id: 06514387
dt: j
an: 2016a.00799
au: Smith, Scott G.
ti: Recursive averaging.
so: Math. Teach. (Reston) 108, No. 7, 553-557 (2015).
py: 2015
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I30
ut: mathematical concepts; sequences; series; recursion; limits
ci:
li: http://www.nctm.org/Publications/mathematics-teacher/2015/Vol108/Issue7/Recursive-Averaging/
ab: Summary: In this article, Scott Smith presents an innocent problem that was
transformed by several timely “what if?” questions into a rewarding
investigation of some interesting mathematics. These investigations led
to two conclusions: (1) Developing generalizations from patterns can be
as rewarding to obtain as they are hard to discern; and (2) Sometimes
the most productive question to pose is, “Can this result be
generalized?”. Although Smith did not prove the general case in his
own investigation, he writes here that he thought it was still
satisfying to uncover patterns and discover that these patterns were
themselves considered by others in the mathematics community. (ERIC)
rv: