Math instruction took another big hit recently. “Big” because the New York Times, one of the top U.S. newspapers ran it as a cover story of its magazine section. So here again, amid the Common Core standards in math that ask teachers to go beyond the “right” answer and periodic efforts over the past century (yes, I mean “century”) to move math teaching away from learning the rules of arithmetic, algebraic equations, and geometry proofs, comes another blast at how teachers teach math.

Elizabeth Green’s well-written article (drawn from a forthcoming book) on persistent patterns (mostly ineffective) in teachers implementing the New Math of the 1960s, the New NEW math of the 1980s, and now the math Common Core standards shines yet another light on the puzzle of why teachers teach as they do. And why policy after policy adopted to change math instruction has failed time and again in practice leaving each generation innumerate. Green has her own answers which to my experience as a teacher, historian, and researcher make a great deal of sense.

Moreover, as Green braids many threads together to explain persistence in poor math teaching, she also identifies others that begin to capture the complexity of  teaching. Her answers as to what to do are, however, largely unsatisfying because she excludes pieces necessary to complete the puzzle. Without the full puzzle picture on the jigsaw box, glomming onto a few pieces risks even yet another failure to remedy the puzzling persistence of poor math instruction.

Green does not blame teachers. She points to state and federal policies, teacher education institutions, and the taken-for-granted way that new teachers have learned about teaching from watching a few feet away how teachers have taught them for 16-plus years. All of this captures important threads in unraveling the puzzle of persistent failure in routine, teacher-centered math instruction focused less on understanding deeply and practically math concepts and more on knowing the rules to get the right answer. But not all of the threads.

Nowhere does Green mention the power of the age-graded school to influence how teachers teach.

The age-graded school (e.g., K-5, K-8, 6-8, 9-12), a 19th century innovation, has become an unquestioned mainstay of school organization in the 21st century. Today, most taxpayers and voters have gone to kindergarten at age 5, studied Egyptian mummies in the 6th grade, took algebra in the 8th or 9th grade and then left 12th grade with a diploma.

If any school reform–in the sense of making fundamental changes in organization, curriculum, and instruction–can be considered a success it is the age-graded school. Consider longevity–the first age-graded structure of eight classrooms appeared in Quincy (MA) in the late 1840s. Or consider  effectiveness. The age-graded school has processed efficiently millions of students over the past century and a half, sorted out achievers from non-achievers, and now graduates nearly three-quarters of those entering high school Or adaptability. The age-graded school exists in Europe, Asia, Africa, Latin America, and North America covering rural, urban, and suburban districts.

As an organization, the age-graded school allocates children and youth by their ages to school “grades”; it sends teachers into separate classrooms and prescribes a curriculum carved up into 36-week chunks for each grade. Teachers and students cover each chunk assuming that all children will move uniformly through the 36-weeks to be annually promoted.

The age-graded school is also an institution that has plans for those who work within its confines. The organization isolates and insulates teachers from one another, perpetuates teacher-centered pedagogy,  and prevents a large fraction of students from achieving academically. It is the sea in which teachers, students, principals, and parents swim yet few contemporary reformers have asked about the water in which they share daily. To switch metaphors, the age-graded school is a one-size-fits-all structure.

Why have most school reformers and educational entrepreneurs been reluctant to examine an organization that influences daily behavior of nearly 4 million adults and well over 50 million children? Dominant social beliefs of parents and educators about a “real” school, that is, one where children learn to read in 1stgrade, receive report cards, and get promoted have politically narrowed reform options in transforming schools. For example, when a charter school applicant proposes a new school the chances of receiving official approval and parental acceptance increase if it is a familiar age-graded one, not one where most teachers team teach and groups of multi-age children (ages 5-8, 9-11) learn together. Sure, occasional reformers create non-graded schools, the School of One, and particular community schools but they are outliers.

These familiar age-graded schools–don’t ask fish to consider the water they swim in–are missing in unraveling the puzzle of persistent ways of teaching math that Elizabeth Green has so nicely laid before us.