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5 Principles for a Problem-Solving Classroom - Brilliant or Insane - 0 views

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shared by Trent Merica on 06 Apr 15 - No Cached

Standards for Mathematical Practice (SMP) contain important guidance about how students should think and work in a math classroom.
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Conjecture. In a traditional mathematics classroom, the primary goal is for students to get the right answers to questions and exercises. In a classroom where conjecture is encouraged, students ask most of the questions, and the answer to a question is very often another question. Inquiry is important, as is a little-used skill known as “problem-finding.”
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Collaboration. In a traditional classroom, students work alone, and the emphasis is on an individual’s skill fluency. Problem solving classrooms are all about the “we”. Think The Avengers, not the Lone Ranger (though even he had Tonto). Group work is far more prevalent in a problem-solving classroom than individual work, and students are encouraged to share ideas, answers, and ask for help. Though there is a time for individual performance, in a problem solving culture, the other students are cheerleaders instead of competitors (see #5).
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Communication. In a traditional classroom, communication is primarily one way: the teacher explaining a procedure or algorithm to students. In a problem-oriented classroom, students must learn to communicate frequently about problems and how they solve them. They focus on vocabulary, writing, and metacognition. The core of mathematics communication is the formulation and support of mathematical arguments. English Language Arts standards will be mentioned here, since they should interact with math standards.
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Chaos. Though this sounds sketchy, it is simply encapsulating the idea that real math work is messy. In a traditional classroom, neatness and order rule the day. Students must learn a procedure and then replicate it with mechanical precision. Real problems, on the other hand, require experimentation, false starts, mistakes, and corrections, sometimes over and over again. Thomas Edison famously said, about the path to finding the right filament for his light bulb, “I have not failed. I’ve just found 10,000 ways that won’t work.”
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Celebration. In a traditional classroom, recognition is given for right answers and high grades. In a problem-solving culture, anything that leads towards a solution is celebrated: finding one small step of a complicated problem, thinking of an innovative approach even if if doesn’t pan out, or even making a spectacular mistake and asking for help. Effort is rewarded over achievement, reflecting Carol Dweck’s work on growth and fixed mindsets.
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