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Effectively Using Students’ Mathematical Thinking Blake E. Peterson and Keith R. Leatham Brigham Young University Provo, Utah July 13, 2009

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Project Focusing Student Teaching on Students’ Mathematical Thinking Blake E. Peterson & Keith R. Leatham

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Philosophy The secret of education lies in respecting the pupil. --Ralph Waldo Emerson Good teaching is more a giving of right questions than a giving of right answers. --Josef Albers

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Once you have asked engaging questions, what do you do with the student responses?

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Process of using students’ thinking 1.Listen to and understand our students’ thinking 2.Recognize the teachable moment 3.Use the thinking in a pedagogical and mathematical way

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Roadblocks to listening and understanding Competing demands □ Classroom management □ Time □ What you are going to say next Poor questions

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Excerpts from a lesson

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Video clip about trendlines. Is the ST listening? What questions might be appropriate to follow up on the student thinking that has been presented?

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Process of using students’ thinking 1.Listen to and understand your students’ thinking 2.Recognize the teachable moment

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Roadblocks to recognizing Assumption of Understanding □ Fill in the blanks □ We tend to be so happy to get a response that is close to what we were looking for that we don’t push for more detail. □ We assume the student understands even if the response is only partially complete. □ Simply remind

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Roadblocks to recognizing Assumption of Understanding □ Fill in the blanks □ Simply remind Skepticism: the mark and even the pose of the educated mind. --Dewey Shoot for optimistic skepticism not skeptical optimism

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Roadblocks to recognizing Assumption of Understanding □ Fill in the blanks □ Simply remind Funneling

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Process of using students’ thinking 1.Listen to and understand your students’ thinking 2.Recognize the teachable moment 3.Use the thinking in a pedagogical and mathematical way

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Roadblocks to effective use Do not know how □ Mathematics □ Pedagogy □ Curriculum

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Roadblocks to effective use Do not know how □ Mathematics □ Pedagogy □ Curriculum Naïve use □ Student thinking as a triggertrigger □ Mere presence of the correct solution □ Mere presentation of multiple solutions Incomplete use

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Video clip of student solutions to predicting what would happen with a 6 layer bridge. What is the mathematics behind these three solutions? What questions could be asked to further pursue the thinking?

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Process of using students’ thinking 1.Listen to and understand your students’ thinking 2.Recognize the teachable moment 3.Use the thinking in a pedagogical and mathematical way

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Blake E. Peterson peterson@mathed.byu.edu www.mathed.byu.edu/~peterson and Keith R. Leatham kleatham@mathed.byu.edu www.mathed.byu.edu/kleatham peterson@mathed.byu.edu kleatham@mathed.byu.edu Thank You

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