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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

Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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Page 1: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 2: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 3: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 4: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 5: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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)

Page 6: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,
Page 7: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 8: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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)

Page 9: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 10: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 11: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Mathematics Focus Area Courses for MCEA Majors

Problem Solving Geometry Discrete Probability and Statistics Algebraic Structures Calculus Experience

Page 12: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 13: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 14: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Discrete Probability & Statistics

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

Page 15: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Probability Dice Task

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

Page 16: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 17: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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?

Page 18: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 19: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 20: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 21: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 22: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 23: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Classroom Connections

Student work samples

Page 24: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 25: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 26: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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.

Page 27: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Geometry

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

Page 28: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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?

Page 29: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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

Page 30: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

Algebraic Structures

Elementary logic Set Theory Functions Operations Algebraic Structures Number Theory

Page 31: Mathematics Fellowships: Providing Mathematics Content to Middle-grades Teachers Kevin McLeod, Mathematics, UW-Milwaukee Hank Kepner, Mathematics Education,

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?

1

3