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.


The Language That We Use

I recently engaged in a spirited discussion prompted by Patrick Honner (@mrhonner) on twitter and on his blog. The original post that started this whole discussion can be found here and it is well worth your time. Engaging comments there an on the twitters and a friendly suggestion by Patrick himself has me writing here, thinking out loud.  To set the stage for this post, an image from Patrick’s post is important.

Screen Shot 2016-07-31 at 8.34.15 PM

A quick glance at this certainly suggests that these are congruent figures until you look more carefully at how the question is worded. This is a pretty classic example of the kind of question that makes students think that test writers are gaming the system to catch them in a mistake. We are looking at two figures that are equivalent to each other. A rigid transformation maps one onto the other. However, that mapping does not map them in the order suggested. A classic mistake that I lost points for as a student and one that, sadly, I admit that I have probably deducted points for when grading. The debate on the blog and on twitter raised some really challenging questions about our goals with this type of specificity. Yes, mathematics is a precise language and precision is a powerful habit to try to help develop. However, I keep thinking about my fun Geometry class from last year. When we were discussing how to determine whether  a triangle with given side lengths was acute, right, or obtuse we worked out a strategy where we assumed that the Pythagorean Theorem would hold and we decided what the consequence was when it did not. This led to my students saying things like this; “If the hypotenuse is bigger than we thought it would be, then the triangle is obtuse.” Now, I know that the largest side of an obtuse triangle is not called the hypotenuse. When pressed on the issue I suspect that almost all of my students knew this as well. Optimistically, I want to say that they know this as well, but is is early August… My concern here is that I was letting them down by letting them be a bit lazy with their language. What I did at the time was to gently remind them that hypotenuse was not the best word to use there but I understood what they meant when they said it. Should I have made a bigger deal about this at the time? Was I being understanding and flexible? Was I being undisciplined and imprecise? I suspect that there is a decent amount of both of these in my actions and I have to admit that I did not think too deeply about it at the time. In the wake of the conversation that Patrick moderated, I am thinking deeply about it. It is also early August (again, I note this) and it is the time of year that my brain reflexively starts dwelling on teaching again. I am also thinking about a distinction that I got dinged for as a student but this time it is one that I do not ding my students for. I remember losing points in proofs if I jumped from saying that if two segments were each the same length then they are congruent. This is, obviously, true but I was expected to take a pit stop by making two statements along the way instead of jumping straight to congruence. I know that equivalence of measure and congruence of segments (or the same argument with angles) are slightly different meanings. A nice explanation is here at the Math Forum. But I feel pretty strongly that my 9th and 10th grade Geometry students are not tuned in to the subtle differences and I think I am prepared to defend my point of view that they do not need to be. I want my students to be able to think out loud and I DO want them to be careful and precise in their use of language but I do not want them to think that this is some sort of ‘gotcha’ game where I am looking for mistakes and looking for reasons to penalize them.

I am thankful to Patrick for getting this conversation started and for gently nudging me to try and work out my thoughts more thoroughly on this issue. I am interested in hearing from other teachers – particularly Geometry teachers – on how they try to navigate these conversations. How precise should our high school students, especially freshmen and sophomores, be when discussing these issues?

As always, feel free to jump in on the comments section or reach out to me through twitter where I am @mrdardy