The Common Core math standards have been contentious since they were launched several years ago, with many parents taking to social media to complain about their kids getting incomprehensible homework. Kids are now expected, for example, to explain how multiplication works using the “box” and “lattice” methods. These methods take longer, and are harder to master at first, but have been shown by some research to be more effective than the multiply-and-carry method, particularly for kids who have trouble memorizing things. And while they may be new for this generation of parents, they have been around since at least the 13th century.
The research and philosophy behind the new math standards aren’t new either: They mirror the ideas espoused by the Mathematical Association of America’s National Committee on Mathematical Requirements, which formed in 1916 and put together a plan to reform math education in the United States. Until then, math education consisted of few attempts at helping students reach a deeper understanding. One impetus for reform was that, while the country had become a leader in technological and industrial innovation in the early 20th century, and while more students were taking algebra and geometry than before, many of its schools had yet to be as sophisticated or academically rigorous as those in Europe.
The suggestions contained in the committee’s 600-page-plus report, “The Reorganization of Mathematics in Secondary Education,” should be familiar to anyone who has pored over the Common Core standards. They encouraged the teaching of algebra concepts as early as the sixth grade. They promoted understanding over rote memorization using practical math applications. They stressed the importance of a solid math education—including in areas like geometry and even trigonometry—for all students, whether they go into engineering or philosophy, college or the workforce.
One of the primary purposes of math education, the authors stated, was “to develop those habits of thought and of action which will make these powers effective in the life of the individual.” But no matter how exhaustive, the report did not bring about the changes for which the committee had hoped.
That initiative gave way to the increasingly popular progressive education-reform movement, which preached that a deeper understanding of math wasn’t practical for most Americans—that the way it was taught didn’t take into account their interests and thus squashed their will to learn. Less math is more, the thinking went. Because this movement won, instead of raising the numeracy of the general public and ensuring it was better equipped to navigate the increasingly sophisticated technology and global economy, American schools allowed an entire generation of students to fall behind mathematically. Because it usually only takes one generation to erase the gains of the previous one, Baby Boomers, Xers, and older Millennials are still nowhere near as numerate as they should be.
And while many helped make this happen, a lot of the blame lies with one well-meaning, extremely influential educator: William Heard Kilpatrick, Columbia University Teachers College’s “million-dollar professor.”
Kilpatrick (who earned his moniker not for his salary but because his packed lectures swelled Columbia’s coffers), had a lot of cult-leader-esque charisma. “At times there did seem to be a mysterious and unexplainable ambience surrounding Kilpatrick as he taught,” writes Kilpatrick’s biographer, the professor and historian John Beineke, in And there were giants in this land: The Life of William Heard Kilpatrick. “He would teach classes at Teachers College with 500 or 600 students in an auditorium, and individuals would speak of feeling as though they were the only ones in the room.” This may explain why, when Kilpatrick told his adoring crowds that “we have in the past taught algebra and geometry to too many, not too few,” they took him seriously. Kilpatrick believed that anything beyond arithmetic was useless to most of the population. He even worried that the instruction of complex math was harmful to everyday living.
He didn’t always feel that way, having studied math at Mercer and Johns Hopkins universities and spending the earlier part of his life as a primary- and secondary-school math teacher and math professor. What made him turn against the subject? Blame a heady mix of social science, including Darwinism and psychology, and a clear distaste for authority of any kind.
Kilpatrick was born in 1871 in White Plains, Georgia, to a Baptist preacher with enough charisma of his own to become one of the state’s most prominent religious leaders. Kilpatrick rejected his father’s faith as a teen, chose a career in math and science, and soon became a professor at his undergraduate alma mater. But academia would offer no respite from religion: In 1906, he was accused of heresy for refusing to affirm his belief in the Virgin Birth, and resigned from Mercer in disgrace.
A year after that, he enrolled as a grad student at Teachers College. The best way to describe how much influence the school had on American education at the time would be to compare education with a major religion, and Teachers College with that religion’s holy city. As Beineke put it, Teachers College, which was established, “had become, even before its 25th anniversary, a Mecca for the study of education.” It was the first academic institution to effectively turn teaching into a profession, and soon after its founding in 1887 attracted the most influential pedagogues of the day. Its faculty included John Dewey, the pioneer of the progressive-education movement, whose mantra espoused “child-led learning,” in which the student, not the teacher, decides what should be learned. In progressive schools, teachers were no longer implacable authority figures, but gentle guides and partners in education.
