Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers

1. Mathematics Fellowships:Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education, UW-Milwaukee Melissa Hedges, Milwaukee Public Schools Beth Schefelker, Milwaukee Public Schools 12th AMTE Annual Conference Tulsa, Oklahoma January 24-26, 2008

2. Presentation outline • Background on the Milwaukee Mathematics Partnership • UW-Milwaukee teacher preparation program and mathematics focus courses • Mathematics Fellows program • Program outcomes and evaluation • Conclusions • Discussion

3. Mathematical Education of Teachers (MET) Report • Prospective teachers need mathematics courses that develop a deep understanding of the mathematics that they teach. • The mathematical education of teachers should be seen as a partnership between mathematics faculty and mathematics education faculty. • There needs to be more collaboration between mathematics faculty and school mathematics teachers.

4. Milwaukee Mathematics Partnership (MMP) • NSF-funded Math and Science Partnership (MSP) grant • Core partners: Milwaukee Public Schools, UW-Milwaukee, and Milwaukee Area Technical College • Goal: build the capacity to offer challenging mathematics to all MPS students

5. Milwaukee Public Schools • 93,000 students in 218 schools • Largest school district in Wisconsin • 27th largest district in the nation • Nearly 6200 teachers • 87% minority student population: 58% African American, 20% Hispanic, 13% White, 5% Asian, 1% Native American • 75% receive free or reduced lunch • Student achievement is well below state averages; gaps persist for all subgroups (Source: 2005-2006 MPS Report Card)

7. MET Report Recommendations Prospective middle grades teachers of mathematics should be required to take at least 21 semester-hours of mathematics, that includes at least 12 semester-hours on fundamental ideas of school mathematics appropriate for middle grades teachers. CBMS. (2001). The Mathematical Education of Teachers.

8. UW-Milwaukee Teacher Programs • Early Childhood (ECE, Birth-age 8) • Middle Childhood through Early Adolescence (MCEA, grades 1-8) • Early Adolescence through Adolescence (EAA, grades 6-12)

9. Mathematics Design Teams • Implement recommendations of the MET Report, to the extent possible within the ECE/MCEA program structure. • Develop mathematical knowledge needed for teaching. • Mathematics content tied to classroom practice.

10. Design Team Philosophy for Pre-service Courses • Mathematics faculty provide rigorous mathematics content. • Mathematics education faculty focus on mathematical knowledge for teaching. • Classroom teachers (Teacher-in-residence) make connections to classroom practice.

11. Mathematics Focus Area Coursesfor MCEA Majors • Problem Solving • Geometry • Discrete Probability and Statistics • Algebraic Structures • Calculus Experience

12. Problem Solving & Critical Thinking • Reflect on Process of problem-solving • Emphasis: • mathematical discourse and classroom as a learning community • understanding and engaging with mathematics • extensions of solved problems • Construct problem-solving strategies

13. Flipping Coins Place six coins on the table in the arrangement shown in the first row below. What is the fewest number of flips needed to produce the second row, if you can only flip two adjacent coins at a time? H T H T H T H H H T T T

14. Discrete Probability & Statistics • Experimental likelihoods • Simple probability models • Conditional probability • Expected value • Complex probability models

15. Probability Dice Task If we roll two dice, how often will the total 7 occur?

16. Probability Dice Task • Two dice are to be rolled and the sum determined • Repeat this random experiment 25 times, and record your results • Organize and display the results of your experiment

17. Testing for Bias A city police department needs to fill 15 vacancies at the rank of captain from among 100 qualified candidates, 40 of whom are identified as being from minority groups. 1 minority candidate is promoted. Is this evidence of bias? What if 4 minority candidates were promoted?

18. MPS Mathematics Fellows Program • MCEA minor offered to practicing MPS teachers, over 15 months • 53 teachers enrolled in at least one course • 27 completed at least 4 courses • 10 completed 4 focus courses, Intermediate Algebra, and Calculus

19. Mathematics Fellows Changes in MKT Instrument Sources: The University of Michigan, Learning Mathematics for Teaching (LMT) Project, and The University of Kentucky, Diagnostic Teacher Assessments in Mathematics (DTAMS) Project

20. Math Fellows’ comments: Problem-Solving • I had always been afraid of problems…This course made me undertake ALL problems with trust and almost happiness, because now I know I can solve them • I avoided problem solving and didn’t like it until I took the course you offered. Now my students receive problem solving…with nearly every assignment.

21. Math Fellows’ comments: Other Focus Courses • This course has taught me to look at Geometry in a new light. I feel that I will be more confident teaching Geometry in the future • I lost fear and found that probability is something actually enjoyable and teachable • I have a deeper understanding of algebraic reasoning and problem-solving

22. Math Fellows’ comments: Calculus • I plan to make sure my students get an understanding of how subject areas connect. This was helpful to me because I wasn’t sure about this until I took calculus • I teach middle school physics and this deeper level of understanding will help me teach some of the more abstract concepts with confidence

23. Classroom Connections • Student work samples

24. Conclusions • Students in the UW-M focus courses acquire a more positive disposition towards mathematics • Students acquire increased MKT • The separate problem-solving course is invaluable • There is value in middle-grades teachers studying calculus

25. MET Report Recommendations Prospective middle grades teachers of mathematics should take coursework in: • Number and Operations • Algebra and Functions • Measurement and Geometry • Data Analysis, Statistics and Probability • (Optionally) Calculus, focusing on concepts and applications CBMS. (2001). The Mathematical Education of Teachers.

26. The Triangle Game Place the whole numbers from 1 to 6 around a triangle, with one number at each vertex and one number in the middle of each side, so that the sums of the three numbers along each of the sides are the same.

27. Geometry • Geometry as a measuring tool • Spherical Geometry • Rigid Motions • Geometry as a logical system

28. Visualizing Intersections Which of the following can occur as the intersection of a plane and a cube? A single point A line segment A triangle A square A non-square rectangle What other shapes are possible?

29. Axioms for Student Government Committees (abbreviated) • There is at least one committee • There is no committee to which all students belong • Any two distinct students belong to exactly one committee together • For any two distinct committees, there is at least one student who belongs to both of them • Exactly three students belong to each committee

30. Algebraic Structures • Elementary logic • Set Theory • Functions • Operations • Algebraic Structures • Number Theory

31. Modular arithmetic • What could we mean by 1/3 in Z7? • Which elements of Zn have additive inverses? • Which elements have multiplicative inverses? • When can we solve linear equations in Zn?