Rules and Representations

https://www.uni-trier.de/fileadmin/fb1/prof/PSY/PAE/Forschung/SieglerEtAl2011.pdf

An integrated theory of whole number and fractions development.

The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual-process model of judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals.

/pdf/base-rate-respect-from-ecological-rationality-to-dual-4et7guxsmp.pdf

Base-rate respect: From ecological rationality to dual processes.

https://opencuny.org/citycollegespring2015/files/2015/02/the-development-of-students-understanding-of-the-numerical-value-of-fractions.pdf

The development of students’ understanding of the numerical value of fractions

https://files.eric.ed.gov/fulltext/ED552807.pdf

Fractions: the new frontier for theories of numerical development

Many researchers agree that children's difficulty with fraction and rational numbers is associated with their whole number knowledge, but they disagree on the origin of the whole number bias. This article reviews three explanations of the nature of the bias. These accounts diverge on the questions of whether or not early quantitative representation originates from a numerical-specific cognitive mechanism, and whether or not the early quantitative representation privileges discrete quantity. The review suggests that there does not yet appear to be sufficient evidence to decide among the competing accounts as to the nature of the whole number bias. Yet, in the search for the understanding, two important issues have been brought up with regard to learning and teaching fraction and rational numbers. One question is related to how learning about fraction and rational numbers may be organized in such a way to be less strained for taking advantage of the prior knowledge of whole numbers. The second issue is conc...

Yujing Ni

Papers

Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias