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
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Background on the Milwaukee
Mathematics Partnership
UW-Milwaukee teacher preparation
program and mathematics focus
courses
Mathematics Fellows program
Program outcomes and evaluation
Conclusions
Discussion
Mathematical Education of
Teachers (MET) Report
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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.
Milwaukee Mathematics
Partnership (MMP)
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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
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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
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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
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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
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Mathematics faculty provide rigorous
mathematics content.
Mathematics education faculty focus on
mathematical knowledge for teaching.
Classroom teachers (Teacher-inresidence) make connections to
classroom practice.
Mathematics Focus Area
Courses for MCEA Majors
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Problem Solving
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Geometry
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Discrete Probability and Statistics
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Algebraic Structures
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Calculus Experience
Problem Solving & Critical Thinking
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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
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
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Experimental likelihoods
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Simple probability models
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Conditional probability
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Expected value
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Complex probability models
Probability Dice Task
If we roll two dice, how often will
the total 7 occur?
Probability Dice Task
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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
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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
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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
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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
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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
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Student work samples
Conclusions
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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 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.
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
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Geometry as a measuring tool
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Spherical Geometry
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Rigid Motions
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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)
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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
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Elementary logic
Set Theory
Functions
Operations
Algebraic Structures
Number Theory
Modular arithmetic
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What could we mean by 1/313 in Z7?
Which elements of Zn have additive
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inverses?
Which elements have multiplicative
inverses?
When can we solve linear equations
in Zn?