Matthias Kawski , Department of Mathematics Arizona State University

1. The balance - a (rapidly) moving target:Experiences from 5 years teaching in an integrated engineering curriculum Matthias Kawski, Department of Mathematics Arizona State University Tempe, AZ 85287, USA http://math.la.asu.edu/~kawski kawski@asu.edu Manual skills - theory - applications - technology - design - teamwork This work was partially supported by the National Science Foundation through the grant DUE 97-52453 (Vector Calculus via Linearization: Visualization and Modern Applications), through the Coop. Agreement EEC 92-21460 (The Foundation Coalition), and by an equipment donation from the Intel Corporation.

2. Overview • ABET 2000 • Foundation Coalition • Team projects • Conclusion

3. ABET 2000 http://www.abet.org/eac/eac2000.htm CRITERIA FOR ACCREDITING PROGRAMS IN ENGINEERING IN THE US Criterion 3. Program Outcomes and Assessment Engineering programs must demonstrate that their graduates have (a) an ability to apply knowledge of mathematics, science, and engineering (b) an ability to design and conduct experiments, as well as to analyze and interpret data (c) an ability to design a system, component, or process to meet desired needs (d) an ability to function on multi-disciplinary teams (e) an ability to identify, formulate, and solve engineering problems (f) an understanding of professional and ethical responsibility (g) an ability to communicate effectively (h) the broad education necessary to understand the impact of engineering solutions in a global and societal context (i) a recognition of the need for, and an ability to engage in life-long learning (j) a knowledge of contemporary issues (k) an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. Criterion 4. Professional Component The Professional Component requirements specify subject areas appropriate to engineering but do not prescribe specific courses. The engineering faculty …….. The professional component must include (a) one year of a combination of college level mathematics and basic sciences (some with experimental experience) appropriate to the discipline

4. ENGINEERING CRITERIA 2000 PROGRAM CRITERIA PROGRAM CRITERIA FOR ELECTRICAL, COMPUTER, AND SIMILARLY NAMED ENGINEERING PROGRAMS Submitted by The Institute of Electrical and Electronics Engineers, Inc These program criteria apply to engineering programs which include electrical, electronic, computer, or similar modifiers in their titles. 1. Curriculum The structure of the curriculum must provide both breadth and depth across the range of engineering topics implied by the title of the program. Graduates must have demonstrated knowledge of probability and statistics, including applications appropriate to the program name and objectives; knowledge of mathematics through differential and integral calculus, basic sciences, and engineering sciences necessary to analyze and design complex devices and systems containing hardware and software components, as appropriate to program objectives. Graduates of programs containing the modifier "electrical" in the title must also have demonstrated a knowledge of advanced mathematics, typically including differential equations, linear algebra, complex variables, and discrete mathematics. Graduates of programs containing the modifier "computer" in the title must have demonstrated a knowledge of discrete mathematics.

5. ABET 2000 http://www.abet.org/eac/eac2000.htm GONE are dozens of pages of specific requirements New, very brief, outcomes-oriented criteria • do not require any courses in a math department • do not prescribe specific syllabi and manual skills • emphasize teamwork, technology, applications • emphasize assessment - improvement cycles ABET 2000 looks a lot like MSE reform -- there is a major difference: ABET has teeth that bite, NAS-MSEB does not, NSF DUE carrots are small compared to ABET’s teeth.

6. The Foundation Coalition The NSF, ABET, …. are dead serious. The FC alone is to receive 30 Mill. $ from the NSF over twice 5 years.And the FC is only one of 6 original coalitions, most refunded for second 5 year term.(Compare calc reform?)

7. Foundation Coalition Courses at ASU • Team-based learning • Technology intensive • Integrated Curriculum1st Year: Intro to Engineering, Calculus 1+2, Physics, Chemistry, English composition2nd Year: Vector Calculus, Diff Eqns,Mechanics (previously with: Electric Circuits,Linear Algebra, Intro Macroeconomics)

8. 2nd engineering freshmen projectThe “bungee omelet drop”, due week 13of first semester! “The goal of the project was to design a bungee cord that would allow a payload, in this case, an egg, to come as close to the ground as possible without damaging the payload. The egg was to be dropped from ASU's Sun Angel Track Stadium's bleachers. Damage to the payload could have been incurred in one of two ways. First, the payload may be damaged by hitting the ground. Second, the pay- load may be damaged by decelerating too rapidly.Freshmen mathematics?

9. A first semester team project, due in week 13:Model the free-fall / elastic stretch including dampingcalculate, optimize, design release mechanism... Objectives: Longest possible free-fall , as close to the ground as possible, constraints on max acceleration Engineers INTEGRATE the nonlinear, second order, only piecewise smooth, DE no matter whether math delivers or not -- use EXCEL in the first semester for what math usually barely delivers in the fourth semester.

10. “Design” Or, sometimes it takes only fairly small changes to give a standard math topic a marked engineering twist….. A small, but crucial modification of a traditional application: The traditional “physics” problem analyzes rolling objects on an inclined plane. It goes as far as asking which object will win the race (compare: D. Drucker’s “Mathematical Roller Derby” in CMJ 11/1992). The calculus link are moments of inertia, i.e. iterated integrals, and a simple separable DE. The problem solution never goes beyond the level of “analysis”. The “engineering” problem goes one, CRITICAL STEP further: We ask thestudents to “apply” the knowledge gained by DESIGNING and BUILDING a rolling object that will win a race in the class!The results are amazingly fast: Further useof calculus yields an optimal design with J=0.08 ma2 as opposed to J=0.40 ma2 for a solid billiards queue ball!!! PROUD winners and winning design

11. Aiming high: A third semester project What level of math?

12. Current research -- not just 300 year old stuff! Theory matters! Theory matters! Use technology -- no time for hand manipulations.

13. q2 Traditional emphasis, physics point of view:Conservative ( = integrable ) vector fields, “closed loops lift to a potential surface” q1 Modern emphasis, engineering point of view: Controllable ( = nonintegrable ) vector fields, “design the closed loop in base so that the vertical gap of the lifted curve is as desired”. Traditional: Given F and C findDa (boring w/ computer algebra system)Modern: Given F and Dafind C (intelligent, ubiquitous applications)

14. “And where did the integration techniques go?” • Very disconnected debate:math/engineering old-timers those preparing for ABET 2000 • Need to set priorities! Better stay close to ABET 2000! • “Prepare for the next course” is no justification • Professional engineers don’t have time to integrate by handthey use computers for both reliability and efficiency ($$). • Isolated knowledge is useless -- must be able to APPLY the knowledge to solve “problems”. In case you wondered: We do have basic-skills “mastery tests” using JohnOrr’s O-Line Testing System)

15. Which way is the balance moving? Afterwords ABET 2000 means 2000 only 59 weeks from now!GET MOVING FAST! Redmond and SiliValleydon’t rest - NEVER. Youcan’t catch up -- but your students might fall even further behind. You can’t be too slow teaching tech • Theory • Hand manipulation • Technology • “Covering” all topics • Application, integration • Design. Creativity (bungee!) • Solution templates (bungee!) • Inquiry-based learning. • Problem solving • Working alone • Work in heterogeneous teams • Communication skills