The University of Texas at Arlington Department of Mathematics

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The University of Texas at ArlingtonDepartment
of Mathematics
GK-12 MAVS Program
Program Director Dr. Minerva Cordero
Co-Principal Investigators Dr. Tuncay
Aktosun Dr. James Epperson Dr. Theresa
Jorgensen Dr. Jianping Zhu Program Coordinator
Ms. Cecelia Levings
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Overview

• Project title Mathematically Aligned Vertical
  Strands connecting mathematics research and
  pedagogy for GK-12 Fellows and teachers (MAVS
  project)
• Involves 8 fellows and 8 teachers
• Funded by the NSF GK-12 program 2.85 million
  from 2009 2014.

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Overview

• One of the goals of the MAVS GK-12 Project at
  the University of Texas at Arlington is to
  create a seamless transition in mathematics that
  bridges the school curriculum to graduate level
  research. 
• Challenges
• Abstract nature of mathematics research
• Understanding school curriculum and standard
• Bringing fellows, teachers, research advisors,
  and GK-12 mentors together

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Overview

• Our Strategies 
• Vertical integration
• Team structure that facilitates collaboration and
  coordination (mentoring triad and teaching quad)
  
• Intensive summer program for fellows and teachers
• MAVS Seminars that promote interactions and
  sharing of best practice
• Innovative lesson plans and projects that brings
  graduate level research to school classrooms

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Vertical Content Strands
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Vertical team

• At the heart of the MAVS project are cohesive
  vertical teams of graduate students, K-12
  teachers, and mathematicians.

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Vertical Team
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The GK-12 (MAVS) Fellows

• All MAVS fellows are graduate students in the
  University of Texas at Arlington Department of
  Mathematics who have have begun independent
  research.
• These students are pursuing either the Masters or
  Ph.D. track - it should be noted that independent
  research is a requirement of both degrees.
• Eight graduate fellows per year are being
  supported.

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2010-2011 Fellows

• GK-12 fellows working in mathematics research at
  UTA
• Jason Bacon Algebra
• Justin Blackwell Applied Mathematics
• Angie Brown Geometry
• Jason Gilgenbach Statistics
• Antonio Lopez Applied Mathematics
• Aubrey Rhoden Applied Mathematics
• Catherine Rogers Applied Mathematics
• Padmini Veerapen Algebra

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The K-12 Mentor Teachers

• Eight mentor teachers per year are participating
  in the MAVS project four from Sam Houston High
  School (SHHS) and four from its feeder junior
  high schools.
• Each mentor teacher is assigned as chief mentor
  teacher of one graduate fellow for the project
  year.
• MAVS fellows spend their K-12 school contact
  hours in the classroom of their assigned mentor
  teacher.

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2009-2010 Mentor Teachers

• Sam Houston High School
• Alicia Geppert
• Kimberly Helixon
• Gina Kaucher
• Thang Tran
• Carter Junior High
• Daree Yancey
• Hutcheson Junior High Ashlee Dephilippis
• Workman Junior High Kelly Randell
  Christopher Boyd

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GK-12 Team Structure

• Teaching Quad groups consisting of two MAVS
  fellows with a mentor junior high teacher and a
  mentor high school teacher
• Mentoring TriadMAVS fellow, research advisor,
  and MAVS faculty mentor
• The MAVS faculty mentor bridges the communication
  between the Teaching Quad Team and the Mentoring
  Triad and facilitates the communication with the
  district mathematics supervisors and school
  administrators.

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GK-12 MAVS Teaching Quads Research Triads
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2009-2010 Quads
Quad I SAM HOUSTON HS Alicia Geppert Workman JH Kelly Randell UTA Catherine Rogers UTA Padmini Veerapen
Quad II SAM HOUSTON HS Kim Helixon WORKMAN J H Christopher Boyd UTA Angie Brown UTA Jason Gilgenbach
Quad III SAM HOUSTON HS Gina Kaucher Carter JH Daree Yancey UTA Jason Bacon UTA Aubrey Rhoden
Quad IV SAM HOUSTON HS Thang Tran Hutcheson JH Ashlee Defilippis UTA Justin Blackwell UTA Antonio Lopez
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Summer Program

• Summer Professional Development Institute
  (two weeks)
• Fellows present research
• Teachers discuss curriculum-scope and sequence
• Together each fellow-teacher pair designs six
  research lessons

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Summer PDI
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MAVS Seminar

• Throughout the school year, the GK-12 project
  PIs, fellows, teachers, and faculty meet for MAVS
  seminars.
• The seminars are held weekly at the beginning of
  an academic year, then bi-weekly, and monthly in
  the later part of the academic year.
• The MAVS seminar has two components
• A research component
• A teaching component
• The seminars are scheduled on a rotating basis
  among UT Arlington and the campuses of
  participating schools
• Teaching Quads meet to collaborate, trouble
  shoot, and share best practices
• Fellows present classroom lessons or research

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MAVS Seminar

• Each graduate fellow is required to present twice
  per year at this seminar. The first
  presentation will focus on the mathematical
  research they are conducting under the guidance
  of their research advisor. The second
  presentation will focus on their progress on
  implementing their research into their GK-12
  activities and their experiences in the
  classroom.
• The fellows research advisor will attend both of
  these presentations.

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MAVS Seminar

• Fellows, mentor teachers, and the project PIs
  all meet for informal discussions about
  challenges and issues in bringing graduate level
  research into middle and high school classrooms.
  
• Discussions at these meetings also focus on how
  the mentoring relationships are developing, what
  is going well, what should be modified, how
  lessons were implemented in the schools and any
  evidence of students' success.

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Fellows in the classroom
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Fellows in the classroom
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Research Projects
Medical Imaging in the Ninth Grade
By Aubrey Rhoden (MAVS Fellow) and Kimberly
Helixon (Mentor Teacher)
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Research Projects

• Medical Imaging using Computed Tomography

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Research Projects
Collaboration
The UNT Medical Center performed experiments
on mice to determine the effect that inclusions
such as blood clots would have upon the bodys
temperature.
The biomedical engineering department at UTA has
also justified this method in a different case
using optical tomography.
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Research Projects
With the Dirichlet boundary condition
on
Where w(x,y) is the temperature at location
(x,y) ( the solution of the diffusion
equation) p(x,y) is the perfusion coefficient at
location (x,y) (also included in this
coefficient is the thermal conductivity,
specific heat, and density all of which are
considered constant throughout the
domain) f(x,y) is the heat source
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Goals
From The boundary of the forward Problem one can
reconstruct the blood perfusion to determine
where blood clots or strokes occurred.
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Linear Approximation
Given seven equations with finite domains the
student is expected to graph these equations that
represent a one dimensional slice of body tissue
compared with the blood perfusion.
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Point-Slope Formula
Given this graph the students are expected to
find the equations for line segments A, B, C and
D. The students were also expected to Identify
the domain and range of each segment.
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Quadratic Approximation
Importance concept introduced to the students
Piecewise linear functions can be used to
approximate complex curves.
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Quadratic Approximation
Given seven equations with finite domains,
students are asked to graph these quadratic
equations that represent a one-dimensional
slice of body tissue compared with the blood
perfusion.
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Compare the Results
The students will compare and contrast the
differences between linear and quadratic models
with the same data points.
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Conclusions
Importance concept introduced to the students
The approximation can be improved by using more
sophisticated piecewise functions.