This is only my second year teaching 6th and 7th grade math. I work at a school with a lot of students who score a level 3 or 4 on the state exam; for example, most of the students I teach who struggled in my class last year, still got a 3 or 4! So there are different challenges to teaching these students – I need way more extensions than I’m used to needing. I don’t need to scaffold as much (and in fact, I need to consider carefully whether I’m over-scaffolding and underestimating what they can do on their own).

Additionally, since this is only my second year teaching these two grades, I’m not as familiar with the curriculum: both the content in these two grades and the arc or story of the math. I am still figuring out the big ideas, and how best to build them together. I have a 3 – 5 year “plan” or expectation. Last year, I was just merely considering the topics and skills from a stand-point of making sure that I knew all of the topics AND that I knew the skills myself. Unfortunately, this meant that last year, I didn’t necessarily do my best teaching. Some topics were taught in ways that were more true to my pedagogical beliefs, while others were delivered in a way more congruent with my colleague’s beliefs, because I was using their curriculum to do my instruction.

This year, I’ve started to make changes. I’ve considered how I want to build the arc of the various units I am teaching, and I’m thinking about better problems to use with my students. I’m thinking about how to find the rich tasks for students to engage in, as well as the different instructional models I can leverage for different types of tasks. In the course of participating in my MfA PLTs and other PDs, I’m trying out various instructional routines and best practices – everything from the routines for reasoning from Amy Lucenta and Grace Kelmanik to number strings from Kara Imm and Pamela Weber Harris. I tried out an “important stuff, neat stuff, tough stuff,” style packet from PCMI. I have been using some of the content from CMP3, as well as some of the content from Openmiddle.com, openupresources from Illustrative Mathematics. I’ve continued to use some of the resources from my colleagues (especially in the first seventh grade unit on Probability, since it’s drawn from Engage NY in a very specific manner – though I confess that’s currently my least favorite unit because I feel the least ownership and understanding and enjoyment of it).

I am still tweaking the arcs of my curriculum, and considering how and when to cover the various content areas. I’m considering how to pull the various resources together to create a coherent set of units and to address the major skills and avenues for thinking. I’m considering how to build a mathematical community of learners and how to strengthen my students’ mathematical curiosity. I’m enjoying this work, but I do sometimes have to take the “long vision” – I’m not going to perfect my curriculum overnight. I am still making sense of the big ideas and mapping the topics that I have to teach to the fundamental layers of mathematics.

This week in particular, I spent a lot of time using the Illustrative Mathematics 6th grade unit 4 on division of fractions and thinking about which parts were necessary for my students and my classroom, and which things were unfeasible. I’m excited to hear the conversations my students are having, and the ways in which they’re developing their understanding. Earlier today, I had one student confess to the whole class (after multiplying by the reciprocal), “I know to do that, but I don’t know why.” We talked about making sense of the algorithm, and connected it to the diagram another student had drawn – suddenly, it became clear that the reciprocal was the number of that fraction in one whole – and multiplying it by how many wholes you had would get you the total number of that fraction in the dividend. We haven’t done every experience in the Illustrative Mathematics curriculum (and we’re going out of order because my school has a particular arc to our units), but it was such a rich conversation. I’ll write more about it in a separate post. My students have been making sense of models.

Meanwhile, in 7th grade, I’ve been using the routines for reasoning to develop my students’ understanding of how to write equivalent expressions. We did three Contemplate then Calculates to develop my students’ ability to chunk diagrams and see how to find the tenth, hundredth, and nth stages. Today, we launched a new routine: Connecting Representations. I was surprised by the results of it – and again, I’ll make a separate post about this.

The other thing I’ve been doing is collecting more and more student work and analyzing their thinking. In teaching a rational number operations unit in 7th grade, I made a close analysis of the kinds of mistakes the students were making on the quizzes. This will help me both this year, in teaching some of those same skills to my 6th graders as well as going back and doing targeted instruction for students who still made certain mistakes. It will help me even more next year, in planning specific activities to help my students unpack certain common misconceptions and develop a deeper understanding.

Finally, I’ve been thinking about ways to engage my students. I don’t want any of my students to be bored, I want to manage the range of learners in my classroom, and I want to develop a mathematical community more. I have begun to notice that there are fewer and fewer hands going up in my classes (especially in the 7th grade!), and I constantly hear from the same students. I am seeking new routines to change up who the talkers are. I don’t want to do random cold-calling, but I think in January, I might ask students to fill out a survey/reflection about their class participation and to start tracking which students are raising their hands and/or being called on/sharing.

The other thing I want to work on is the small group and partner conversations being more equitable. I use visibly random groupings (students get a card each day to find their new seat), but I’ve begun to notice that when I approach a random group and ask them “What have you discussed?” during a turn-and-talk, it is almost always a boy who jumps in to answer first. And if two students both start talking simultaneously, the boy often talks over the girl to continue and the girl usually backs off to allow the boy to finish his idea. I’ve started naming students and making eye contact with the girls to be conscious of hearing more of the girls in my math class. Probably another post on that at some point.

Sometimes, I have trouble wrapping up my thoughts in a post like this, because I don’t have the answer to the questions I pose. Continue the conversation with me on twitter at @MrKitMath.