
06454550
j
2015d.00549
Pierson Bishop, Jessica
Lamb, Lisa L.
Philipp, Randolph A.
Whitacre, Ian
Schappelle, Bonnie P.
Lewis, Melinda L.
Obstacles and affordances for integer reasoning: an analysis of children's thinking and the history of mathematics.
J. Res. Math. Educ. 45, No. 1, 1961 (2014).
2014
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
F42
D72
C32
A30
history of mathematics
mathematical concepts
comprehension
negative numbers
cognitive processes
thinking skills
cognitive affordances
cognitive obstacle
integers
http://www.nctm.org/publications/article.aspx?id=40288
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 610 to identify critical, persistent cognitive obstacles and powerful ways of thinking that may help learners to overcome obstacles.