id: 06505016
dt: j
an: 2015f.00204
au: Uptegrove, Elizabeth B.
ti: Shared communication in building mathematical ideas: a longitudinal study.
so: J. Math. Behav. 40, Part A, 106-130 (2015).
py: 2015
pu: Elsevier, New York, NY
la: EN
cc: C50 D50 K20
ut: mathematical register; communication; representations; combinatorics;
Pascal’s triangle
ci:
li: doi:10.1016/j.jmathb.2015.02.001
ab: Summary: Students make sense of mathematical ideas using a variety of
representations including physical models, pictures, diagrams, spoken
words, and mathematical symbols. As students’ understanding of
mathematical ideas becomes more general and abstract, there is a need
to express these ideas using mathematical notation. This paper
describes students’ movement from model building and personal
notations to elegant use of mathematical symbols that show their
understanding of advanced counting ideas. Specifically, this paper
shows how earlier ideas from investigations of specific combinatorics
problems (questions about making pizzas with different toppings and
using cubes to build towers) are retrieved and built upon using the
formal mathematical register to explain the meaning of Pascal’s
Identity, the addition rule of Pascal’s Triangle. This analysis also
shows the power of shared communication in mathematical problem
solving.
rv: