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

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

3. 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

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

6. 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

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

8. Excerpts from a lesson

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

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

11. 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

12. 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

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

14. 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

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

17. 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

18. 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?

19. 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

20. 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