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Look closely at the picture I started this post with: both problem-solving and inquiry are mentioned.To the former: problem-solving classrooms will always have an element of creativity, unless we force our own methods, techniques and processes on our students.(Given a classroom culture of math talk, our students will find their voices. Doesn’t that sound like critical and creative thinking, combined in one neat mathematical package?
Further compounding the problem, critical and creative thinking are, at best, ill-defined.
Obviously, this is not helpful – if the math processes are the actions of doing math, it makes sense then that these actions will, at times, encompass critical and creative thinking.
A balanced math program with strong foundations and a spirit of questioning will always lead to interesting lines of inquiry-questions, leading to more questions.
One of the best parts of really getting to know your students is starting to see inside their idiosyncratic mathematical thinking.
Creativity is there to be found in the math classroom. There are some astounding numbers floating around about the ratio of students asking questions, to teachers asking questions, in a typical math classroom. Once your classroom is an open space for wonder, your students don’t stop wondering!
Inquiry is also hidden in that little line in the picture from the curriculum above. Questions lead to answers, leading to more questions (I once called this the “inquiry tumbleweed”).I was waiting to be bowled over by stunningly divergent solution paths. Since, I have been watching for more subtle evidence of creativity.Students using new thinking tools, or subtly tweaking a solution path or process they may have got from talking with their classmates.It will always be our job to consolidate purposefully, and to offer suggestions as to more efficient or effective solutions.The range and variety of the student work, with all its understandings and misunderstandings will lead us to that point.Einstein may have said something about how if you understand something, you can explain it to a child.If we can explain the quantum world without jargon, we can explain educational concepts without jargon, so here goes.Video Series: Current Educational Issues Video Series Publisher: Foundation for Critical Thinking Length: 59 minutes Format: VHS or DVD With Alan Schoenfeld and Richard Paul.Good for all levels of math and science instruction.But if you are a student, and you are doing a mathematical problem or task, you are making something new every single time.There will be patterns and trends in the strategies and tools that individual students use that further differentiate more “unique” or “divergent” work which will perhaps “more” creative.