1. Teacher Preparation and Professional Development: The Mathematical Knowledge Teachers Need University of Wisconsin–Milwaukee School of Education 18 th Annual Research Conference March 16, 2006 Dr. DeAnn Huinker, huinker@uwm.edu Dr. Henry Kepner, kepner@uwm.edu Melissa Hedges, mhedges@uwm.edu www.mmp.uwm.edu This material is based upon work supported by the National Science Foundation Grant No. EHR-0314898.

2. Guiding Question What is the scope and nature of the mathematical knowledge needed for teaching?

3. Purpose Develop, teach, and revise mathematics content and methods courses to prepare prospective teachers with a deep understanding of mathematical content needed for teaching Design Team Members  Mathematician  Mathematics educator  MPS Teacher-in-Residence  Classroom teachers

4. Problem Solving  UWM Math Dept Dr. Richard O’Malley  TIR Sharonda Harris  Math Educator – Kelly Kaiser Discrete Probability and Statistics  UWM Math Dept Dr. Richard Stockbridge  Math Educator Dr. Hank Kepner  UWM Math Dept Gary Luck  MATC Math Dept Dave Ruszkiewicz  K-12 coordinator & Statistics Educator Pat Hopfensperger Geometry  UWM Math Dept Dr. Ric Ancel Dr. Kevin McLeod  Math Educator  Dr. Hank Kepner  TIR Melissa Hedges Algebraic Structures  UWM Math Dept Dr. Craig Guilbault  Middle School Teacher Connie Laughlin  MPS classroom teacher Nancy Jo Grochowwski Mathematical Explorations for Elementary Teachers I and II  UWM Math Dept & Coordinator Explorations I and II Gary Luck  MATC Math Dept Dave Ruszkiewicz  MATC Math Dept Dr. Tom Geil  Math Educator Dr. Hank Kepner  Math Educator/MPS classroom teacher Meghan Steinmeyer Secondary Capstone Course  UWM Math Dept Dr. Kevin McLeod  Math Educator Dr. Hank Kepner  TIR Dan Lotesto Design Team Courses and Membership

5. Alignment –MPS Comprehensive Mathematics Framework –National and state standards & MPS Learning Targets –MET Report Recommendations Extensive review of materials specific to each course Guiding questions: What should teachers know? How should they learn it and why? Course Development Resources

6. Encompasses –“Common” knowledge of mathematics that any well-educated adult should have –“Specialized” to the work of teaching and that only teachers need to know Source: Ball, D.L. & Bass, H. (2005). Who knows mathematics well enough to teach third grade? American Educator. Mathematical Knowledge Needed for Teaching

7. Some interesting dilemmas… Why do we “move the decimal point” when we multiply decimals by ten? Is zero even or odd? For fractions, why is 0/12 = 0 and 12/0 undefined? How is 7 x 0 different from 0 x 7? 35 x 25 ≠ (30 x 20) + (5 x 5) Why? Is a rectangle a square or is a square a rectangle? Why? Knowing Mathematics for Teaching

8. Compute 35  25 Share strategies. Mathematical Knowledge for Teaching: An Example

9. Which of these students is using a method that could be used to multiply any two whole numbers? Appraising Unusual Student Solutions

10. Knowing mathematics for teaching includes knowing and being able to do the mathematics that we would want any competent adult to know. But knowing mathematics for teaching also requires more, and this “more” is not merely skill in teaching the material. Ball, D.L. (2003). What mathematical knowledge is needed for teaching mathematics? Secretary’s Summit on Mathematics, U.S. Department of Education, February 6, 2003; Washington, D.C. Available at http://www.ed.gov/inits/mathscience.

11. Demands depth and detail that goes well beyond what is needed to carry out the algorithm  Use instructional materials wisely  Assess student progress  Make sound judgment about presentation, emphasis, and sequencing often fluently and with little time Size up a typical wrong answer Offer clear mathematical explanations Use mathematical symbols with care Possess a specialized fluency with math language Pose good problems and tasks Introduce representations that highlight mathematical meaning of selected tasks Knowing Mathematics for Teaching

12. Analyzing Student Errors Mrs. Jackson is getting ready for the state assessment, and is planning mini- lessons for students around particular difficulties that they are having with subtracting from large whole numbers. To target her instruction more effectively, she wants to work with groups of students who are making the same kind of error, so she looks at a recent quiz to see what they tend to do. She sees the following three student mistakes: Which have the same kind of error? (Mark ONE answer.) a.I and II b.I and III c.II and III d.I, II, and III Analyzing Student Errors

13. Assessment tools:  Content Knowledge for Teaching Mathematics Measures  Developed by The University of Michigan – Learning Mathematics for Teaching/Study of Instructional Improvement  Large-scale survey-based measures of mathematical knowledge for teaching Measuring Mathematical Knowledge for Teaching

14. Items –Written by mathematics educators, mathematicians, professional developers, and classroom teachers –Relate to situations that teachers face in their daily work set in teaching scenarios Measure two types of mathematical knowledge: –“Common” knowledge of mathematics that any well- educated adult should have –“Specialized” to the work of teaching Multiple choice format About the Measures

15. Current use of measures Pre/post data for the following Design Team courses:  Explorations in Mathematics for Elementary Teachers I and II at UWM and parallel courses at MATC  Geometry for Elementary Education Majors Other arenas for testing:  MPS Mathematics Teacher Leaders  Courses for teachers enrolled in the Math Fellows program Current Uses of the Measures

16. t = 3.174 (df=49) p = 0.003 nMeanSD Pretest50- 0.680.66 Posttest50- 0.410.75 Results for Mathematical Explorations I MATH 175 Domain: Number and Operations (ES)

17. nMeanSD Pretest22- 0.510.56 Posttest22-0.020.65 Results for Mathematical Explorations II Math 176 t=34.250 (df=21) p=.000 Domain: Geometry (ES)

18. Results for Geometry Math 277 Domain: Geometry (MS) nMeanSD Pretest18- 0.380.38 Posttest18+ 0.191.02 t=2.42 (df =17) p=.027

19. Next steps… Do teachers’ scores predict that they teach with mathematical skill, or that their students learn more, or better? How might we connect teachers’ scores to student achievement data? More open-ended items to show reasoning Next Steps...

20. Mathematical knowledge for teaching must be serviceable for the mathematical work that teaching entails, for offering clear explanations, to posing good problems to students, to mapping across alternative models, to examining instructional materials with a keen and critical mathematical eye, to modifying or correcting inaccurate or incorrect expositions. Ball, D.L. (2003). What mathematical knowledge is needed for teaching mathematics? prepared for the Secretary’s Summit on Mathematics, U.S. Department of Education, February 6, 2003; Washington, D.C. Available at http://www.ed.gov/inits/mathscience. (p. 8) http://www.ed.gov/inits/mathscience