id: 06145601
dt: j
an: 2013b.00698
au: Somchaipeng, Tongta; Kruatong, Tussatrin; Panijpan, Bhinyo
ti: Using disks as models for proofs of series.
so: Math. Teach. (Reston) 106, No. 1, 46-50 (2012).
py: 2012
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: I34 U64
ut: mathematical logic; high school students; secondary school mathematics;
core curriculum; state standards; series; sums of squares; sums of
cubes; manipulative materials
ci:
li: doi:10.5951/mathteacher.106.1.0046
http://www.nctm.org/publications/article.aspx?id=33622
ab: Summary: Exploring and deriving proofs of closed-form expressions for
series can be fun for students. However, for some students, a physical
representation of such problems is more meaningful. Various approaches
have been designed to help students visualize squares of sums and sums
of squares; these approaches may be arithmetic-algebraic or
combinatorial in nature, or they may involve mathematical induction. In
the activity described in this article, students use balls and disks to
prove the general formulas for sums of squares and cubes. (ERIC)
rv: