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The Quantile® Framework for Mathematics Quantifies the Mathematics Ability Needed for College and Career Readiness

Abstract

The objective of this research is to answer the question, “What mathematics must a student be capable of performing to be ready for college or a career?” To address the question we analyzed mathematical concepts and skills that students may encounter as they begin their postsecondary education and/or enter the workplace. The answer is predicated on two perspectives: (a) mathematical readiness for college implies being ready for instruction in advanced mathematics courses associated with the beginning of the postsecondary educational experience; and, (b) readiness for the mathematical demands of careers implies, at a minimum, sufficient mathematical ability to perform well on the mathematics content required for a high school diploma. To answer the key question, we analyzed the difficulty of mathematical skills and concepts incorporated into the mathematics lessons found in mathematics texts commonly used in the United States. The Quantile® Framework for Mathematics provides the measurement foundation to place on a common scale both student mathematics ability and the difficulty of mathematical skills and concepts. Thus, we infer requisite student ability from the observed difficulty of mathematical skills and concepts contained in mathematics lessons presented in mathematics textbooks. We regard mathematics ability as an individual, malleable attribute, which improves with instruction and practice.

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