Logic-Based Taxonomy of Mathematical Reasoning

摘要

The paper delineates the construction of a taxonomy for mathematical reasoning based on logic. Such a taxonomy provides heretofore unattained control of both schematic and computational complexity levels by expressing each equation as a conditional statement (modus ponens), which makes possible the identification of the composition of each antecedent and consequent in the conditional. Item analysis data are presented from federal test administrations which corroborate the effectiveness of these logic-based schematic and computational controls.