When I first started planning lessons, each lesson took *ages* to plan. I don’t really remember exactly what I wrote except that usually the lessons were based on choosing example problems to go over, producing a worksheet for students to work on, and assigning homework questions. Eventually I finally had some textbooks for students and so these lessons ended up being reduced to references to page numbers and questions in those textbooks.

At some point I decided that being very economical with my planning was the mark of good teaching and so my lesson “plans” ended up being really short. “Teach Pythagoras” was an actual lesson plan I wrote. Of course, “Teach Pythagoras” is not a lesson plan. It’s not even really a topic. It’s a short-hand for pick some examples, tell kids how to solve those examples in an ad hoc fashion, followed by make up some examples for kids to try and solve themselves.

When I started using longer-term projects, that meant planning lessons got even easier as I could assign a time-line to the completion of the project and in each day I would support students either with some examples for the whole class to move their work in the project forward or by circulating through the class to help students out.

Up until this stage, any student mathematical discussions that occurred were ad hoc and almost always initiated by students. Not once in my classroom teaching experiences did I plan for student discussion.

About three years ago, I started a new job as a formative assessment specialist. It was then that I first read Peg Smith’s Thinking Through a Lesson protocol. As I read the article, I realized right then that I had spent most of my career planning poorly.

Next I read Dan Willingham’s book on Why Don’t Students Like School? and realized that I had spent most of my career planning tasks for students to do and not planning the thinking I wanted students to do. Tasks prompt thinking but what thinking? Here’s an example of a lesson that could have been one my early lessons. What are children being asked to think about?

Fortunately, I had an opportunity to test out these new ideas around planning for myself. I started teaching my son and between 6 and 8 other kids close to his age in a Saturday class. I decided to plan the student thinking, to try out the Thinking Through a Lesson Protocol, and most importantly, to ask other people to comment on my plans. Here’s my first lesson plan for this class. It’s by no means perfect but it has far more detail on what I will do in response to what I expect students to do, and the first example I can recall of a lesson where I explicitly planned a whole group discussion.

But who has time to plan lessons at this level of detail five days a week, potentially 4 or 5 times each day? The level of planning linked above is unsustainable for classroom teachers.

Last summer we started introducing instructional activities to teachers across our project. Instructional activities, as defined by Magdalene Lampert and Filippo Graziani, are “designs for interaction that organize classroom instruction”. Essentially they define a set of moves a teacher makes to position students to talk to each other about mathematical ideas, surface student thinking about those mathematical ideas, and then orchestrate a classroom discussion around the ideas in order to focus students on a mathematical goal.

These instructional activities have the advantage of bounding the scope of decisions a teacher can potentially make when planning a lesson while focusing the decisions that are made ahead of the lesson on planning for the thinking students will do, and then in the lesson enactment, allowing teachers and students the space to think about and respond to each others’ thinking. The routineness of an instructional activity, if the same structure is used many times, allows thinking about roles, what’s coming up next, to fade into the background so that more thinking can be focused on the mathematical ideas.

When planning one of these instructional activities, I find myself choosing an appropriate task based on some understanding of anticipated student thinking, then imagining how students might approach the task and what they will think about, then considering how to sequence the different strategies student might use toward a big mathematical idea, and then creating the resources to enable me to use the instructional activity in the classroom. This level of planning is sustainable.

As I reflect on my own development of planning over the course of my career, it seems to me that I would have benefited from knowing about planning routines that other people use. I would have benefited from learning at least a few instructional activities so that I didn’t need to plan every aspect of my teaching. I would have benefited from access to tasks where student thinking was anticipated for me. I don’t think a highly scripted curriculum would have developed me as a professional (but maybe my students would have benefited). I would have benefited from seeing how other people sequenced mathematical ideas.

In short, I would have benefited from more explicit teaching of how to plan lessons.

## ben says:

This post really resonated with me. What I find is that even being thoughtful about the planning process ala Peg Smith does not guarantee great lessons. But writing down what happened both good and bad afterwards and thinking about incremental changes for next time can be powerful.

January 28, 2016 — 4:37 pm

## David Wees says:

Hi Ben,

Yes, Thinking Through a Lesson Plan doesn’t guarantee a great lesson BUT I strongly suspect that the process makes it easier to identify the issues with a lesson afterward and to reflect and iterate on it in the future.

David

January 29, 2016 — 2:08 am

## Mark says:

I think a big issue is when teachers are forced to follow the curriculum (textbook lessons). There are weeks spent in 8th grade on laws of exponents and systems of equations. The ultimate outcome is, can the kids simplify exponents and can kids find the intersections of two linear equations using multiple methods. I wish there was a book or online document that was almost like an encyclopedia for what you are talking about on most major middle school lessons.

January 29, 2016 — 11:46 am

## Mark says:

I really like the math new visions document in your article. I have a hard time however matching up the activities with the major drivers of our Algebra curriculum; solving multi-step equations, graphing linear equations, finding the slope, finding the y intercept, simplifying exponents, systems of equations. Is there somewhere in the document where those goals pop out? They also seems like there is a learning curve without professional development. All the PD in my district is about new online platforms, assessment, and standards. (Frustrating)

January 29, 2016 — 12:01 pm

## David Wees says:

Mark,

If you look at our Algebra course, maybe it will help to see the activities positioned within units of study:

http://math.newvisions.org/algebra-i

Here is a fairly detailed description of and set of resources for implementing Contemplate then Calculate, one of the two instructional activities embedded in our curriculum.

David

January 29, 2016 — 12:44 pm

## Mark says:

Looks good. What type of schools (districts) do this in math? I would think private/charter schools mostly or schools that are really on the brink of failure. It appears that if kids aren’t used to doing this & as a teacher you do it, their conversations are 3-4 minutes tops. We teach 80 minutes straight.

January 29, 2016 — 12:53 pm

## David Wees says:

Our project supports a group of 75 New York City public high schools. These activities are designed not to take an entire period and the conversations between students are intended to be short, usually 2 to 4 minutes depending on the activity. Having a more focused conversation helps students participate and talk about what you’d like them to talk about – the mathematics.

We have some teachers who have seen real changes in their students as a result of using these kinds of resources and this kind of teaching.

If you have 80 minute blocks, then you could potentially use one of these Contemplate then Calculate activities as a opener each day, ideally an activity that will help kids be ready to think about whatever it is you want to teach that day.

January 29, 2016 — 1:02 pm

## Mark says:

I am trying to get away from whole group instruction, our Danielson observation system despises it. I usually now hand out work and go around and ask kids questions to lead them to the answers via questioning. I still feel I am shortchanging the kids. Many of them don’t have the basic skills.

I have tried projects during observations and the planning doesn’t seem worth the time spent. The scores don’t justify the time.

How do you ask engaging questions over 40 minutes of an observation?

January 29, 2016 — 1:47 pm

## David Wees says:

Mark,

You really can’t sustain leading a whole class discussion over 40 minutes. You almost definitely want to chunk the class into smaller bits. Check out the lesson plans that go along with these Connecting Representations tasks and the associated slides. You’ll see examples of really deliberate questions being asked and slides that support students in remembering what is being asked (the representations themselves are posted, usually on chart paper, so that students have access to them during the lesson) and suggested timings for students to consider the questions, first independently, and then in their pairs.

February 2, 2016 — 9:27 am