Kilpatrick soon became Dewey’s closest protege, and as he got deeper and deeper into the progressive philosophy, he set his sights on reforming math education, making it less about building the intellect and more about whether it was needed for everyday living. The best way to do this, he decided, was to also tap into the burgeoning social-efficiency movement endorsed by several colleagues at Teachers College, including Dewey and the psychologist Edward Thorndike. Social-efficiency proponents believed that universal education was a flawed approach in schools because different populations had different needs and intelligence levels.
By 1915, Kilpatrick wielded such influence in education circles that he was asked to head a National Education Association committee tasked by the U.S. Bureau of Education with devising ways to reform math instruction. Its 1920 report, “The Problem of Mathematics in Secondary Education,” became part of a larger treatise on public education that provided a roadmap for America’s schools for decades to come.
Like the MAA’s report, “Problem of Mathematics” encouraged basic algebraic concepts in junior high school and the importance of practical math. But that’s about all the two have in common. The former, which was far more lightweight, stated algebra, geometry, and any higher math was a waste of time for most students. Advanced math, it posited, wasn’t critical for understanding greater life lessons. Such an idea is conservative, it argued:
To the extremist of this school the “faculty of reasoning,” for example, could be trained on any material where reasoning was involved (the more evident the reasoning, the better the training), and any facility of reasoning gained in that particular activity, could, it was thought, be accordingly directed at will with little loss of effectiveness to any other situation where good reasoning was desired. In probably no study did this older doctrine of “mental discipline” find larger scope than in mathematics, in arithmetic to an appreciable extent, more in algebra, most of all in geometry.
The authors’ rejection of math as critical for overall problem-solving ability was based largely on research by Thorndike, the education psychologist, who earlier in the century had conducted a lot of experiments on cats to gauge how animals learn. He would lock cats in rigged boxes, then see if they could figure out how to step on the right lever to get out, and, if they could, if they could do it again and how quickly. Subsequent studies on soldiers during World War I showed that humans, like cats, don’t necessarily improve their ability to solve a problem just because they’ve previously solved lots of problems. The studies suggested that problems are only easier for the soldiers the subsequent time if they’re very similar to problems the soldiers previously solved.
Relying on Thorndike’s findings, the report’s authors warned high schools against offering advanced math to students who didn’t demonstrate great interest or obvious talent in the subject or who didn’t intend to go into engineering or hard science (these students being invariably female). They concluded that there should even be restrictions for the engineers, too; the country’s future bridge or machine designers didn’t need to waste time on math that was too theoretical. The remaining students were essentially limited to arithmetic (although some more-advanced math was suggested for trades such as machinery and plumbing).
While the “Problem of Mathematics” report itself was likely not as influential as the men behind it, what happened in the next two decades is noteworthy. According to the 1970 text Mathematics in the Evolving Schools: A History of Mathematics Education in the United States, the number of students taking algebra and geometry dropped despite growth in high-school enrollment overall. In 1922, 40 percent of American students were taking algebra, and 23 percent were taking geometry. By 1934, the rates had dropped to 30 percent and 17 percent, respectively. When the United States entered WWII, the military reportedly had to offer enlisted men and officers in all military branches remedial math classes so they could fulfill their duties; many were struggling with tasks as basic as bookkeeping.
Kilpatrick died at the age of 93 in 1965, four years before Neil Armstrong and Buzz Aldrin landed on the moon—a feat that relied in part on a good understanding of algebra and geometry. Although his movement’s ideas about math had largely fallen out of favor by then, those belonging to the other camp—the one that espoused deeper understanding—didn’t quite catch on either. Many, if not most, of the country’s schools reverted back to teaching math the way it was taught at the beginning of the century. It wasn’t until a half century later that the opponents’ ideas began to gain traction nationwide, and whether or not they stick is far from clear. In the end, it may all come down to how many parents complain about it on Twitter.
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