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Mazzocco and her colleagues previously found that the ability to estimate approximate quantities without counting generally improves during childhood and is related to math achievement

Mazzocco’s group studied 71 ninth-graders whose math abilities had been tested annually since kindergarten. Students completed two quantity estimation tasks. In one series of trials, participants saw an array of blue and yellow dots flash for a fraction of a second on a computer screen and indicated whether more blue or yellow dots had appeared. In other trials, students saw nine to 15 yellow dots flash on a screen and estimated how many dots were shown.

Mazzocco’s group studied 71 ninth-graders whose math abilities had been tested annually since kindergarten. Students completed two quantity estimation tasks. In one series of trials, participants saw an array of blue and yellow dots flash for a fraction of a second on a computer screen and indicated whether more blue or yellow dots had appeared. In other trials, students saw nine to 15 yellow dots flash on a screen and estimated how many dots were shown.

Thirty-six percent of high school seniors in 11 states scored Below Basic in math on the 2009 National Assessment of Educational Progress, the nation's exam of student achievement

One out of every four eighth-graders in the entire country is mathematically illiterate.

the percentage of U.S. doctorates in engineering awarded to foreign students has increased from 47 percent to 57 percent between 1989 and 2009