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 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. 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 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 Why Our Core Math Program? Graduates anticipate and respond effectively to the uncertainties of a changing technological, social, political, and economic world. 6 Academic Program Goals Intellectual Domain 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 7 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 8 Core Mathematics of Yesterday CORE Math Evolves… 1980s Differential Calculus Integral Calculus Multivariable Calculus Differential Eqns / Prob & Stats 10 The Giordano/Arney Years 1988 - 2000 Restructuring of the Math Core Program Philosophy: Pump and not a Filter 7 into 4 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 11 CORE Math Evolves… 1980s Differential Calculus 1990s Integral Calculus Discrete Dynamical Systems and Intro to Calculus MA 103 Multivariable Calculus Single Variable Calculus & ODEs MA 104 Differential Eqns / Prob & Stats Multivariable Calculus MA 205 Probability & Statistics MA 206 12 CORE Math Evolves… 1980s Differential Calculus 1990s Integral Calculus Discrete Dynamical Systems and Intro to Calculus MA 103 2000s Multivariable Calculus Single Variable Calculus & ODEs 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 13 The Krahn/Phillips Years 2001 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 14 Core Mathematics of Today Core Math Book CORE MATHEMATICS Link on department web site under Core Math ACADEMIC YEAR 2012 – 2013 16 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 17 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 19 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 20 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 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 21 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 22 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? 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 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. Introduces differential calculus The course integrates computers and handheld calculators 28

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# Departmental Review and Analysis for AY 2002-2003