that they needed to be congruent because their angles had to match up. This was not the time to launch into a conversation about similarity and I decided it was not the time to talk about the restrictions of AAA conclusions between triangles. We have talked about equilateral triangles of different sizes and we are (mostly) okay with that, but I felt that that conversation would be a diversion here. Instead, we kept at the calculating and we looked at side lengths. Once we agreed that they were not congruent, I pointed to the slope of the line and talked about the fact that his instinct was foiled by the fact that x and y lengths were not changing at the same rate. The whole conversation took quite some time, might have been 15 minutes by the time the whole thing was done, but I felt that we had done some important heavy lifting.

If you recognize the above problem as your own, feel free to claim it and let me know. Know in advance that I am very grateful for such a rich problem to tie together ideas of distances, slopes, line equations, properties of squares, and triangle congruencies all into one tidy package!


Questions about Questioning

I feel I am long overdue to write this blog post. In part, this is due to, you know, life getting in the way. In part it is because I have about three posts swirling around in my head right now. Next week our students are taking term finals so I will have a little more unstructured time and I may finally get around to writing more. That is, if I get around to writing plans for the short stint between thanksgiving and winter holidays.

Today, I am going to try and make sense of a fantastic post by Mark Chubb (@MarkChubb3) that can be found here. In the post (which you DEFINITELY should read) Mark raises important questions about the questions we ask our students AND the purpose, the goal, of those questions. I often tell a story about a student who graduated back in 1993 named Ashley. I had the privilege of teaching Ashley for four years in a row up through Calculus BC. The week before her AP exam I asked her how she was feeling. She told me that she was not worried at all because she knew that if she got stuck on a problem she would hear my voice in her head asking her what that problem reminded her of or what have we done in the past when we have seen this. I was flattered that she had internalized some of the strategies we had worked on together and I felt good that she felt comfort in my leading questions that I had been asking her over the years. She was also a tremendous student who was in a group of talented kids who pushed each other over that four year span. Since then, however, I have begun to question myself about the sort of questions I pose. I still believe that most of my students would be able to effectively work through problems they are presented if they can have an internal monologue that is similar to the conversations we have as a group. What I worry about is whether my guided questions are taking away their agency, their ability to discern what they think is important in a problem. I made it through high school math pretty successfully and I have confidence that I can guide students through this journey. But posts like Mark’s, and conversations I have had through this blog, in conferences, through twitter all push me in the direction of making my voice less central in my class. I have taken great strides in this direction in the past few years, but I still feel that I talk too much, that I initiate conversations and lines of questioning too often. That I impose my sensibilities about what to notice and what to wonder about on my students. The trouble is that many of them are happy to have me, and their other teachers, take on this burden. It is easier, it feels more stable and safe to hear the expert in the room direct the conversation. I know that this is not the best strategy but I too often fall into this trap.

I am going to lift a portion of Mark’s post here to draw attention to the central question about questions that I think he was trying to raise.


Funneling vs. Focusing Questions

As part of my own learning, I have really started to notice the types of questions I ask.  There is a really big difference here between funneling and focusingquestions:


Think about this from the students’ perspective.  What happens when we start to question them?

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After reading this and playing back a number of classes in my head, classes that I was really proud of, classes where I felt that my students had made some major breakthroughs, I realized that I do FAR too much funneling and not enough focusing. An easy excuse is that my students struggle in metacognitive processes, so it is more painful and time-consuming to do this. And, just like my students want the more comforting path of me telling them what is important, I am prone to take the comforting role of the guiding questioner. But my students are not going to get better at monitoring and understanding their own thinking this way. They are not going to take ownership of what they feel is important in a problem this way. They can get to be better mathematicians and be more successful at high school math, but I fear that I am training students to be mini mrdardys instead of being better high school mathematicians as themselves.


Our school is moving to a new schedule model next year. We will be on a seven day cycle where in each rotation we meet four times for 50 minutes and one time for 90 minutes. This will force us to re-examine how we run our classes, how we will value and plan for our time together with students. There are many layers of what we will have to examine but for myself, I think that I will be going back to Mark’s post over and over, I’ll be looking at a few classes that I have had videotaped and I will be working out how to hand ownership of ideas to my students. I will be working on how to make sure that the classroom and the class time we spend together is not so dependent on my point of view and my insights into problems. I want my students to leave my class better high school mathematicians, that is absolutely true. But I want them to be better models of themselves as high school mathematicians, not imitations of me. As Ben Folds sang once, I do the best imitation of myself. I don’t need my students to be imitations of me.


Experimenting with Visible Random Groupings

In some ways I think that I am intellectually adventurous, that I am willing to try something new in my classroom. In other ways I struggle with change. I try to make myself feel better about this by reminding myself that we all struggle with this in varying degrees.

