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Ring the Changes in Math

Any idea what this title means? By British tradition, "ring the changes" means to make something more interesting by changing it in some way. Or, it means to state and restate something over and over again in different ways. Both of these interpretations fit the teaching of mathematics!

Also, both interpretations hint at the expression's origin, which is quite mathematical. In bell ringing, a "change" means ringing a series of bells in a different order. Thus, with 6 bells, there are 6! = 720 changes possible (i.e. 720 different orders for ringing the bells).

Now, 12 bells is the largest number used in a series of ringing. This allows for 12! = 479,001,600 changes, which will not occur.

Supposedly, the largest number ever rung on a series of church bells is 16,000 changes. The process took a group of human bell-ringers about 9 hours.

Before accepting that last claim, check the math! Ringing 16000 changes in 9 hours equals about 1778 changes in one hour, or about 30 changes in one minute. This means that a change had to be rung every 2 seconds...and every change had to involve a sequence of at least 8 bells. Impossible I say!

But, ringing in changes in math education is not only possible...but is a good practice!

Source: C. Funk's 2107 Curious Word Origins, Sayings & Expressions, 1993, p. 29.