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Whodunit? Exploring Proportional Reasoning Through the Footprint Problem
Author(s) -
KoellnerClark Karen,
Lesh Richard
Publication year - 2003
Publication title -
school science and mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.135
H-Index - 2
eISSN - 1949-8594
pISSN - 0036-6803
DOI - 10.1111/j.1949-8594.2003.tb18224.x
Subject(s) - proportional reasoning , context (archaeology) , multiplicative function , mathematics education , set (abstract data type) , abstract reasoning , footprint , syllogism , adaptive reasoning , block (permutation group theory) , mathematics , computer science , epistemology , psychology , artificial intelligence , cognition , combinatorics , model based reasoning , philosophy , programming language , mathematical analysis , paleontology , neuroscience , biology , knowledge representation and reasoning
This paper describes a proportional reasoning problem set within a real‐life context and a complete analysis of one small group discussion of this problem over the course of a 90‐minute block. The seventh‐grade students' discourse is described to provide insights into typical mathematical interpretations of this problem, as well as some generalizations for other problems of this type. The interpretations provided reveal the gradual development of proportional reasoning in a local context from additive to multiplicative understandings.