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?

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. 4 West Point Leader Development System (WPLDS = old CLEDS) FRAMEWORK 6 DIMENSIONS (previously domains)

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. 5

6 Why Our Core Math Program? Graduates anticipate and respond effectively to the uncertainties of a changing technological, social, political, and economic world.

7 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 Needs of the Army Needs of the Academic Discipline Needs of Society Academic Customers Chemistry Physics Economics 3 CES ABET MSE Majors FEE Necessary Contexts Mathematics & Science Engineering & Technology Information Technology Historical Perspective Cultural Perspective Understanding Human Behavior Creativity Communication Continued Intellectual Development Some tensions in addressing all EFAOCW West Point Leader Development System

Core Mathematics of Yesterday

10 CORE Math Evolves… 1980s

11 The Giordano/Arney Years 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 …

12 CORE Math Evolves… 1980s 1990s MA 103 MA 104MA 205MA 206

13 CORE Math Evolves… 1980s 1990s MA 103 MA 104MA 205MA s MA 103MA 104MA 205MA 206

14 The Krahn/Phillips Years 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

Core Math Book 16 Link on department web site under Core Math

17 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 New!

Math Solution Real World Transformation Solve Using Most Appropriate Technique Communicate & Reflect Historical Approach Math Model Usually given Numerical Answer suffices Traditional Area of Emphasis

Present Approach 19 Interpret: Communicate & Reflect Mathematical Model Mathematical Solution Solve Using Most Appropriate Techniques Real World Iterative Process Transform: Identify What is Given, What to Find Develop Solution Plan

Present Approach 20 Interpret: Communicate & Reflect Mathematical Model Mathematical Solution Solve Using Most Appropriate Techniques Real World Iterative Process Key – Balance all 3 legs of the triangle Transform: Identify What is Given, What to Find Develop Solution Plan Additional Areas of Emphasis

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 KobylskiMathematics Dr. Frank WattenbergMathematics Dr. Adam KalksteinGeography and Environmental Engineering Dr. Scott Silverstone Social Sciences COL Joseph Shannon Chemistry LTC John HartkePhysics COL Diane RyanBehavioral 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 21

22 The Core Mathematics Program MA103 COL Kobylski, MAJ Weld MA104 LTC Lunday, MAJ Trujillo MA205 COL Hartley, MAJ LaCasse MA206 LTC Jackson, MAJ Cummiskey MA101 MAJ Jackson MA104 LTC Lunday, MAJ Trujillo MA205 COLHartley, MAJ LaCasse MA206 LTC Jackson, MAJ Cummiskey MA100 MAJ Jackson MA153 LTC Outing, MAJ Swedberg MA255 LTC Outing, MAJ Swedberg MA206 LTC Jackson, MAJ Cummiskey

Core Mathematics of Tomorrow

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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 YEARS FROM NOW…BE THE LEADERS Where is future of math? Example: less calculus, more…data analysis, graph theory, linear algebra?

BACKUP 27

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. 28

29 Math and Science Program Goal Graduates are scientifically literate and are capable of applying scientific, mathematical, and computational modes of thought to the solution of complex problems. How do we know? Therefore: The core program – for all students – involves : acquiring a body of knowledge. developing thought processes. Helps students grow as life- long learners. Demonstrates the ability to:Goal Standard: Understand the fundamental scientific principles that underlie military technology. Understand the geophysical processes that govern the air-land-space environment. Discern the scientific features or aspects of complex problems. Construct mathematical models to facilitate the understanding and solution of problems. Select and apply appropriate mathematical methods as well as algorithmic and other computational techniques in the course of solving problems. Comprehend scientific literature appearing in the popular press.

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