Verification of Algebra Step Problems: A Chronometric Study of Human Problem Solving. Technical Report No. 253. Psychology and Education Series.

Abstract A class of simple problem solving tasks requiring fast accurate solutions is introduced. In an experiment subjects memorized a mapping rule represented by lists of words labeled by cue words and made true/false decisions about conjunctions of propositions of the form “ Y is in the list labeled by X ”, written “ X → Y ”. Response times are analyzed using a “stage modeling” technique where problem solving algorithms are composed using a small set of psychological operations that have real time characteristics specified parametrically. The theoretical analysis shows that response time performance is adequately described in terms of the sequential application of elementary psychological operations. Unexpectedly, it was found that the proposition “ X → Y and X → Z ” was verified as quickly as the apparently simpler “ X → Y ”. A case is presented for the modeling technique as applied to memory and problem solving tasks in terms of theoretical parsimony, statistical simplicity, and flexibility in investigative empirical research. Suggestions are made as to possible theoretical relations among fast problem solving, more complex and slower problem solving, and research in fundamental memory processes.

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