The balance - a (rapidly) moving target: Experiences from 5 years teaching in an integrated engineering curriculum

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The balance - a (rapidly) moving
targetExperiences 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_at_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.
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Overview

• ABET 2000
• Foundation Coalition
• Team projects
• Conclusion

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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

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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.

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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 ABETs teeth.

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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?)
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Foundation Coalition Courses at ASU

• Team-based learning
• Technology intensive
• Integrated Curriculum1st Year Intro to
  Engineering, Calculus 12, Physics, Chemistry,
  English composition2nd Year Vector Calculus,
  Diff Eqns,Mechanics (previously with Electric
  Circuits,Linear Algebra, Intro Macroeconomics)

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2nd engineering freshmen projectThe bungee
omelet drop, due week 13 of 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?
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A first semester team project, due in week
13Model 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.
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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. Druckers 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
J0.08 ma2 as opposed to J0.40 ma2 for a solid
billiards queue ball!!!
PROUD winners and winning design
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Aiming high A third semester project
What level of math?
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Current research -- not just 300 year old stuff!
Theory matters!
Theory matters!
Use technology -- no time for hand manipulations.
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q2
Traditional emphasis, physics point of
viewConservative ( 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 find Da (boring w/
computer algebra system)Modern Given F and Da
find C (intelligent, ubiquitous applications)
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And where did the integration techniques go?

• Very disconnected debatemath/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 dont 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 JohnOrrs O-Line Testing
  System)

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Which way is the balance moving?

• 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

Afterwords ABET 2000 means 2000 only 59 weeks
from now!GET MOVING FAST! Redmond and
SiliValleydont rest - NEVER. Youcant catch up
-- but your students might fall even further
behind. You cant be too slow teaching tech