go Deeper

Prior to the meeting:

The group selects a tape segment that offers rich possibilities for discussion about A/O/I. The teacher(s) whose tapes are watched has veto power over framing and direction.

At the meeting:

The teacher (or a team member) explains context and what he or she was trying to achieve. We should hand out copies of the A/O/I observation & conversation guide pages as resources for reflection, and possibly point to other tools. The main handouts are the observation/discussion questions in slides 17-18. Stress that the main goal of this conversation is to think about the ways students are and can be supported to explain their ideas, listen to each other, and build collective understandings.

Agency, Ownership, and Identity Strategies

When a student shares an idea, write their name on the board next to it when you record it. Refer to that idea as “so-and-so’s idea” or “so-and-so’s strategy”. Keep track of whose ideas have been highlighted, and try to get to all class members over a several-week period. Some teachers have student names or pictures on magnets, so they can easily place them next to ideas.

Time alone first

Routinely give students some time (5 minutes or so) to work alone on a problem and begin to solve it before hearing peers’ ideas. Let students know what they’ll be expected to share with a partner or group after their independent work, e.g. “Your strategy to solve the problem, and what you’ve found so far” or “What you plan to do and what you find puzzling about this problem.”

Student-led questioning routine

Establish a routine of student-led questions and challenges after viewing each student presentation or work. For example, students might routinely finish their presentation by asking the class “Do you have comments or questions?” and calling on classmates. (get some short video clips to illustrate)

Turn it Back to the Students

The teacher does not say whether solutions are correct or incorrect, but rather shifts the authority back to the class as a whole. “What do you all think?” “What questions do you have for [student’s name]?” “Is that an answer that makes sense for this problem? How do you know?”

Wait a turn

During whole class discussions, try letting two (three, four, five...) students speak in a row before you say something.

When students are stuck, ask questions that help them articulate what they know What are 3 things you know about this problem? What is confusing about this problem?

Start with the end

Start a unit with a rich problem that draws out ideas that will be useful throughout the unit and helps students build them. In some textbooks, these problems typically occur at the end of the unit. In contrast, some research-based textbooks use rich problems to begin the unit, so that students can actually develop new procedures or ideas of the unit using their prior knowledge. Such experiences help students realize they can develop procedures they have not yet been taught.

What do you wish you knew?

At the end of a test or quiz, ask students to choose at least one problem they aren’t sure they did correctly and write a quick reflection about what they think they’re missing or what tool/method/idea they think would be useful to solve the problem correctly.

Confidence Thermometer

At the end of a lesson or unit, ask students to rate how comfortable they are with key idea(s), by coloring in an empty bar (or thermometer) next to each key idea. Students can who feel comfortable with a given idea can share tips for studying it or making sense of it.

Create a Debate

Use two pieces of work that typify different ways of thinking about a problem; one might be a common misconception. Have students describe what each student might be thinking and which is correct.

In Figure X, you can see a proportional and non-proportional attempt to solve a picture enlargement problem that a middle-school teacher presented at the beginning of a lesson, in order to re-engage students in a concept that was problematic in the prior lesson. The teacher asked what “Student A” and “Student B” were thinking, why they might think that, and how to figure out which is correct. The teacher then asked students to apply Student A’s and Student B’s way of thinking to another problem, related to lemonade solutions, and to explain what would happen.

You can heighten excitement by having students commit to one idea or solution and have each side try to persuade the other. If you have students’ names or pictures on magnets, they can place them next to the idea they agree with, and move them when their opinion changes– perhaps with the agreement that they write in their journals why their thinking changed if they move their magnet.

Give Less Information

Many problems can be tweaked so that students are given less information, and have to discover more. For example, students might be asked to discover whether something is true, rather than to “prove” it (which assumes it is true). Students might have to figure out the tools and models they will use in problem-solving, not given them as part of the problem set-up.

Reflective Journals.

Reflective journals can begin simply, by asking students to respond to a single question like: What did I learn today? Every day, teachers can choose 3 journal entries to read to everyone at the beginning of the next lesson, that revisit content, embody habits they are trying to build in the whole class, etc. Over a couple weeks, all students’ journals are chosen. [cl can provide videos] Journals can become a place where students write the problem, record their thinking, how it changed, and why, and reflect on what they did not know previously that they know now.