Core Mathematics Curriculum
yesterday, today, (& tomorrow)
COL Rod Sturdivant
Core Program Director
Department of Mathematical Sciences
United States Military Academy
Why Core Mathematics
Why Core Mathematics
Why 4 semesters?
West Point Leader Development System
(WPLDS = old CLEDS) FRAMEWORK
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Intellectual
6 DIMENSIONS
Physical
(previously domains)
Military
Human Spirit: Graduates understand and continuously develop their human
spirit to have the strength of character and worldview to adapt effectively to combat and the
uncertainties of a changing world.
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Moral-Ethical: Graduates who live the Professional Military Ethic develop
morally, enabling them to identify moral and ethical issues, discern what is right, make
proper decisions and take appropriate action.
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Social: Graduates interact appropriately with others in a wide range of social and
professional settings, displaying proper etiquette and dress, consideration for others, and
respect for social and professional conventions and traditions.
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West Point Leader Development System
10 OUTCOMES
1. Lead and inspire their units to accomplish the mission.
2. Embrace their role as a United States Army officer.
3. Demonstrate a broad perspective that is open to new ideas and experiences.
4. Understand ambiguous situations and solve complex problems
5. Make sound and timely decisions under stress.
6. Communicate effectively with all audiences.
7. Demonstrate proficiency in military and physical skills required to succeed in
combat.
8. Demonstrate mental and physical toughness--with the strength of spirit to
persevere
and win.
9. Demonstrate respect for others and work effectively with different cultures and
people.
10. Live honorably--with uncompromising integrity.
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Why Our Core Math Program?
Graduates anticipate and
respond effectively to the
uncertainties of a changing
technological, social,
political, and economic
world.
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Academic Program Goals
Intellectual Domain
Six Domains of Knowledge
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Math and Science
(Supports other domains)
Engineering and Technology (3 Course Engineering Sequence)
Information Technology
(Algorithmic/Computational Thinking)
Cultural Perspective
(threads)
Historical Perspective
(threads)
Understanding Human Behavior (threads)
and are able to:
•
•
•
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communicate (listen, read, speak, and write) effectively,
think and act creatively,
recognize moral issues,
demonstrate the capability and desire to pursue continued intellectual
development
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One Program; Many “Customers”
Needs of Society
Some tensions in
addressing all
Needs of the
Academic Discipline
Needs of the Army
EFAOCW
Academic Customers
Chemistry
Physics
Economics
3 CES
ABET
MSE Majors
FEE
West Point Leader
Development
System
Necessary Contexts
Mathematics & Science
Engineering & Technology
Information Technology
Historical Perspective
Cultural Perspective
Understanding Human Behavior
Creativity
Communication
Continued Intellectual Development
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Core Mathematics of
Yesterday
CORE Math Evolves…
1980s
Differential
Calculus
Integral
Calculus
Multivariable
Calculus
Differential Eqns
/ Prob & Stats
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The Giordano/Arney Years
1988 - 2000
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Restructuring of the Math Core Program
Philosophy: Pump and not a Filter
7 into 4
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Math as a Filter …
Discrete Mathematics (dynamical systems)
Linear Algebra
Single Variable Calculus
Multi-Variable Calculus
Vector Calculus
Differential Equations
Probability and Statistics
Project InterMath – ILAPs
External - Presence in the Math Community
Tech: HP28/48, TI – 89 & mobile computer
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CORE Math Evolves…
Differential
Calculus
1980s
1990s
Integral
Calculus
Multivariable
Calculus
Discrete Dynamical
Single Variable
Systems and
Calculus & ODEs
Intro to Calculus
MA 103
MA 104
Differential Eqns
/ Prob & Stats
Multivariable
Calculus
MA 205
Probability &
Statistics
MA 206
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CORE Math Evolves…
Differential
Calculus
1980s
1990s
Integral
Calculus
Multivariable
Calculus
Discrete Dynamical
Single Variable
Systems and
Calculus & ODEs
Intro to Calculus
MA 103
2000s
MA 104
Math Modeling
&
Intro to Calculus
MA 103
Differential Eqns
/ Prob & Stats
Multivariable
Calculus
MA 205
Differential
Calculus
MA 104
Probability &
Statistics
MA 206
Integral
Calculus & ODEs
MA 205
Probability &
Statistics
MA 206
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The Krahn/Phillips Years
2001 
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Modeling & Problem Solving
Creating Experiences
Balancing the Needs ….. of everyone.
