Reasoning About Proportional Lumpability

Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions

Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions Wenke Möhring, Nora S. Newcombe, Susan C. Levine & Andrea Frick To cite this article: Wenke Möhring, Nora S. Newcombe, Susan C. Levine & Andrea Frick (2016) Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions, Journal of Cognition and Development, 17:1, 67-84, DOI: 10.1080/15248372....

Visual manipulatives for proportional reasoning

The use of a visual representation in learning about proportional relations studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability sixth-grade mathematics students using the Jasper A...

Contextual lumpability

Quantitative analysis of computer systems is often based on Markovian models. Among the formalisms that are used in practice, Markovian process algebras have found many applications, also thanks to their compositional nature that allows one to specify systems as interacting individual automata that carry out actions. Nevertheless, as with all state-based modelling techniques, Markovian process ...

The Proportional Reasoning Abilities of Preschool Children

Proportional Reasoning in a Boolean Setting

Extrapolations are often based on parallels made between two situations that are thus compared. Comparative information may pertain to similarities as well as to dissimilarities. Analogical proportions, i.e., statements of the form “A is to B as C is to D”, provide a natural way for stating such a parallel. In the Boolean setting, logical proportions, a recently introduced notion that generaliz...