Math Critical Thinking Problems

Math Critical Thinking Problems-28
I was waiting to be bowled over by stunningly divergent solution paths. Since, I have been watching for more subtle evidence of creativity.

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.Our young mathematicians will make judgements as they are solving problems, deciding which path to follow, and when.

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(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?

I have a dislike for overly complicated frameworks and definitions that clutter and obscure important concepts.

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.

Third, I don’t buy the typical (and somewhat ill-defined) notion that creativity and critical thinking are only typical of “higher order thinkers.” It depressed me to no end when I did my literature review on these two topics and found that much of the work on these two types of thinking were done with gifted learners.

The other common line of thinking is that critical and creative thinking are somehow opposite, or at odds or competing with each other. Typically this binary is set up as “making” versus “assessing” or “judging.” I believe that both are intrinsically tied together.“These two ways of thinking are complementary and equally important.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”).The key thing is that students are becoming more confident in their judgements as young mathematicians.I want them to be able to use their mathematical thinking tools to decide “what’s best,” or “what’s fair.” I want them to justify their thinking.There is so much information available to us in this world that we don't know what is true and what is not.That's why it's important for students to analyze, think effectively, and understand that not everything is black and white.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.I want them always probing the mathematical world around them with their confident judgments.This is one of my favourite things to tweet now and again: This work came out of our Learn Teach Lead project involving proportional reasoning:

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