WRITING ABOUT CONTINUITY

Derek Thompson

Assistant Professor of Mathematics

Taylor University

drthompson@taylor.edu

Mathfest 2014

Portland, OR

9:45 A.M., August 8, 2014

MOTIVATION FOR THE PROJECT Assessment Committee

Writing Assessments, Spring 2013 Yowch.

Writing Across the Curriculum My own liberal arts experience Engineers need to write too! Even Calculus…. Why not?

Calc I is practically a gen ed Grammar, but also ‘writing out the math’ Origin of idea: I can’t find it! Sorry!

Why Continuity? I introduced limits the first day by asking what continuity

means. It’s always difficult to correct thinking when students –

think- they already understand the concept.

THE ACTUAL ASSIGNMENT Think of three graphs that have physical

meaning – one should have an infinite discontinuity (vertical asymptote), one should have a jump discontinuity, and the last one should have a removable discontinuity (hole). Explain the discontinuity in terms of the physical meaning of the graph.

At least 500 words Normal homework assignment (10 pts) 5 points for style (grammar), 5 points for

correct mathematics Be creative… please!

RESULTS A lot of incorrect verbiage (e.g. “the point x”) And definitions (“as x gets closer to a, f(x) gets

closer to f(a)” for limit as x -> a of f) Clarity about axes A lot of repeated, boring examples They mostly hated it I was happy to see wrong ideas…

Students weren’t aware they had them Some of them, I wasn’t aware of either!

Some very clever/interesting papers A chance for some students to think about their

career in their chosen major

ASYMPTOTES The Bad:

Roller CoasterDiscrete Variables (my fault)Horizontal vs. Vertical (judgment call)

The Good:Residue Jafar

JUMP DISCONTINUITIES The Bad:

Iron Man vs. Nightcrawler The Good:

Price vs. Weight (common example)Disney Princesses vs. Time

The Medium:RPM vs. Speed (nitpicky)

REMOVABLE DISCONTINUITY The Bad:

Bridge“Moments” (CD skipping)Was this your card?

The Good:Wash on a bet (common example)Let me guess your weight/heightWreck-It Ralph Glitch (judgment call)

FINAL THOUGHTS Extremely helpful assignment (for me AND them) In the future, will give more examples/direction Possibly pre-approve ideas (too much repetition) Thank you!