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