The teacher engages the students in thinking by discussing connections after read-alouds. But, the students are usually really talkative about the book after they get done and start talking to each other, but the teacher shuts down the talk and has each student raise his/her hand when he/she wants to say something. I would have them turn and talk with a partner about what they thought about the book before I brought it all together. That way the students can say what they need to say, and the discussion with the entire group is shorter because all of the students are not rambling on, they can collect their thoughts beforehand.
She engages their thinking also when they are doing math together. After they have done a problem, she asks different students how they did the problem and talked about the different strategies to do a problem. The teacher is doing a lot of the thinking though, because many of the students do not connect the different strategies- they use their strategy and that's all. To change this, I might have them talk at their tables and show how they got the answer, so it is more student-oriented. I know she has the right idea, because one collaborative mind can do much more than many single minds can, but I think that the students do not really pay attention to the other strategies because they found a good way to do each problem, so that's what they do.
As I've said throughout, your thinking is becoming so professional! You're right...strategic questions and prompts focused on challenging, purposeful, and "do-able" tasks will create a rigorous, thinking classroom!
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