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Core Mathematics Curriculumyesterday, today, (& tomorrow)
COL Rod SturdivantCore Program Director
Department of Mathematical Sciences
United States Military Academy
Why Core Mathematics
Why Core Mathematics
Why 4 semesters?
4
Intellectual Physical 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.
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.
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.
West Point Leader Development System (WPLDS = old CLEDS) FRAMEWORK
6 DIMENSIONS (previously domains)
5
West Point Leader Development System10 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
Six Domains of Knowledge• 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:• communicate (listen, read, speak, and write) effectively,• think and act creatively,• recognize moral issues,• demonstrate the capability and desire to pursue continued intellectual
development
Intellectual Domain
One Program; Many “Customers”
8
Core Mathematics Program
Needs of the ArmyNeeds of the Academic Discipline
Needs of Society
Academic CustomersChemistryPhysicsEconomics3 CESABETMSE MajorsFEE
Necessary ContextsMathematics & ScienceEngineering & TechnologyInformation TechnologyHistorical PerspectiveCultural PerspectiveUnderstanding Human BehaviorCreativityCommunicationContinued Intellectual Development
Some tensions in addressing all
EFAOCW
West Point LeaderDevelopmentSystem
Core Mathematics of Yesterday
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CORE Math Evolves…Differential
Calculus Integral Calculus
Multivariable Calculus
Differential Eqns / Prob & Stats
1980s
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The Giordano/Arney Years1988 - 2000
Restructuring of the Math Core Program Philosophy: Pump and not a Filter 7 into 4
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
Math as a Filter …
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CORE Math Evolves…Differential
Calculus Integral Calculus
Multivariable Calculus
Differential Eqns / Prob & Stats
1980s
Discrete Dynamical Systems and
Intro to Calculus
Single Variable Calculus & ODEs
Multivariable Calculus
Probability & Statistics
1990s
MA 103 MA 104 MA 205 MA 206
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CORE Math Evolves…Differential
Calculus Integral Calculus
Multivariable Calculus
Differential Eqns / Prob & Stats
1980s
Discrete Dynamical Systems and
Intro to Calculus
Single Variable Calculus & ODEs
Multivariable Calculus
Probability & Statistics
1990s
MA 103 MA 104 MA 205 MA 206
Math Modeling &
Intro to Calculus
Differential Calculus
Integral Calculus & ODEs
Probability & Statistics
2000s
MA 103 MA 104 MA 205 MA 206
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The Krahn/Phillips Years2001 -
Modeling & Problem Solving Creating Experiences Balancing the Needs ….. of everyone. Expanding our External Presence
Army, USMA, & larger Math Community Faculty Development
Promoting Interdisciplinary Participation Expanding the Advanced Math Program Tech:
Laptop Computers The Death of Calculators - Rebirth of the TI-30
Core Mathematics of Today
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Core Math BookCORE MATHEMATICS
ACADEMIC YEAR 2012 – 2013
Link on department web site under Core Math
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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
Supporting Role: Technology- Appropriately & Effectively - Aid to Understanding- Role in Problem Solving
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
Habits of Mind
Interdisciplinary Problem Solving
Problem Solving
Technology Skills
Communication
Body of Knowledge
New!
MathSolution
Real World
Transformation
Solve Using Most Appropriate TechniqueCommunicate & Reflect
Historical Approach
MathModel
Usually given
Numerical Answersuffices
TraditionalArea of
Emphasis
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Present Approach
Interpret:
Communicate & Reflect
MathematicalModel
MathematicalSolution
SolveUsing MostAppropriateTechniques
RealWorld
IterativeProcess
Transform:
Identify What is
Given,
What to Find
Develop Solution Plan
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Present Approach
Interpret:
Communicate & Reflect
MathematicalModel
MathematicalSolution
SolveUsing MostAppropriateTechniques
RealWorld
IterativeProcess
Key – Balance all 3 legs of the triangle
Transform:
Identify What is
Given,
What to Find
Develop Solution Plan
Additional Areas ofEmphasis
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 MathematicsDr. Frank Wattenberg MathematicsDr. Adam Kalkstein Geography and Environmental
EngineeringDr. Scott Silverstone Social SciencesCOL Joseph Shannon ChemistryLTC John Hartke PhysicsCOL Diane Ryan 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
MA103COL Kobylski, MAJ Weld
MA104LTC Lunday, MAJ Trujillo
MA205COL Hartley, MAJ LaCasse
MA206LTC Jackson, MAJ Cummiskey
MA101MAJ Jackson
MA104LTC Lunday, MAJ Trujillo
MA205COLHartley, MAJ LaCasse
MA206LTC Jackson, MAJ Cummiskey
MA100MAJ Jackson
MA153LTC Outing, MAJ Swedberg
MA255LTC Outing, MAJ Swedberg
MA206LTC Jackson, MAJ Cummiskey
Core Mathematics of Tomorrow
?
Points of (short term) emphasis• 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
• Develop options for next iteration of Core Math program– 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?
27
BACKUP
28
MA103 – Then and Now
1993 – 2005
Discrete Dynamical Systems & Intr Calc
Mathematical modeling using difference equations in the form of discrete dynamical systems.
Motivates the study of the calculus. Elementary matrix algebra
Introduces differential calculus The course integrates computers and
handheld calculators
2005 –
MA103 Mathematical Modeling & Intr Calc
Applied mathematics through modeling
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.