## ….but rather, to prepare a lesson from which ALL the students can learn!

… according to the way that Japanese math teachers are taught their craft, as described below. You will find that these methods, which include Lesson Study, are pretty much the exact opposite of American “Direct Instruction” or “Teaching Like A Champion.” Given that nobody claims that Japanese students lag behind American ones in math or science, perhaps we in the US could profit from examining how other nations’ teachers do it. Note also that this description is of mathematics lessons in elementary school, not middle or high school.

Please read the following description and leave comments on what you think.

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**It’s not the teacher’s job to teach the students!**

By Tom McDougal

What?? You might be thinking. What else could the teacher’s job be but to teach?

The teacher’s job is to ensure that students learn, all of them, we hope, though we know we will usually fall short.

In Japan, most (elementary) math lessons are designed as “teaching through problem solving” lessons (TtP). A teaching through problem solving lesson typically includes the following parts:

(There is sometimes overlap, and a back-and-forth between some of these, e.g. #4 & #5 may be combined.)

While students are working on the task (#3), the teacher walks around the room, monitoring their progress. Japanese educators have a term for this,* kikkan shido*, or “providing] guidance between the desks.” They recognize that there are different ways to do* kikkan shido*, and it is often a subject of discussion in Lesson Study. During planning, for example, a team will usually discuss how – or whether – the teacher should respond to a student who exhibits a particular misconception; during the post-lesson discussion, there may be argument about whether the* kikkan shid*o was effective. And, it is considered a skill that new teachers need to develop.

Teachers who are inexperienced with TtP lessons often make an unfortunate error while doing *kikkan shido*: they see a student who is struggling, or who has done something wrong, and they stop and help that student. After several minutes the teacher moves on, encounters another student who is having trouble, helps that student, and so on. Then, suddenly, time is up, and the lesson ends.

There are at least four important drawbacks to this type of* kikkan shido*. First, as my description suggests, it uses up a lot of time. The teacher may never get around to all of the students, and other students who need help may never get it. Second, by addressing misconceptions privately rather than publicly, the teacher deprives other students of the opportunity to analyze those misconceptions and learn why they are incorrect. Any experienced teacher knows that certain misconceptions are very common, so when one student makes an error that stems from a common misconception, that offers an opportunity to “inoculate” other students against making the same error sometime later.

The third problem with tutoring students individually is that it conflicts with the whole premise of teaching through problem solving. You expect that some, or even all, of the students will have difficulty with the task; that’s why it’s called “problem solving” and not “practice.” Teaching through problem solving involves an expectation that students will have difficulty, but that the comparison and discussion phase will address their difficulties and that, by the end of the lesson, all (or almost all) of the students will have learned what they need to know.

And fourth, we want to help students learn to give viable arguments and to critique the reasoning of others, the third Standard for Mathematical Practice in the Common Core State Standards. To accomplish this, we need for students to share and discuss different, perhaps conflicting solutions. **Students need to do the critiquing, not the teacher.**

Caring teachers naturally feel drawn to help struggling students: they feel like it is their duty to help those students right now. To counteract that impulse, I say, bluntly:

It is not the teacher’s job to teach the students. It’s the teacher’s job to

*create a lesson*that teaches the students.