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The emotional energy around "having a problem" can make some want to quickly begin brainstorming solutions. However, good solutions come from a deep and nuanced understanding of a problem, and address the root issue--not just surface symptoms.
To get past surface-level symptoms, it can be helpful to slow down the problem-solving discussion and require students to answer many questions about the problem before any brainstorming of solutions begins.
Some questions worth discussing before moving into the solutions phase of a discussion are:
During this phase of the discussion, the facilitator often must intervene to keep students from jumping into a solution phase of the discussion. For this reason, it is often helpful to establish a time-limit before which solution discussion is not allowed.
That said, it can be unsatisfying to simply unfold layer after layer of a problem without eventually at least some discussion of what solutions are suggested by any given aspect of the problem. Remember, the goal of this module is to help students learn to develop multiple solutions.
You can amplify this activity by having students first brainstorm this list for themselves. For example, you might prompt them to brainstorm "All the things anyone, anywhere might want to know about this problem before even considering a solution."
We all want students to carry our teachings into their lives. Often, however, we must make our intentions very plain for students to understand that an assignment will equip them with skills and empower them, and is not an arbitrary hoop through which they must jump.
For this reason, frame each activity using these four steps:
Among the most useful things we as teachers can do during class discussion is shut our mouths. In an oft-cited meta-analysis of wait-time research, Tobin (1987) described findings of greater engagement and achievement when teachers waited at least three to five seconds after asking a discussion question before speaking again. Above this threshold, higher level thinking was observed and student academic performance improved. However, teachers behaving "normally" only tend to wait about one second. Students need a few moments to digest what they have recently heard, formulate their responses, and work up the courage to speak. Slow down, and more of your students will keep up with you.
Reference: Tobin, K. (1987). The role of wait time in higher cognitive level learning. Review of Educational Research, 57, 1: 69-95.