Tuesday, March 29, 2011
Chapter 1 Discussion Prompt
Wow! So many great quotes, points, and food for thought already in this first chapter! Reading about Camille's classroom implementation helped to bring the teachers' workshop principles to life. One idea I've been more conscious of with my students relates to open-ended questioning and waiting until a little later to "fix" the mathematics vocabulary (p. 18). How often might our good intentions to quickly guide students toward the concepts we want them to develop be interfering with their own long-term understanding? (See also Camille's comment on p. 16, "They're just doing it because I asked them to. But what are they really learning.?") In what ways could we more carefully construct learning experiences and use questioning so students develop concepts that will last and transfer over time?
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This pretty much sums it up for me:
ReplyDelete"When invited to engage in structuring, they build cohesive structures with many pathways and interconnections. In contrast, when presented with preformed structures, students often process them as isolate bits, associated only with the activity or topic by which they were introduced." p.12
Students need to GET it and that takes working through it. The factor piece was illuminating.
Like Virginia, I stared and highlighted the idea of allowing for connections to be made, rather than presenting the preformed structures.
ReplyDeleteI also felt that the section on p. 10, which was a quote from Kevin Devlin's work, summed up much of what I feel. Students need to "develop a tenacity to work through important struggles" and "learn to appreciate the fun of puzzlement."
Too often, I find that students want us, as teachers, to tell them how to "DO" it, rather than taking the time, patience and risks - with its accompanying rewards- to problem solve.
Teaching students how to TRY to problem solve is so fundamental to whatever concept is being studied.
I have shared with some of you a big AHA! I had while recently listening to Marilyn Burns speak. She commented about a school where the BIG 3 areas of emphasis (at least process-wise) were: 1) Use academic language; 2) Stick with problems; 3) Explain reasoning. Sounds like a great plan, huh??
ReplyDeleteI loved reading about the teachers' struggles with the factors problem. The notion of sharing and the huge benefits of it were really brought home. Here are my big take-aways:
ReplyDelete1) When concepts are "taught", the understandings are disconnected.
2) For students to make generalizations, students need to discover the relationships within the number system. This allows them to "build multiple pathways and interconnections."
The power of sharing work and strategies with each other.
3) Students are so programmed to think that they are only looking for what the teacher wants rather than what they have discovered.
4) I too liked when Camille didn't focus on correcting the student but rather allowed the ideas to develop.