Suppose you were an alien trying to understand how people in the United States feel about the Common Core School Standards for Mathematics (CCSSM). You could look at the Internet, mass media, YouTube and all of the other venues available. Walking away from them, you would be very confused about whether the U.S. loves or hates the CCSSM, whether…

Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the…

At grade 7, Common Core's content standards call for the use of long division to find the decimal representation of a rational number. With an eye to reconciling this requirement with Common Core's call for "a balanced combination of procedure and understanding," a more transparent form of long division is developed. This leads to the…

This article, by the author of "Why Johnny Can't Add," finds the New Math to be a failure as an instructional method since it is based on a reliance on artificial, complicated axioms that were invented to satisfy the needs of professional mathematicians, not students. (JA)

It was hypothesized that a supplemental unit in mathematical proof would increase students' chances of success in linear algebra. (Authors/JA)

The author shows that the set of all sequences in which each term is the sum of the two previous terms forms a vector space of dimension two. He uses this result to obtain the formula for the Fibonacci sequence and applies the same technique to other linear recursive relations. (MM)

The author suggests that a close analysis of existing calculus courses indicates that some of the material can be explained much more clearly by using some of the language of set theory. He gives examples showing that many of the pedagogical problems arising in calculus can be overcome by using a graphical approach. (FL)

Problems in modern math instruction for learning disabled students include language and vocabulary, a lack of appropriate emphasis on mastery, the use of set notation in the primary grades, inadequate teacher inservice education in modern math, and the elimination of parents as teaching partners. (CL)

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)