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
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
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.
Mathematical Education of Teachers (MET) Report
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
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)
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.
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)
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.
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.
Mathematics Focus Area Courses for MCEA Majors
Problem Solving Geometry Discrete Probability and Statistics Algebraic Structures Calculus Experience
Problem Solving & Critical Thinking
Reflect on Process of problem-solving
Emphasis:mathematical discourse and
classroom as a learning communityunderstanding and engaging with
mathematicsextensions of solved problems
Construct problem-solving strategies
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
Discrete Probability & Statistics
Experimental likelihoods Simple probability models Conditional probability Expected value Complex probability models
Probability Dice Task
If we roll two dice, how often will the total 7 occur?
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
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?
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
Mathematics Fellows Changes in MKT
N Pretest (SD) Posttest (SD) Change Sig
Number and Operations
21 0.23 (0.96) 0.40 (0.85) 0.17 .231
Algebra 21 -0.63 (0.85) -0.28 (0.87) 0.35 .008
Geometry 21 0.23 (0.96) 0.40 (0.85) 0.17 .231
Statistics (Reasoning)
12 4.50 (1.50) 6.75 (1.91) 2.25 .004
Statistics (Pedagogy)
12 4.33 (2.67) 5.75 (1.96) 1.42 .012
Probability 12 9.75 (3.72) 13.67 (3.08) 3.92 .001
Instrument Sources: The University of Michigan, Learning Mathematics for Teaching (LMT) Project, and
The University of Kentucky, Diagnostic Teacher Assessments in Mathematics (DTAMS) Project
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.
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
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
Classroom Connections
Student work samples
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
MET Report Recommendations
Prospective middle grades teachers of mathematics should take coursework in:Number and OperationsAlgebra and FunctionsMeasurement and GeometryData Analysis, Statistics and Probability (Optionally) Calculus, focusing on concepts and applications
CBMS. (2001). The Mathematical Education of Teachers.
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.
Geometry
Geometry as a measuring tool Spherical Geometry Rigid Motions Geometry as a logical system
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?
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
Algebraic Structures
Elementary logic Set Theory Functions Operations Algebraic Structures Number Theory
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?
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