My coworker wants to know: what is the history behind the reverse
orientation of numeric keypads on computer keyboards/calculators vs.
that of a phone dialpad?

A few quick links would suffice.

Hi grammatoncleric,

The answer seems to be that the ten-key layout existed first, and when
the telephone company introduced touch-tone dialing in the 1960's,
they did a careful study and concluded that the current telephone
layout would work best.

It may have been a consideration that there were letters already
associated with the digits and the selected layout puts the alphabet
in a natural order, going left to right and top to bottom as in normal
text.

There is also a theory that the layout was chosen because if the
ten-key layout were chosen, people experienced with adding machines
would dial faster than the telephone network could respond.  This
sounds bogus to me.

You can read more about it in the following links.

A good place to start is the Keyboard Trivia page of the Calculator
Reference website.  It quotes two books and a news story that present
and evaluate various theories.

http://www.vcalc.net/Keyboard.htm

The Bell System Memorial website page on Touch Tone dialing deals with
the question.

http://www.bellsystemmemorial.com/telephones-technical_dials-touchtone.html

That site also provides a copy of a paper by R. L. Deininger, "Human
Factors Engineering Studies of the Design and Use of Pushbutton
Telephone Sets," from the Bell System Technical Journal, July 1960.

http://www.bellsystemmemorial.com/pdf/touchtone_hf.pdf

The Wikipedia article on dual-tone multi-frequency says that eighteen
layouts were tested and the one selected had fewer keying errors than
the ten-key layout.

http://en.wikipedia.org/wiki/Dual-tone_multi-frequency

I hope this answers your question adequately.  If you need any more
information, please ask for a clarification.

--efn