id: 06454550
dt: j
an: 2015d.00549
au: Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre,
Ian; Schappelle, Bonnie P.; Lewis, Melinda L.
ti: Obstacles and affordances for integer reasoning: an analysis of
children’s thinking and the history of mathematics.
so: J. Res. Math. Educ. 45, No. 1, 19-61 (2014).
py: 2014
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: F42 D72 C32 A30
ut: history of mathematics; mathematical concepts; comprehension; negative
numbers; cognitive processes; thinking skills; cognitive affordances;
cognitive obstacle; integers
ci:
li: http://www.nctm.org/publications/article.aspx?id=40288
ab: Summary: We identify and document 3 cognitive obstacles, 3 cognitive
affordances, and 1 type of integer understanding that can function as
either an obstacle or affordance for learners while they extend their
numeric domains from whole numbers to include negative integers. In
particular, we highlight 2 key subsets of integer reasoning:
understanding or knowledge that may, initially, interfere with one’s
learning integers (which we call cognitive obstacles) and understanding
or knowledge that may afford progress in understanding and operating
with integers (which we call cognitive affordances). We analyzed
historical mathematical writings related to integers as well as
clinical interviews with children ages 6‒10 to identify critical,
persistent cognitive obstacles and powerful ways of thinking that may
help learners to overcome obstacles.
rv: