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I also maintain that, provided we don’t oversimplify our mathematical tasks to take students’ judgements away, they will be constantly hypothesizing, choosing, testing, and revising their work.
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.
Our young mathematicians will make judgements as they are solving problems, deciding which path to follow, and when.
They will pick the best representations for their mathematical work, and their own idiosyncratic mathematical voice will come out.
For a long time, I felt like creativity was that certain “je ne sais quoi” of the math classroom, a “know it when I see it” type of thing.
When I thought this, I probably didn’t have a broad enough definition of creative thinking.Here are my personal working definitions of each: Yes, these are deliberately economical.Yes, you could add to these definitions if you wanted to.They need to work together in harmony to address perceived dilemmas, paradoxes, opportunities, challenges, or concerns (Treffinger, Isaksen, & Stead-Dorval, 2006).Further, Poincare said something to the effect that mathematical creativity is simply discernment, or choice. 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.The role of teachers in teaching critical thinking is debated- see Daniel Willingham’s piece What is critical and creative thinking in the math classroom? I am starting from the presumption that all kids are capable of critical and creative thinking.My second presumption is that mathematical knowledge and skill gained as children grow older allows them to think creatively and critically.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”).