Ok I'll start. My son and I were having a meal at Portillo's (an iconic Chicagoland food joint) when he was home from University of Arizona several years ago as a young student in th Eller School of Management. He lamented that in his high school AP calculus class they never really taught him what to do with all those functions. So I got out a napkin, scribbled a graph of a rate function (like millions of dollars per month profits) and drew some Riemannian rectangles, created a sum, did some unit cancelling and voila! There we have the total profits. I then wrote some official math notation, too, using sigma, limits and integral symbols. His response, "I wish they would have told me that." Out of fairness to his fine teachers, my son was a pretty lay back seniorâ€¦they very likely did tell him that.

So what problems do I like when making a point in a calculus class? I like those discrete ones like in Stewart where there's a table of motorcycle rates over time intervals and total distance is requested. I like related rates problems that cry out for inclusion of units so the unit canceling makes the results sensible. And in business calc, I love a wide variety of word problems like the ones supplied in the Bittenger text we use. I love to make up crazy functions that have average values that can be considered and calculated without calculus (more closely related to things like weighted grading), then show how the calculus does the same thing for functions where that's not possible.

I'm finding it difficult to do this on my phone, so please excuse typos.

Looking forward to your thoughts!

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Linda Blanco

Professor and Department Chair

Joliet Jr College

Joliet IL

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Original Message:

Sent: 11-01-2021 06:44:51

From: Linda Blanco

Subject: IMPACT in Action - Productive Disposition

The IMPACTful Thoughts blog mentions there are 5 strands from the National Research Council (NRC) referenced in the IMPACT document Proficiency chapter. The 5th strand is Productive Disposition:

The habitual inclination to see mathematics as sensible, useful, and worthwhile,

coupled with a belief in diligence and one's own efficacy.

*How can one apply productive disposition to show proficiency in mathematics at the intensive level?*

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Linda Blanco

Professor and Department Chair

Joliet Jr College

Joliet IL

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