To enable students to build the new mathematical ideas, four instructional routines are especially important in TTP classrooms:
- board organization
- student reflective journals
- teacher questioning
- neriage (“kneading”) discussion
In this section, you will investigate the basics of each of these instructional routines, and learn about how they foster student learning.
2.1: Board Organization
A well-organized board can help students by creating a public record of the lesson so that students can:
- Revisit each element of the lesson as needed–for example, refer back to the problem, related prior knowledge, a key model or illustration, etc.
- Compare different solution strategies and consider how their own thinking relates
- See the mathematical expression, visual model and verbal description associated with each solution strategy
- Experience an organized model for their own note-taking and reflection
- Become “meta-cognitive” as they see how new ideas are developed in mathematics
Board organization supports equity, by keeping information available to students who need extra time to read or integrate information. Likewise, students who are momentarily distracted can revisit the lesson’s ideas and re-enter the lesson.
In Japan, board writing often seems spontaneous, because it features ideas and student work that emerge during the lesson. In fact, teachers typically plan board writing in advance of the lesson, by thinking about the key ideas and pictures on the board that will spark, capture and advance students’ thinking. International comparisons reveal that Japanese mathematics teachers use the board more frequently than do teachers in Germany and the U.S., and that Japanese teachers tend to keep the board writing throughout the lesson, rather than erasing parts of it during the lesson. The board writing provides a record of the lesson that students can consult as they summarize and reflect on what they learned.
Creating a board plan also can help teachers by providing an opportunity to think through the whole lesson--from posing the problem, to student work that will be shared, to the key ideas that will emerge from the neriage discussion. A sample board is shown below.