In my last blog post, I shared my mental model for how to teach a lesson that incorporates both studentcentered inquiry and direct instruction.
There are eight steps in this instructional model, but it really is three main phases: introduction, inquiry, and direct instruction.
This lesson structure is very similar to the 5 Practices for Orchestrating Productive Conversations that is popular in the United States: anticipate, monitor, select, sequence, connect.
It is also based on a Japanese lesson structure called bansho. Bansho is a method of teaching developed in Japan that focuses on teaching math through problem solving. It allows students to see connections and progressions of the thinking involved when developing strategies to solve a problem.
Preparing to implement a math lesson with Bansho (board writing)
 Choose a problem: “Getting Started”

 Choose a good word problem that aligns with the learning goal for the lesson.
 Ensure the problem has multiple access points and allows students to solve the problem in a variety of ways.
 Determine how you will introduce the problem to students. Three Read protocol?
 Anticipate student responses: “Working on it”

 Solve the problem in a variety of ways: concrete manipulatives, pictorial representations, alternate strategies and algorithms, standard algorithm, etc.
 Identify two or three anticipated solution methods that you plan to highlight during the student discussion portion of the lesson.
 Sequence the highlighted strategies to guide the class towards the lesson’s learning goal.
 Anticipate incorrect solutions and guiding questions you might use to support students
 Plan how you will use the whiteboard

 Visualize how much of the board pace will be used for the different parts of the lesson: introduction, inquiry, direct instruction
 Prepare problem stem and question stem. If you are planning to introduce the problem via the ThreeRead Protocol, then you will also need board space to record the quantities and questions proposed by students.
 Use a different colored whiteboard marker for annotating student solutions that will be shared.
 Prepare for the Discussion and Application: “Wrapping it up”

 Anticipate how will you knit together the various methods students share with the lesson learning goal.
 Prepare how you might annotate the anticipated student solutions to connect that thinking to the lesson learning goal.
 Choose a second problem students will solve to practice the lesson’s learning goal.
 Independent practice or go through the cycle a second time.

 Select one or two similar problems that students will either solve independently or they will work on the problems through the bansho cycle again
 Solve the problems. You will post the answers while students are independently working on the one or two problems.
I record my thoughts in this template that is formatted to look like how I want the whiteboard to look by the end of the lesson.
Here is a completed lesson plan…
In this lesson plan, I noticed that I forgot to identify which of the six anticipated student responses I would highlight and use in the class discussion portion.
Here is an 8th grade example…
It takes perhaps 10 minutes to complete a lesson plan. Then I do the lesson with my students the next day. As students are working, I try to make the whiteboard look just like I planned it.
My goal is to complete the lesson without having to erase anything from the whiteboard. Keeping everything on the whiteboard allows students to see connections and progressions of the thinking involved when developing strategies to solve a problem. It also allows students to compare and contrast the various methods shared.
Here is a way to imagine the flow of the lesson that you are preparing. You might anticipate that you will go through this cycle two or three times during your lesson.
In conclusion…Why Bansho?
Bansho is an instructional strategy that captures the development of students’ individual and collective thinking. Bansho allows students to:
 solve problems in ways that make sense to them
 build understanding of tools, strategies, and concepts by listening to, discussing, and reflecting on their peers’ solutions
 build understanding of concepts through explicit connectionmaking facilitated by the teacher’s board writing
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