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.


Brief Thoughts About Classroom Closing Strategies

I am still processing the keynote speech that Tracy Zager (@TracyZager) gave at TMC16 and I hope to write a coherent blog post about it soon. One thought that is on my mind because of her is that I need to make a serious commitment to thinking more deeply about how my classes end each day. FAR too often they end with me, or a student, noticing that time is up (we do not have beginning or ending bells for our classes) and everybody packing up quickly and scurrying off to their next class. This has to stop. It is not fair to my students AND it undermines any habits of thoughtful reflection that I claim to be important for me and for my students.

At my last school I had an alarm clock app on my laptop that was relatively easy to manage. I programmed it every morning to sound with 3 minutes left in class. I had it linked to a portion of Steve Reich’sĀ Music for 18 Musicians on my iTunes library. What happened at this point was that the music faded in and increased in volume for about 30 seconds. This was our cue to start wrapping up class. My students got in the habit of using this time to slowly pack up their page while we tried to have a conversation about what went on in class that day. When I changed schools I changed laptops and I did not find a similarly friendly app. I also was not thrilled with how those conversations went so I sort of abandoned this idea. Looking back, I am pretty disappointed in myself about this. Whether or not I can find an appropriate timer app (I could, of course, just use something as direct as a kitchen timer) I certainly did not need to abandon this idea. We have been having conversations at our school about our schedule and about the busyness of each day for our students. Our classes are in three different building on our campus and there are many times during the day where the five minute passing time between classes is a stretch for some of our students. If they simply dash from one class to the next with no structured opportunity to pause and reflect, then we teachers should not be surprised when there is less than ideal recall about recent conversations and activities in class. I do not want to obsess about each minute we spend together and get defensive about the idea that ‘class time’ ends before the actual end of the scheduled class. Looking back at the habit I tried to instill at my last school, I think I was coming from a good place. I often framed these two to three minute chats just in the light of ‘What do we know now that we did not know 40 minutes ago?’ and I suspect that this is a decent place to start. However, as with most classroom practices, if I am not diligent and thoughtful about its implementation, I suspect that students will simply see my class as one that ‘ends’ three minutes sooner than it is scheduled for. I also think that they would be largely appreciative of this extra time to breathe, to dash to the bathroom, or to simply stroll to their next class at a more leisurely pace. Honestly, this little advantage in and of itself would not be a bad thing. But I have larger goals than that. I want my students to start to get in the habit of reflecting on our time spent together, to think about how we have grown as a group in our time together, to pause and reflect on an important problem we discussed, a surprising result we found, or a challenge that still lies before us. If I have any real hope of this happening, I need to be a disciplined and structured role model for this habit and, I think I need to be transparent about this. I want to discuss this as a goal at the beginning of the year and I want to refer back to this conversation. Recently I shared a document I created calledĀ How to Succeed in Geometry. You can find it here. It is a draft in progress and I intend to create similar docs for my other courses. I need to add in some more description at the beginning about how we will conduct discussions in class (thanks to the great TMC16 morning session run by Matt Baker (@stoodle) and Chris Luzniak (@pispeak)), how we will try to end our time together on most days, and how we are going to commit to paying attention to each other and not just to what old Mr. Dardy has to say on any given day.

Please help me flesh out and improve my ideas about classroom closing strategies by sharing your questions, comments, stories of success in this area either here in the comments or over on the twitters where I am @mrdardy