W. Stephen Wilson teaches mathematics at Mayor Bloomberg ‘s alma mater, Johns Hopkins University. Last fall he conducted an experiment on the students in his Calculus I course.

Professor Wilson administered the same final exam to last fall’s students that he used for the same course in the fall of 1989. He chose that year because he was able to obtain data for both his exam and the SAT math scores for both cohorts of students.

The surprise: the 1989 students did much better than their 2006 counterparts.

Everyday much ink is spilled discussing the failure of America’s schools. Most of this discussion centers on the children who never learn basic skills, those who never graduate high school. But the crisis goes much deeper.

By the conventional analysis, the students at Johns Hopkins represent success. All graduated high school and did so well that they were able to win admission to a prestigious institution of higher learning. Since 1989, with the help of Mr. Bloomberg’s generosity, Johns Hopkins became a more selective college. In 1989, 49% of applicants were offered admission, today only 27%. The number of applicants has also increased — by 148%. These figures would suggest that Professor Wilson’s calculus students would be doing better, not worse. So what has changed?

Some years back, the reporting of the results of the common standardized tests was altered, not to show the average achievement of students in a school or a district, but to determine the percentage achieving or exceeding something called “grade level,” a measure of minimal competence. By this gauge, the child who is barely getting by, meeting this minimal standard counts equally with the super-star prodigy pondering quantum physics.

Is it any wonder that instruction has been dumbed down in American schools, when educrats are rewarded and honored not for bringing more children to the top, but for nudging more over some contrived midpoint of mediocrity?

Professor Wilson points out that 1989 also marked a milestone in the teaching of mathematics. The National Council of Teachers of Mathematics abandoned traditional math instruction in favor of a new approach — constructivist mathematics. This method downplays pencil and paper computations in favor of calculator use, an idea facilitated by the College Board by permitting test takers to use calculators on the scholastic aptitude test. This concept was quickly adopted by the progressive educational establishment that largely controls both public and private K-12 instruction in American schools. New York City has mandated such a constructivist program, “Everyday Math,” since 2003.

Professor Wilson suggests that perhaps the drop in math ability of his recent students results from these “new” methods. So pervasive is this conclusion that recently the National Council of Teachers of Mathematics itself backed away from its own earlier recommendations and is once again promoting traditional instruction.

Math is not the only area impacted by this “march to the middle.” Content area instruction has carefully been removed from American classrooms, a phenomenon that a University of Virginia professor named E.D. Hirsch Jr. noticed decades ago. Mr. Hirsch has come up with a real-world solution — a content-rich back-to-basics curriculum called Core Knowledge that is winning favor with schools and parents across the country. Two states are considering adopting Mr. Hirsch’s program as their official curriculum, a number sure to increase as the alarm over the current state of American schools grows.

There is evidence of a payoff to those educators who follow Mr. Hirsch’s prescription. Rather than increase test scores through mindless test prep, an exercise that becomes less effective as children grow older, evidenced by the precipitous national drop in scores between grades four and eight, adherence to a Core Knowledge curriculum promises sustainable improvement.

Chancellor Klein is now in the midst of a structural reorganization of New York’s schools. This began with the plan to restructure school bus routes, an idea that has resulted in much criticism directed at the mayor and the chancellor. To oversee this, a private consultant, Alvarez & Marsal, was chosen without competitive bidding, and failed at the same task in St. Louis, a school district about one-thirtieth the size of ours.

Rather than focus on the real issue of what goes on in our classrooms, what our students are being taught, and how they are taught it, once again school leaders are busy rearranging the deck chairs on the Titanic. No “school reform” based on organizational schemes has been shown to work, not here or elsewhere.

In this new restructuring, one that promises to “empower” principals, we are somehow forgetting that the purpose of our schools is not to empower adults, but children. The only way to intellectual empowerment is through the transfer of knowledge from one generation to the next, a truth that, though inconvenient to some in the educational establishment, is true.