Laptops for Everyone

Aaron KlebanoffDepartment of Mathematics

Rose-Hulman Institute of Technology

Why the excitement over computers?

Time for more practical problems and less concern about computational

details Visual Mathematics

graphs are easy to make animations

Laptops vs. Computer Labs

Minor Distinction CL: Hassle to get to lab L: Hassle to carry around the laptop.

Major Distinction CL: Students hesitant/slow to learn L: Students quickly become experts

Some skills are necessary to understand fundamental concepts

algebra skills. FC: slope (derivative): FC: function

– concept and notation are both stumbling blocks.– Students often try to solve a function.

f(x) = sin(x) looks like an equation, but it isn’t

– ... or find the value of an equation. and when we always write, f(0) = sin(0), aren’t we just

finding the value of an equation?

d

b

c

a

dc

ba

Some skills are necessary to understand FCs (cont.)

Selected techniques from calculus & ODEs. FC: transform hard problem into easy one

– substitution techniques for integration, polar coordinates, Laplace transforms

FC: derivative is a rate of change; integration is accumulation.

– rules reinforce and give students something concrete to work with.

What skills are really necessary?

Cover the bases. Students need practice with algebraic operations and functions calculus techniques that improve algebra skills differential equation techniques that improve

calculus and algebra skills.

Most students probably don’t need arithemetic practice (long division, sqrt,etc.) messy algebraic equations messy calculus calculations

More Good and Bad News

Good News First! Students actually want to be able to perform

computations without the computer And now, the bad news which may help

explain the good news... “Back to Basics” drive is growing strong

– popular press– politics– educators too! (I do NOT count myself among them.)

Practical Concerns

Set-up/Shut-down Time Projection Systems Networking/Games/etc. during class Exam policy Teaching CAS syntax vs. mathematics Decency issues

So, how should we use them?

Graphics and animations Pattern Seeking Checking work (done by hand) Performing intermediate calculations to

maintain focus on the big picture.

Take Home Message

Students can learn calculus and differential equations -- and gain a deeper understanding than they would have without the technology.

Practicing computation (without machines) still has its place.