core mathematics curriculum yesterday, today, (& tomorrow) col rod sturdivant core program...

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?

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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)

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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”

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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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1980s

Discrete Dynamical Systems and

Intro to Calculus

Single Variable Calculus & ODEs


Probability & Statistics

1990s

MA 103 MA 104 MA 205 MA 206

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1980s

Discrete Dynamical Systems and

Intro to Calculus

Single Variable Calculus & ODEs



1990s

MA 103 MA 104 MA 205 MA 206

Math Modeling &

Intro to Calculus

Differential Calculus

Integral Calculus & ODEs


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


MA100MAJ Jackson

MA153LTC Outing, MAJ Swedberg

MA255LTC Outing, MAJ Swedberg


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?

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BACKUP

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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.

core mathematics curriculum yesterday, today, (& tomorrow) col rod sturdivant core program...

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