Japanese Feedback on My Teaching

On Friday, February 21, 2014 I was invited by Dr. Doug Corey of Brigham Young University (when I was an undergraduate at BYU, I was one of Dr. Corey's research assistants) and Dr. Ninomiya of Saitama University and several other graduate and undergraduate students. Please see my blog post about that "research lesson." (coming soon!)

Then on Tuesday, February 25, 2014 Dr. Corey, Dr. Ninomiya, and a graduate assistant came to my school and observed three lessons. Two that were using the Flipped Mastery model, and a Geometry lesson about Translations and Reflections. After that 85 minute lesson we sat down and talked about the lesson. Since graduating from BYU about five years ago I have never received such though provoking feedback a single lesson.

Kadai (underlying deeper mathematical idea)

The first comment that Dr. Ninomiya made to me was describing mondai (pronounced moan-die) and kadai (pronounced ka-die). The mondai are the kind of problems or questions that are asked to the students. The kadai are the underlying deeper mathematical ideas. The goal of the lesson is not for students to solve the mondai, but to think and learn about the kadai. The kadai is sometimes a phased as "Let's think about ________". The kadai isn't specifically shared with students, but teachers will talk about the kadai as the goal of the lesson with the students. This is especially true at the end of the lesson, with a summary of what students have done by solving these problems.

Dr. Ninomiya didn't understand the kadai of my lesson... because there wasn't one. American curriculum is a collection of separate topics and problem sets, it doesn't lend itself easily to underlying big mathematical ideas. On the other hand, Japanese curriculum is more focused and builds upon a single mathematical idea over several lessons. As I progress as teacher through my career, I have been thinking of pulling away from the textbook (not from the Standards). I don't know how valuable remember types of problems are in the long term. This seems like a topic for another blog post. At the very least, I can work on framing the lesson within a kadai.

Notes and Summaries

Another topic that we discussed was students effectively using their notebook. In my class, the students watch a 10 minute video, take notes, and then write a summary. Dr. Ninomiya liked the idea that I had my students write a summary. He said that many teachers want their students to do lots of problems, but it is better that students are asked to summarize what they learned. It becomes a synthases exercise.

In my class, for about an hour, we do problems from the textbook. The students write down the answer on individual white boards. I do this because:

1. Students enjoy it. At the beginning, the students loved the idea of using white boards. Even after using them everyday for months, they still enjoy it. Maybe after using paper and pencil so much, they like the change.
2. Because students are writing with a large white board marker, it is very easy for me to scan the room and see what all of their answers are. I then know what mistakes have been made and the kind of thinking my students do.

Dr. Ninomiya commented about the fact that students don't have a record of what they did in class. Once they erase their white board, then it is gone. They can never go back to that problem and look at it. Notes have several purposes:

• Record of what they, the student, did: The textbook isn't always what they did, but their notebook is a record of what they did. (By the way, because textbooks are so small and thin, students are encouraged to bring, not only their textbook to class, but all of their math textbooks from junior high school or high school to class.)
• Notes remind students of what they did last class: Teachers ask students to review their notes from last class, so they can continue the ideas from last class and build onto the previous class period's discussion.
• Notes are used to study: Studying for semester exams are very important, and a student's notes are very useful when preparing for these exams. These notes are for their future self.

I don't think I am ready to give up white boards, because of the above reasons, but I think students could add things to their notes as we are doing problems on white boards.

Whys that I might implement these ideas in the future:

• Require more from the summary: Right now my student's summaries are very simple and are only two or three sentences long. I want to look into Cornell Notes and other AVID materials and see what they say about summaries.
• Use their summaries at the beginning of the lesson: Occasionally have them switch notebooks with someone around them and have them read each other summaries. Are there any important ideas that this person left out?
• Add to their notes during the lesson: My students usually don't write down the example problems that are in the videos in their notes. They just don't see value in them. (This is one reason why I been shortening the videos by removing about half of the example.) I want to change this perspective. I want my students to work out a problem or two, in their notes, show their work and write down explanations.
• Add and clarify their summaries at the end of the lesson: At the end of the lesson, the students need the teacher to remind them what they did that day. This also gives a teacher a chance to summarize the lesson and, by example, the importance of summarizing the lesson. By the way this is called the matome (pronounced mah-toe-mei) in Japanese education. The students will then add or clarify what they have written from the summary.