Philosophy of the Math Department
Mathematical Literacy
All students must be mathematically literate
They must perform in the workplace They will be lifelong learners They must be problem solvers
Mathematical Literacy for Engineers
Used to learn engineering concepts Apply concepts in real life situations Be a lifelong learner in chosen
professionMathematics is the tool
that makes these possible
Mathematics is the tool that makes these possible
Demands of Advancing Technology Today’s engineer needs a working
knowledge of Patterns Functions Algebra Spatial relationships Geometry Measurement Data analysis Probability Competent use of technology
Use of Technology in the Classroom
We are riding on a wave of change
It is not going away We cannot reject it or ignore it ABET requires it We must find a balance of how best to
use these new technologies Without sacrificing basic mathematical
skills
Engineering programs must demonstrate that their students attain: …
k) an ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice.
Engineering programs must demonstrate that their students attain: …
k) an ability to use the techniques, skills, and modern engineering tools necessary for
engineering practice.
Concerns Students who cannot envision basic
functions Inability of students to evaluate the
reasonableness of a calculator answer Lack of basic skills with
Algebra Derivatives Integrals Differential Equations
“students have become less familiar withbasic algebra and
trigonometry. This change has been coincident with their heightened usage of
calculators” Bill Graff
“students have become less familiar withbasic algebra and
trigonometry. This change has been coincident with their heightened usage of
calculators” Bill Graff
Addressing Concerns Stressing basic functions, drilling
recognition Repeatedly discussing whether an
answer given by technology is reasonable
Requiring “Gateway” tests to demonstrate/review basic derivative and integration skills without a calculator
Addressing Concerns Repeated reminders that a calculator can
be used both to solve a hard problem and make a very bad mistake
Learning to use the calculator as a tool Remember that misuse of the tool is not the
tool’s fault A hammer can be used to build a
mansion or break a window
Good Uses of Technology
Discovery teaching Making connections “Messy” problems Using a variety of solution
strategies
Discovery Teaching
Example: Pose the problem of finding the derivative of ln(x) using the limit definition for a derivative
Messy Problems Consider
Is the decomposition what we want the student to learn?
Or is it to be able to use it to do something else with (inverse Laplace transform)?
Shift of Teaching Strategies
Our teaching goals are shifting from Performance of mathematical operations To the use of mathematical concepts.
Assessment methods Two tiered exams
Without the calculator to assess basic understanding of the material
With the calculator to assess problem solving skills
Shift of Teaching Strategies
Use various ways of looking at a problem Formulas Tables of values Graphs Textual descriptions
This aids all learning styles
Shift of Teaching Strategies Consider the classical parachute problem
We must ask more than the usual “after how many seconds will the parachutist hit the ground?”
We give students direction by asking more detailed questions
Have them analyze the motion of the falling body Geometrically, Numerically, and Analytically.
Varieties of Solution Strategies
Try alternate methods to find a solution
Look at the graph Manipulate the formula View the table of values, use
regression to come up with a mathematical model
Implications of Available Technology
Our role as guides in the learning process is more important than ever
Must decide when to use/not use technology
The challenge for all of us … Take advantage of the symbolic computation possibilities and do more mathematics … more engineering
Philosophy of the Math Department