Expanding our External Presence
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Army, USMA, & larger Math Community
Faculty Development
Promoting Interdisciplinary Participation
Expanding the Advanced Math Program
Tech:
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Laptop Computers
The Death of Calculators - Rebirth of the TI-30
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Core Mathematics of
Today
Core Math Book
CORE MATHEMATICS
Link on department web
site under Core Math
ACADEMIC YEAR 2012 – 2013
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Core Mathematics Goals
Mathematical Thinking & Communication
- Develop Habits of Mind
- Build Competent and Confident Problem
Solvers
- Communicate Effectively
- Acquire a Body of Knowledge
Habits
of Mind
Interdisciplinary
Problem Solving
Supporting Role: Technology
- Appropriately & Effectively
- Aid to Understanding
- Role in Problem Solving
Problem
Solving
Technology Skills
Communication
Body of Knowledge
New!
Interdisciplinary Collaboration
- Motivates the Study of Mathematics
- Illustrates the Breadth, Power & Beauty of Mathematics
- Exercises our Program Goals
- Creates Links & Transfers Knowledge
- Promotes Collaboration and Interdisciplinary Teams
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Historical Approach
Math
Model
Real
World
Usually given
Solve
Using Most
Appropriate
Technique
Math
Solution
Numerical Answer
suffices
Traditional
Area of
Emphasis
Present Approach
Mathematical
Model
Real
World
Iterative
Process
Solve
Using Most
Appropriate
Techniques
Mathematical
Solution
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Present Approach
Additional Areas of
Emphasis
Mathematical
Model
Real
World
Iterative
Process
Key – Balance all 3 legs of the triangle
Solve
Using Most
Appropriate
Techniques
Mathematical
Solution
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
Promoting Interdisciplinary Collaboration in
USMA’s Core Program
Academic Excellence Committee Initiatives
 Plebe Program Director’s Meetings
 SENCER Guest Speaker
 SENCER Summer Institute 2011 (July 21-25, 2011)
 Developed an Interdisciplinary Team +
COL Jerry Kobylski
Dr. Frank Wattenberg
Dr. Adam Kalkstein
Dr. Scott Silverstone
COL Joseph Shannon
LTC John Hartke
COL Diane Ryan
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Mathematics
Mathematics
Geography and Environmental Engineering
Social Sciences
Chemistry
Physics
Behavioral Sciences and Leadership
Science Education for New Civic Engagements and Responsibilities
SENCER goal - "cadets become better decision makers with respect to energy and
climate issues."
Energy Workshop (17-20 April 2011)
Core Mathematics Program
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The Core Mathematics Program
MA103
COL Kobylski, MAJ Weld
MA104
LTC Lunday, MAJ Trujillo
MA205
COL Hartley, MAJ LaCasse
MA100
MAJ Jackson
MA101
MA153
MAJ Jackson
LTC Outing, MAJ Swedberg
MA104
MA255
LTC Lunday, MAJ Trujillo
MA206
MA205
LTC Jackson, MAJ Cummiskey
COLHartley, MAJ LaCasse
LTC Outing, MAJ Swedberg
MA206
LTC Jackson, MAJ Cummiskey
MA206
LTC Jackson, MAJ Cummiskey
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Core Mathematics of
Tomorrow
?
Points of (short term) emphasis
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Modeling, problem solving focus throughout
curriculum
Interdisciplinary activities expanded/created – real
world, data driven
Refocus on how to more consistently and naturally
incorporate technology (old and NEW) as a way to
address #1,#2
Look at how others are moving forward with
technology and problem based, modeling curriculum
(are we still the leaders?) – PROJECT MOSAIC for
example
Long term considerations
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Develop options for next iteration of Core Math program
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National meetings
Evaluate/assess current program
Multiple tracks? Reordering? New topics to enhance
modeling/problem solving ?
STUDENTS ARE CHANGING (technology)
WORLD IS CHANGING (technology)
WHAT IS THE APPROPRIATE MATH FOR 10-15 YEARS
FROM NOW…BE THE LEADERS
Where is future of math? Example: less calculus, more…data
analysis, graph theory, linear algebra?
BACKUP
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MA103 – Then and Now
1993 – 2005
Discrete Dynamical Systems & Intr Calc
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Mathematical modeling using
difference equations in the form of
discrete dynamical systems.
Motivates the study of the calculus.
Elementary matrix algebra
2005 –
MA103 Mathematical Modeling & Intr Calc
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Applied mathematics through modeling
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Problem solving strategies and
modeling theory to solve complex and
often ill-defined problems.
Nurtures creativity, critical thinking,
and learning through activities
performed in interdisciplinary settings.
Introduces calculus
The course exploits a variety of
technological tools to develop
numerical, graphical, and analytical
solutions that enhance understanding.
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Introduces differential calculus
The course integrates computers and
handheld calculators
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