This past summer – my third lucky summer at Twitter Math Camp – I finally committed to trying visible random grouping (to be referred to as VRG for the rest of the post) for this academic year. A little background here.

When I moved up north in the fall of 2007 I made a commitment to not have my students in rows and columns. I no longer felt comfortable with most of my students looking at the back of other students’ heads. So, I rearranged the seats at my old school in ‘pods’ of three or four desks. However, I always let students pick where they wanted to sit. As most of us know, even if WE don’t assign seats, the students essentially do this themselves. I comforted myself by thinking about the camaraderie I saw, by listening in on the lively conversations that did not happen when my students sat as if they were in a matrix, and by the fact that I know that I would have preferred life this way as a student. When I moved to my new school I had two long conference style tables so I had two largish groups of students working with each other. Two years ago I ditched the conference table and went back to pods.

Over the past three summers I have heard more and more conversations about the power of rearranging the students, about shaking them out of these simpler comfort zones and encouraging everyone to be comfortable sharing ideas with everyone else in class. Alex Overwijk (@AlexOverwijk) has been an especially articulate proponent. So, this summer I learned about a pretty cool website ( where you can build a roster for a class and anytime you want this program will randomize your class. In groups of 3 or 4 or 5, by the number of ‘teams’ that you want, etc. It creates a cool visual that you can project and the kids get rearranged instead of staying in their friendly neighborhood comfort zone. I committed to trying this for a number of reasons, the primary one being my experience the past few years in Geometry. I had been teaching mostly AP and upper level honors classes and these students mostly knew each other for awhile and they were comfortable sharing ideas and debating/challenging each other at times. Not true of my Geometry class. Even last year’s class which was outgoing, chatty, and engaged. They did a great job in their pods discussing ideas but did not do a good job projecting those ideas out to the class. They always wanted to filter ideas through me and, over the course of the year, inevitably fell into some ruts about who took command when I asked them to work together.

Now, enter VRG. The strongest proponents discuss doing this every single day to continually shake things up. I got a little scared of this because I really value the sense of camaraderie that I have seen developing over the years, so I came to what seems like a nice compromise. On the first day of each week, I shuffle the class. I am now ending the fourth week of the school year and I have some observations I want to share. I am particularly motivated to do so by a twitter chat this morning.

There is sound research in the field about VRG and its effects. This research suggests that the positive effects of this practice are most clearly seen when this happens every day. I do not want to discount this and I do not want to feel like a contrarian. What I want for my classroom is for my scholars to not only know everyone else and hear the ideas of their peers, but I want them to be in a zone that feels comfortable and safe. My prejudice is that this zone is more likely to happen if I have some time to get used to my new teammates. What I have seen in four weeks can be summarized as follows (and I will make separate remarks for my AP Calculus BC group and my Geometry group)

  1. In BC Calculus I have also been incorporating whiteboards that the pods write on together. The combination of whiteboarding (and presenting the ideas of the pod) out to the class along with VRG has been pretty spectacular. Again, these are kids that know each other well, but I have been seeing active conversation across table groups to former teammates that is lively. I can step out of the way and let them bounce ideas around as I wrote about yesterday.
  2. In Geometry we have not done as much whiteboarding, I want to improve on this. What I have seen is students talking to people they did not choose. I see them making guesses to/with their neighbor. I have seen students more willing to stand up and talk. I have heard some lively discussion between students and I know it is not just with their good buddies unless they all magically happen to love each other.
  3. I have been able, in both classes, to call on a wider variety of people because even the shy/underconfident/nervous kid has someone in their group whose ideas they can paraphrase. In the past few years I felt that there was more of a posture of looking to one person in each pod to be the spokesperson. I see less of that now.


When I tweeted out my happiness about weekly VRG I was promptly congratulated AND reminded that this would be even better if it was done daily. I may get there, but I kind of feel that this is my 10% moment. That place where I am making a change I know is for the better but I am limiting myself in my own discomfort a bit so that I can still feel sane and effective in other arenas.


