Post Made Community Wiki by S. Carnahan
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Among basic numeracy issues that I have smuggled in to the classroom (I say "smuggled" because there is a list of topics that I'm supposed to cover) is Euclid's algorithm for GCDs and how to use the results to reduce fractions. No student has complained about this even though I've given them no written material on it besides assigned problems (and sometimes students required to take a course they'd rather not take are inclined to find things to complain about). See #2 at http://www.math.umn.edu/~hardy/1031/hw/2nd.pdf. Another addresses the habit of almost everyone to round 400 to 399.99823764, etc. One of the simplest examples is when you want to evaluate something like $(8/3) \times 57$. Students use their calculators to find that $8/3 \approx 2.667$, then multiply that by $57$, getting $152.019$, although in fact 57 is divisible by 3. Sometimes they even do that when the question is "How many....?" (See #5 at http://www.math.umn.edu/~hardy/1031/hw/1st.pdf.) #4 at http://www.math.umn.edu/~hardy/1031/hw/1st.pdf is also a nice "basic numeracy" problem.

Why is multiplication of finite cardinal numbers commutative, despite the seeming asymmetry in its definition? That's really basic numeracy, but "theoretical" and at the same time very concrete.

Mentioning past geniuses also seems worthwhile. I tell them Carl Gauss was the most famous person to live on earth in the 19th century (except people who did not work in the physical or mathematical sciences) and give them a copy of Wikipedia's "list of topics named after Carl Gauss" (the one on Euler is much longer; there are also such pages on Riemann and various others).

Basic probability seems worth presenting to a broad audience since there are so many different subjects that rely on statistics.

The combinatorial stuff that some basic probability problems rely on afford an opportunity to do "theoretical but concrete" mathematics, as in #2 or #6 at http://www.math.umn.edu/~hardy/1031/hw/1st.pdf (#6 was discussed in class before it was assigned). ("Concrete" is necessary at this level; there is no hope that these students will learn to understand such material at a less concrete level before the semester is over.)

I more frequently use exercises to call students attention to something than to challenge their cleverness.

Oh: As long as I've mentioned "numeracy", how about #1 at http://www.math.umn.edu/~hardy/1031/hw/7th.pdf? It actually seems as if some instructors are not aware of this problem. Why do they neglect to know about such a thing?

Today I've mentioned elsewhere on math overflow that I was amazed at how much could be done in the book by Freedman, Pisani, Purves, and Adhikari with so little knowledge of math on the part of the students. That things like that can be done encourages me to hope that there is some way to present the concept of isomorphism to non-mathematical freshman. It's what math is all about. Math is about "abstract structures" in the sense that it doesn't matter whether the chess pieces are made of wood or are images on the computer monitor, nor does $2 + 3 = 5$ depend on whether you're counting oranges or supreme court justices. Two things are the same abstract structure iff they're isomorphic.

And isomorphism makes "bypass operations" possible; there must be some of those that can be presented to freshman.