Following the standard form: effects of equation format on algebraic modeling.
When people construct algebraic equations to represent quantitative relations, they often reverse the roles of the variables (6S = P instead of 6P = S). Results from three experiments show that a major reason for such reversal errors is people's adherence to, and interpretation of, the Standard Form of algebraic models. College students constructed, selected, and interpreted algebraic models that either had the standard multiplication format (MF: ax = y), or the mathematically equivalent division format (DF: y/a = x). A large minority of participants constructed reversed MF models, whereas most participants who were instructed to use DF equations constructed correct models (Experiment 1). Most participants understood that MF and DF models of the same relation should be mathematically equivalent (Experiment 2), but they drew a conceptual distinction between these models (Experiment 3). The authors discuss the impact of notational conventions on people's interpretation and use of representational tools.
Department of Psychology, University of Washington, Seattle, WA, 98195, USA.
Kristie J
KJ
Fisher
Katja
K
Borchert
Miriam
M
Bassok
D032882:Comprehension; D003210:Concept Formation; D003657:Decision Making; D005260:Female; D006801:Humans; D008297:Male; D008962:Models, Theoretical; D011340:Problem Solving; D013334:Students / Q000523:psychology; D055815:Young Adult
Psychon Bull Rev. 2004 Dec;11(6):1099-104
15875982
Mem Cognit. 2001 Apr;29(3):462-77
11407423
Cogn Psychol. 1998 Mar;35(2):99-134
9570897
Mem Cognit. 2005 Apr;33(3):471-8
16156182
J Exp Psychol Appl. 2007 Dec;13(4):197-223
18194047
Cogn Sci. 2007 Mar 4;31(2):233-56
21635296
Cognition. 1998 Jan;65(2-3):231-62
9557384
J Exp Psychol Learn Mem Cogn. 2007 Jul;33(4):720-33
17576149
Mem Cognit. 1995 May;23(3):354-67
7791603
Cogn Sci. 2008 Mar;32(2):366-97
21635340
J Exp Psychol Learn Mem Cogn. 1988 Jul;14(3):510-20
2969945