Today was a pretty blah day until my last period class. My first three classes all had assessments so I had no fun conversations and I watched work pile up. As I came in to my last class of the day – my Geometry class – one of my Geometry teammates was waiting in my room to share that his students had been making some great strides in GeoGebra. He told me that a number of his students were really beginning to dig into what GeoGebra could do for them, especially now that we are talking about transformations. I used Geogebra extensively when writing my text and I borrowed from resources around the web for activities. One of them was an activity called A-Maze-Ing Vectors which had been created by the amazing Jennifer Silverman (@jensilvermath) and we used that activity the past two years. My teammate who had been waiting to share his good news had asked me this past summer about modifying this activity. We had had trouble completing the activity in one day and it did not take up enough for two solid days. He also had an idea about combining vector transformations on objects more complex than points. He created a pretty wonderful adaptation of the activity (you can find it here) and my students worked through it yesterday. I opened class today by projecting the last page on my AppleTV where we had to navigate a triangle through a maze and I invited a student to come up and draw on the TV (with a dry erase marker, don’t worry!) and I cannot tell you how great the conversation was in class. I sat down – a commitment of mine based on my #TalkLessAM session at TMC16 – and just watched the fireworks unfold. Kids were challenging each other, going up to the TV to draw their ideas, debating distances, talking about slope, worrying about vertices colliding with walls and discussing the option of rotating the triangle as it moved. I was SO thrilled with the engagement and the level of conversation. I credit this to a number of factors. The original activity was terrific and my colleague’s rewriting of it is creative and concise. Kids like drawing on a TV – it feels naughty or something. I sat down and got out of the way. Kids had worked this through the day before in their table groups and were invested in both supporting their teammates and making sure that their memory and their perspective was clearly heard. They were supportive of each other and slightly defensive if someone else had a different approach. After a pretty uneventful day at the end of the week it would have been easy to just limp tot he end of the day, but these kids brought each other to the finish line for the week sprinting. I am optimistic that we can pick up with a similar level of energy on Monday.

Questioning Myself

This is going to be a super quick post and I would LOVE some feedback here and/or over on the twitter (where you can find me @mrdardy)

I am one of three teachers of Geometry at my small school and I am also the chair of our department. I feel that the three of us ought to have pretty similar policies to make life feel a little more unified and fair to our students. I have opted in the past to keep most of Geometry calculator free. I feel that this is one of the last opportunities to try and help firm up some number sense and some self reliance with minor calculations. I also encourage my kiddos to leave answers like the square root of 160 as a final answer or even something like ‘the sum of the first 98 natural numbers would be the number of handshakes’ to help offset any anxiety about calculations beating my students down. I also place very little emphasis, pointwise, on arithmetic mistakes. One of my colleagues pretty vigorously disagrees and feels that having a calculator by their side eases pressure, and is simply a more realistic way to approach life for her students. I find myself questioning my decision here since I do not restrict calculator usage in general in my other classes. I do, however, worry a bit about all of this since I am hearing pretty consistently from recent alums that they head off to college and are not permitted to use calculators in their freshman classes. My recent Calculus students report this very consistently, they take freshman Calculus at college without a calculator. I know that there are all sorts of reasonable arguments that we should not make high school decisions based on college realities. I also know that I am hearing back from a small group of students.

So, I guess all of this rambling is really about one thing – Give me advice! Let me know how you approach this question. Does it depend on the level of the class? Is it a departmental decision? A school or district policy? Am I simply holding on to some quaint idea that mental arithmetic really matters? I fear that I am not being coherent or consistent in how I think about this issue. HELP!

Countdown Mode – Ideas I Want to Commit to This Year

Tomorrow morning I have my last committee meeting before classes. Saturday we have a series of orientation activities and Monday we finally meet our new classes. I know that I am more likely to stick to a resolution if I make it public, so here goes a brief post to hold myself responsible.

As I have written before, I attended a morning session at TMC16 this year that focused on creating a classroom environment that encourages discussion and debate. I think that I have done a good job in the past of creating an environment where small groups have meaningful conversations. What I have not done well is to shake up those group dynamics or to help my students take ownership of their own ideas in presenting them to the class at large. I will be making a couple of changes this year to address each of these issues.

  1. Visible Random Grouping – At the encouragement of a couple of Lisas (Lisa Winer (@Lisaqt314) and Lisa Bejarano (@lisabej_manitou)) I will be using flip this year. I just entered the class lists for a couple of my classes and started playing with it. Pretty pleased so far, I must say. Since I was the type of student who liked to just settle in and speak with the same people all the time, I have given in to that tendency as a teacher. I was convinced by a number of conversations – both in person and through twitter – that I should try something different. I am committed to randomizing my groups at least on the first day of each week. If there is some special activity that needs different sized groups, I will change them on the fly. I am interested in seeing how this play out and I will be writing about this as the year goes on. Two of my classes are currently small enough that we will all sit at one committee sized grouping of tables. The other two will be split into pods.
  2. I am asking the maintenance folks at my school to remove my teacher desk and chair. I want to decentralize myself. Too often students look to filter their ideas through me before they are presented to the entire class. I have a couple of ideas about how to change this. First, by not having a desk there is no logical place to look for approval. I often move around anyway, but I hope that removing my desk means that I need to mingle among groups even more and become less of a central figure int he classroom. I am also committed to an idea I picked up at TMC. When a student has something to say, either a question or a statement, I will sit and that student will stand. We will all attend (hopefully) to the person standing and talking.


I am excited about the upcoming year and about these commitments to creating more space for my students’ ideas to take central stage in my classroom. I look forward to reporting back to everyone.