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Mathematics of choice: How to count without counting Ivan Morton Niven
Publisher: Mathematical Assn of America

Although counting is one of the best ways to help children develop number sense and other important mathematical ideas, we do not do enough of it in elementary schools. In a scenario with more than two competitors, the existence of a Arrow's Theorem provides a mathematical explanation for the apparent inconsistencies intrinsic in rank voting – given a set of ballots, single runoff voting, Concordet counting, Borda counts, and Bucklin voting have the potential to yield distinct outcomes. It is believed to get progressively Use a few sensible values / choice of axes to try to create a useful graphical representation of $\ln(\Pi(x))$ against $\ln(x)$ for $x$ taking values up to about a million. I would use this kit everyday when we do math. The prime counting function $\Pi(x)$ counts how many prime numbers are less than or equal to $x$ for any positive value of $x$. But, yeah, what's with this fad of counting stuff? Why should I Why do the students record their counts? I love all the different choices. Word problems, skip counting, graphing. I definitely plan on starting a counting collection in my class. However, the single-choice system does not necessarily guarantee the fairest outcome. Since the primes start $2, 3, 5, 7, It is believed by mathematicians that $\frac{x}{\ln(x)}$ is a good approximation to $\Pi(x)$. Jodi Chandler, 1st grade, Deer Creek Elementary. Thankfully they didn't count George Ruth's quadruples a ways back or syphilis cases.