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Title: Obstacles and affordances for integer reasoning: An analysis of children’s thinking and the history of mathematics
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 affor- dances). 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.  more » « less
Award ID(s):
0918780
NSF-PAR ID:
10123559
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Journal for research in mathematics education
Volume:
45
Issue:
1
ISSN:
1945-2306
Page Range / eLocation ID:
19 - 61
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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