Proportional reasoning as a heuristic-based process: time constraint and dual task considerations.

The present study interprets the overuse of proportional solution methods from a dual process framework. Dual process theories claim that analytic operations involve time-consuming executive processing, whereas heuristic operations are fast and automatic. In two experiments to test whether proportional reasoning is heuristic-based, the participants solved "proportional" problems, for which proportional solution methods provide correct answers, and "nonproportional" problems known to elicit incorrect answers based on the assumption of proportionality. In Experiment 1, the available solution time was restricted. In Experiment 2, the executive resources were burdened with a secondary task. Both manipulations induced an increase in proportional answers and a decrease in correct answers to nonproportional problems. These results support the hypothesis that the choice for proportional methods is heuristic-based.

[1]  K. Stanovich,et al.  Individual differences in reasoning: Implications for the rationality debate? , 2000, Behavioral and Brain Sciences.

[2]  E. Fischbein,et al.  Intuitions and Schemata in Mathematical Reasoning , 1999 .

[3]  Lieven Verschaffel,et al.  The Linear Imperative: An Inventory and Conceptual Analysis of Students' Overuse of Linearity , 2008 .

[4]  M. Osman An evaluation of dual-process theories of reasoning , 2004, Psychonomic bulletin & review.

[5]  Jonathan Evans,et al.  Logic and human reasoning: an assessment of the deduction paradigm. , 2002, Psychological bulletin.

[6]  J. de Houwer,et al.  Automaticity: a theoretical and conceptual analysis. , 2006, Psychological bulletin.

[7]  Wim De Neys,et al.  Conflict monitoring in dual process theories of thinking , 2008, Cognition.

[8]  C. E. Bethell-Fox,et al.  Mental rotation: effects of stimulus complexity and familiarity , 1988 .

[9]  S. Epstein Integration of the cognitive and the psychodynamic unconscious. , 1994, The American psychologist.

[10]  Jonathan Evans On the resolution of conflict in dual process theories of reasoning , 2007 .

[11]  S. Sloman The empirical case for two systems of reasoning. , 1996 .

[12]  L. Verschaffel,et al.  Not Everything Is Proportional: Effects of Age and Problem Type on Propensities for Overgeneralization , 2005 .

[13]  Thomas R. Post,et al.  Learning and teaching ratio and proportion: Research implications: Middle grades mathematics , 1993 .

[14]  David A. Rettinger,et al.  How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. , 2001, Journal of experimental psychology. General.

[15]  Thomas R. Post,et al.  Learning and teaching ratio and proportion: Research implications , 1993 .

[16]  E. Fischbein,et al.  The Evolution with Age of Probabilistic, Intuitively Based Misconceptions. , 1997 .

[17]  V. Goel Sketches of thought , 1995 .

[18]  Walter Schaeken,et al.  Everyday Conditional Reasoning with Working Memory Preload , 2004 .

[19]  Jonathan Evans,et al.  Rationality and reasoning , 1996 .

[20]  D. Kahneman A perspective on judgment and choice: mapping bounded rationality. , 2003, The American psychologist.

[21]  Wim De Neys,et al.  Dual Processing in Reasoning , 2006, Psychological science.

[22]  Merlyn J. Behr,et al.  Number concepts and operations in the middle grades , 1988 .

[23]  Uri Leron,et al.  The Rationality Debate: Application of Cognitive Psychology to Mathematics Education , 2006 .

[24]  Wim De Neys,et al.  Automatic-heuristic and executive-analytic processing during reasoning: Chronometric and dual-task considerations. , 2006 .

[25]  D. Kahneman A psychological point of view: Violations of rational rules as a diagnostic of mental processes , 2000, Behavioral and Brain Sciences.

[26]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[27]  Lieven Verschaffel,et al.  Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors , 2002 .

[28]  Jonathan Evans The heuristic-analytic theory of reasoning: Extension and evaluation , 2006, Psychonomic bulletin & review.

[29]  Ruth Stavy,et al.  Development of intuitive rules: Evaluating the application of the dual-system framework to understanding children’s intuitive reasoning , 2006, Psychonomic bulletin & review.

[30]  Lieven Verschaffel,et al.  The Illusion of Linearity: Expanding the evidence towards probabilistic reasoning , 2003 .