1. Laptops for Everyone Aaron Klebanoff Department of Mathematics Rose-Hulman Institute of Technology

2. Why the excitement over computers? l Time for more practical problems n and less concern about computational details l Visual Mathematics n graphs are easy to make n animations

3. Laptops vs. Computer Labs l Minor Distinction n CL: Hassle to get to lab n L: Hassle to carry around the laptop. l Major Distinction n CL: Students hesitant/slow to learn n L: Students quickly become experts

4. Some skills are necessary to understand fundamental concepts l algebra skills. n FC: slope (derivative): n FC: function –concept and notation are both stumbling blocks. –Students often try to solve a function. l f(x) = sin(x) looks like an equation, but it isn’t –... or find the value of an equation. l and when we always write, f(0) = sin(0), aren’t we just finding the value of an equation?

5. Some skills are necessary to understand FCs (cont.) l Selected techniques from calculus & ODEs. n FC: transform hard problem into easy one –substitution techniques for integration, polar coordinates, Laplace transforms n FC: derivative is a rate of change; integration is accumulation. –rules reinforce and give students something concrete to work with.

6. What skills are really necessary? l Cover the bases. Students need practice with n algebraic operations and functions n calculus techniques that improve algebra skills n differential equation techniques that improve calculus and algebra skills. l Most students probably don’t need n arithemetic practice (long division, sqrt,etc.) n messy algebraic equations n messy calculus calculations

7. More Good and Bad News l Good News First! n Students actually want to be able to perform computations without the computer l And now, the bad news which may help explain the good news... n “Back to Basics” drive is growing strong –popular press –politics –educators too! (I do NOT count myself among them.)

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

9. So, how should we use them? l Graphics and animations l Pattern Seeking l Checking work (done by hand) l Performing intermediate calculations to maintain focus on the big picture.

10. Take Home Message l Students can learn calculus and differential equations -- and gain a deeper understanding than they would have without the technology. l Practicing computation (without machines) still has its place.