The Math Teacher’s Job is Neither to Teach the Lesson, Nor to Help Individual Students Who are Struggling!

….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.

From Tom McDougal. Lesson Study Alliance, Chicago [and brought to my attention by Jerry Becker. – GFB]
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:

1.  introduce the problem
2.  explicitly pose the task for students
3.  students work on the task (5-10 minutes)
4.  share student ideas
5.  compare and discuss the ideas for the purpose of learning new mathematics
6.  summarize major points from the lesson
7.  student reflections

(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 shido 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.

Of course, some errors are simply the result of sloppiness, or otherwise unrelated to the main learning goals of the lesson. So when the teacher sees an error while conducting kikkan shido, he or she has to decide: should this be addressed privately or publicly? What should I say to this student? Do I expect that, by the end of the lesson, this student will understand what he or she has done wrong? This is a tricky decision, and an important part of lesson planning is anticipating different student responses, correct and incorrect, and deciding ahead of time how to handle them.

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.


Sound Familiar? A Complaint About Excessive Testing in Detroit

Excerpts from a letter from a Detroit Public Schools Federation of Teachers Official:


Dear Dr. Byrd-Bennett:
We are getting a lot of feedback from teachers concerning the overwhelming  amount of testing and progress monitoring they are required to do. While  each of the assessments may have merit, taken as a whole they leave too
little time for instruction. Teachers throughout the district are asking  “When do we have time to teach?”
In addition to the regular curriculum, students are assessed using the Star  Math and Star Reading programs. They work on individualized lessons and  assessments through Accelerated Math and Accelerated Reading. Three times
per year students take a battery of benchmark assessments including up to  five Dibels assessments, Burst, and TRC. Throw in quarterly Q tests that  take two class periods per day for four days each quarter, and two to three
weeks of MEAP testing, and it’s no wonder teachers want more time to teach.

In between benchmarks, teachers are asked to print up to 80 pages of Burst  lessons every two weeks. These lessons are to be taught to the lowest  achieving four to five students in each class for a half hour per day. Some  schools don’t have enough toner to print these lessons, others don’t have  enough copiers, and nobody seems to have enough time. One teacher estimates  that a quarter of her instructional time is devoted to these assessments and
progress monitoring.
On a weekly basis, teachers also are asked to do time-consuming progress  monitoring for Dibels and TRC. Much if this work is done with one student at  a time. While our teachers are doing their best to keep the rest of the  class doing meaningful work, it is not possible to properly monitor and  coach the others while you are testing  individuals.
Two common themes emerge from discussions with teachers throughout the  district. First, these assessments all have some merit individually, but  together, they are too much. Second, we as teachers can handle all this, but  our students are suffering.
One teacher told me that for one day, she ignored Burst, Dibels, TRC,  Accelerated Math and Reading, and all she did was teach. It was the best day  the class had all year! The saddest thing is, this didn’t happen until the  third week of October, and she had to ignore directives to make it happen at  all.


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