Building Thinking Classrooms in Mathematics

6. When, Where, and How Tasks Are Given In a Thinking Classroom

  • The best time to give a task is at the beginning of the class. The longer the teacher talks the more passive the students will become and the less likely they are to think. Shoot for three to five minutes of teacher talk to introduce the task. Don’t worry of some groups don’t understand the task as knowledge mobility will take care of that.
  • While giving tasks on a vertical surface is much better than giving them from textbooks or worksheets, giving them verbally is even better. You may have to put some numbers, shapes, and/or images on the wall, but don’t write the task on the wall. Verbal instructions fast track thinking.

7. What Homework Looks Like In a Thinking Classroom

  • For the most part, homework isn’t working. The kids who need it don’t do it or cheat, and the kids that do it don’t need it. Homework in most classes follows the now-you-try-one approach that is started in class after the teacher works a few sample problems. Students either don’t do it, cheat, get help, or do it themselves in equal numbers. The one’s who do it are engaged in mimicking just like in class.
  • Start by rebranding. Call it “check for understanding” rather than homework. This makes it something the students do for themselves, not for the teacher. Do not grade, collect, or check it. This makes it a safe place to make mistakes. Give the answers with the questions. This allows the students to check themselves. You can give fully worked problems the next day. Have the students discuss which ones are the most important to do. Do all this even if you don’t give homework. It’s ok if they collaborate. Be sure to let parents know what you are doing.

8. How We Foster Student Autonomy In a Thinking Classroom

  • Since a teacher can only work with one group at a time, it’s important to give the students the autonomy to either passively or actively interacting with other groups. This will happen when they are stuck or finished. Finished groups will want to see if their answers agree with other groups, while stuck groups will look around for clues. At the same time the teacher can suggest that a stuck group look around.
  • By being less helpful you get the students to teach each other. As we all know, you learn more teaching someone else. You can also suggest that groups with different answers talk to each other. When groups get the right answer in different ways they should also talk it out. In addition, the teacher has to also be on the lookout for groups that are off task.

9. How We Use Hints and Extensions In a Thinking Classroom

  • Optimal learning happens when there is a balance between the ability of the doer and the challenge of the task. This state is called flow. It also requires clear goals and immediate feedback. When the challenge far exceeds ability, you have frustration. When ability is much greater than the challenge, you have boredom.
  • If you sense a group is frustrated, you can give them a hint. You can give them part of the answer or suggest a strategy. If you sense boredom, you can extend the task keep them in flow. Be sure to vary just one thing as you increase the challenge. While all groups start at the same time, there is differentiation in regard to pacing and which groups get hints or extensions. The best feedback comes from within the group and from neighboring groups.
  • Tell the groups not to go on until everyone in the group understands the problem. Peter gives us five modes of engagement. First the students do the task. Then the teacher asks them to justify their answer. Then they explain how they got their answer and teach it to another group. Finally, they create a more challenging task for other groups.

10. How We Consolidate a Lesson In a Thinking Classroom

  • Consolidation from the bottom must start with the presentation of solutions that all students get. The best way is for the teacher to lead a detailed discussion of the task(s) and solution(s) using student work on the vertical surfaces to work through the different layers of solutions. This is better than the teacher writing on the wall or just talking.
  • Conduct a guided tour of student work, selecting the ones that can best do the job. As students work the teacher can circle content that the students can’t erase. For each example selected, have students who didn’t create the example explain it. This a focused guided tour. Make sure the students continue standing and move to examples that are not adjacent.
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