ematics problem solving.
Mathematics education in the 19th and 20th centuries remained fairly consistent throughout many decades, focusing on rote learning of mathematical tables and the solving of numerical math problems. However, early in the 20th century, William Heard Kilpatrick effected the beginning of changeùprogressive math education concepts that focused on teaching only things that had ôdirect practical value,ö and only to a limited few (Klein). Schools followed after progressivism in the 1930Æs, with the result that in the 1940Æs, ôit became something of a public scandal that army recruits knew so little math that the army itself had to provide training in the arithmetic needed for basic bookkeeping and gunneryö (Klein).
The deleterious effect of progressive education on mathematics education was evidenced by a steady decline in enrollment in advanced high school mathematics courses, and progressive education ôwas forced into retreatö in the 1950Æs (Klein). Statistics showed that whereas 56.9% of high school students took algebra in the 1909-1910 school year, only 24.8% took it in the 1954-1955 school year (Klein). In the late fifties, the New Math movement arose, bringingùamong other thingsùcalculus at the high school level. In the sixties, however, ôa substantial number of mathematicians had already expressed serious reservationsö about New Math, and by the early seventies, the New Math was dead, and education in math and other subjects was going back to the basics (Klein). The Open Education Movement modeled after Summerhill resulted in ôfree schoolsö where students were not taught anything but were invited to learn as they chose; this movement damaged education for everyone, but particularly for disadvantaged students, since they had no educational resources outside of school (Klein).
In the eighties, a wake-up call warning of deteriorating math and science education resulted in the Na...