This week has been an extreme. I recently acquired 17 new students, and trying to get everyone on the same page is pretty hard at times (I have 4th-12th grade). I typically look at transformation functions at the end of the year and I needed to hit upon a few topics to refresh and support their knowledge base.

I have quite a few young students in my class, so we looked at the coordinate plane. We explored the quadrants, the axes and how find a specific location on the plane (ordered pair). I then had them work on an activity from CMP, discussing the city of Euclid- how to move from one point to another, and how to draw specific shapes on the plane given two vertices. This activity was also great for my older students: discussing slopes, properties of shapes, challenging them to find as many different regular shapes as they could given set parameters.

For my next day’s lesson, we explored the mathematics behind movement on the coordinate plane. This was a practice in algebra, and I was very proud of my younger students. We were able to quickly move past the concrete stages, and were able to describe things abstractly. Whenever they felt unsure of things, they were able to accurately create diagrams of the situation. This let into talk of linear equations and how they could be related to the coordinate plane.

Since I recently came back from MCTM-Duluth, @Trianglemancsd’s Which One Doesn’t Belong book was fresh in my mind. I had my students work on this, and there were great mathematical discussions happening in the room. They were talking about symmetry, rotations, reflections, dilation, parallel and perpendicular, orientation, etc. I assigned my students the task of creating their own WODB, with at least two reasons each figure could be chosen. Students really enjoyed this task and I went home feeling very good about things.

THEN the next day came. My first class rolled in- and I saw this:

I asked my students what was wrong, and they said- “Mr. Anderson we are sorry. We really have liked the past couple of days in class but you seem to be teaching us stuff randomly. Why aren’t you teaching us like our other math classes where everything goes in order?” This question really blew me away. First I realized that while I knew what the master plan was, I had not been transparent enough about it with my students. While I am a strong believer that you do not have to present students with an objective of the day when class starts, I also believe that you need to create connections between work students do, every day. I had been lax in this.

So I did what every good math teacher does, * I told them to be quiet, open their books to page 145 and do problems 1-85*! Well, maybe not. I am not a good math teacher if that is the case because I stopped what I was doing, took a second to consider their words and respond to their question without becoming defensive of them questioning my methods. I apologized to them for not telling them the whole story, that I was showing them a piece of the story at a time. I asked how many of them have heard of the program P90X. I think there was only one student who didn’t know what it was. I asked them if they knew what that particular program worked- and they didn’t. It is based on the fact that you need to create muscle confusion- you can’t make gains doing the same thing every day. I was doing the same. I feel that while routine is sought after by many students (and is needed because of their home life), they need some changes in mathematical thinking to keep their brains fresh, thoughts flowing, their minds working. Many mathematical problems depend on varying elements to solve, and many times we create numerous mini-segments of mathematical concepts in order to “help students understand the math easier.” Like I stated before, my students were doing an outstanding job bringing mathematical vocabulary to the table when talking about WODB and had great ideas and understanding when figuring out movement and distance on the coordinate plane. I let them know that we were moving into transformations (no, not Bumblebee) and that they needed all of these elements in order to accomplish it.

As soon as I gave students the over-view of what was going on, I was both happy and sad. I saw students thinking about what we had done and they were making connections. They started asking me about those connections and were predicting what was coming- great! The part that made me sad is that when we began on transformations- they were now once again in the “math comfort zone” and they were not as creative, animated or ready to share their ideas as they once had. They expected me to now put everything together for them and “tell” them what to do, they even were struggling with the “formal” vocabulary of translation, rotation and reflection.

When I reflect (yes, teacher reflection is critical for successful classrooms) on how the day played out and compared that to the previous week, I can’t help but wonder if I had actually did the WRONG thing that day. That once again, I fell into the educator trap of needing to help my students so desperately (partially because I felt I was letting them down) that I took the pencil out of their hand and wrote out the problem for them. I will say that I often take the pencil out of my student’s hands- in order for them to stop and think about the problem before they randomly start writing down half-memorized algorithms. I really now feel that if I had just stopped and told them only that we have been exploring pieces of a puzzle and they were going to put all those pieces together today, that they would have not only understood what we had done this week- but also how it all connected and why.

I really want anyone who reads this to give me feedback on this idea, because I am thinking that a little P90X- some brain confusion for students- will keep their minds sharp and asking themselves how things fit together and anticipate how they will use it in the future.

I have no clue what P90X is, so I won’t comment on that particular analogy.

Instead I will briefly riff on related ideas that inform my own decision making as I construct my courses.

I find myself spending a good deal of time making the narrative structures of my courses explicit for students, and asking them to build that narrative too. I think of it as a long-term objective. I know that many of my students don’t expect a storyline to a math course; they expect a collection of skills that get harder as the course progresses. They may expect each thing to

dependon the thing that came before, but they likely don’t expect things to develop and connect. That makes it my job to model this kind of thinking in a math course, and it makes it my job to ask students to practice this thinking.I have had many moments such as you describe, where students question the structure of the course—both in my middle school teaching back in the day, and in my current college work. I try to welcome those questions and to understand what needs students are expressing. After all, I do want to meet my students’ needs. And I keep my eye on the end game. Where do I want my class to be two months from now, or at the end of the semester? What teaching moves will support getting there? What teaching moves will undermine getting there? What teaching moves are likely to be neutral—neither getting us closer nor impeding our ability to get there? I prioritize the ones that support getting there. I am open to spending some time on the neutral ones, and I’ll resist the ones that impede.

I can’t really say which moves fall into which categories for your goals with your kids in your (very unique!) teaching situation. But if you can talk in an informed way about these kinds of decisions, you’re probably going to be making (mostly) the right ones.

I REALLY like this analogy because I like the idea of mixing things up. This is how kids will see content once they leave school and they need to be able to deal with it.

At the same time, P90X sucks hardcore and you won’t stick with it unless you have total buy-in. Similarly, students will be ok with it if they trust that you have a plan. Otherwise, as they said, it will seem random. I don’t think you need to change the tactic, but maybe clue them in.

This post reminds me of something on Dan Meyer’s blog: The “real world” isn’t a guarantee of student engagement. Place your bet, instead, on cultivating a student’s capacity to puzzle and unpuzzle herself. Whether she ends up a poet or a software engineer (and who knows, really) she’ll be well-served by that capacity as an adult and engaged in its pursuit as a child.

I have felt this way a number of times. But remember, students are used to (and usually expect) to record examples, practice from a textbook, and get clarification when needed. When these expectations are not met, there can be backlash or confusion. Most students work through school by trying to “figure” out the teacher and figure out what the least amount of work is to get the desired grade. I don’t blame them. But when they are asked to do something different, there can be resistance to the change.

Keeping your end goals in mind and continuing to remind students what you are working toward might help them be more comfortable with the uncomfortable, if that makes sense. Good Luck. 🙂