id: 05882028
dt: a
an: 2011c.00722
au: Tarlow, Lynn D.; Uptegrove, Elizabeth B.
ti: Block towers: co-construction of proof.
so: Maher, Carolyn A. (ed.) et al., Combinatorics and reasoning. Representing,
justifying and building isomorphisms. New York, NY: Springer (ISBN
978-0-387-98131-4/hbk; 978-94-007-0614-9/hbk; 978-0-387-98132-1/ebook).
Mathematics Education Library 47, 97-104 (2010).
py: 2010
pu: New York, NY: Springer
la: EN
cc: K24 D54 E54 C34
ut: combinatorics; problem solving; conjecturing; justification; proving;
reasoning; educational research; grade 11
ci:
li: doi:10.1007/978-94-007-0615-6_9
ab: Summary: In previous chapters, we observed elementary school students
working to make sense of the towers problems by building
representations, formulating conjectures, and defending their solutions
in discussions with classmates and researchers. In this chapter, we
observe a cohort of high school juniors as they engage in explorations
and constructions in the towers problem. During this session, the
students found and generalized formulas for solutions to the original
towers problem (building towers when selecting from two colors of
Unifix cubes) and extensions (with more than two colors of cubes),
using methods including controlling for variables, justification by
cases, and inductive reasoning.
rv: B. Ruffer-Henn (Böhl-Iggelheim)