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Title: The Sleep of Reason Produces Monsters: How and When Biased Input Shapes Mathematics Learning
Children's failure to reason often leads to their mathematical performance being shaped by spurious associations from problem input and overgeneralization of inapplicable procedures rather than by whether answers and procedures make sense. In particular, imbalanced distributions of problems, particularly in textbooks, lead children to create spurious associations between arithmetic operations and the numbers they combine; when conceptual knowledge is absent, these spurious associations contribute to the implausible answers, flawed strategies, and violations of principles characteristic of children's mathematics in many areas. To illustrate mechanisms that create flawed strategies in some areas but not others, we contrast computer simulations of fraction and whole number arithmetic. Most of their mechanisms are similar, but the model of fraction arithmetic lacks conceptual knowledge that precludes strategies that violate basic mathematical principles. Presentingbalanced problem distributions and inculcating conceptual knowledge for distinguishing flawed from legitimate strategies are promising means for improving children's learning.  more » « less
Award ID(s):
1844140
PAR ID:
10173002
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Annual Review of Developmental Psychology
Volume:
2
Issue:
1
ISSN:
2640-7922
Page Range / eLocation ID:
413 to 435
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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