Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers

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Mathematics FellowshipsProviding 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

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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

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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.

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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

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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)

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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.
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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)

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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.

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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.

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Mathematics Focus Area Courses for MCEA Majors

• Problem Solving
• Geometry
• Discrete Probability and Statistics
• Algebraic Structures
• Calculus Experience

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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

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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
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Discrete Probability Statistics

• Experimental likelihoods
• Simple probability models
• Conditional probability
• Expected value
• Complex probability models

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Probability Dice Task

• If we roll two dice, how often will the total 7
  occur?

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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

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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?

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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

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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

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Math Fellows comments Problem-Solving

• I had always been afraid of problemsThis course
  made me undertake ALL problems with trust and
  almost happiness, because now I know I can solve
  them
• I avoided problem solving and didnt like it
  until I took the course you offered. Now my
  students receive problem solvingwith nearly
  every assignment.

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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

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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 wasnt 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

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Classroom Connections

• Student work samples

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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

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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.
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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.

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Geometry

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

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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?

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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

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Algebraic Structures

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

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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?