The paper-pencil standard algorithms are the best tools for beginners to do basic arithmetic. So, why are they not the primary focus in elementary school arithmetic? It seems that standard algorithms, which require the memorization and auto recall of single-digit number facts, have been displaced by "standards of mathematical practice" and "alternative algorithms" (i.e., reform math). In short, students are taught reform math, not standard arithmetic.
We need to apply statistical methods with care, especially when negotiating big data, says Stephen M. Stigler. In education, we depend too much on averages. "Averaging is a radical idea: you can actually gain information by throwing information away." writes Stigler. In averaging, the identities of the test takers are tossed, which means that no test score holds more weight.
But, a school's average (arithmetic mean) in math is influenced by individuals. Indeed, math ability and performance of students vary widely. In averaging, however, all the test scores are treated the same. Mary's score of 100 is treated the same as Billy's score of 50. Consequently, several very high scores can cover up the lower scores of many of the other students and skew or distort the data's average up to an "acceptable level." In short, poor math achievement is covered up by averaging.
Some reasons for high graduation rates in many high schools include online credit recovery, grade inflation, and watered-down courses. But these reasons hurt students. Richard N. Haass summarizes the problem: "Students are leaving school without the math and science skills needed for jobs in modern industry." Furthermore, they lack the math and reading skills for college. Up to 88% of students enrolling at a community college are placed in remedial math (algebra). Clearly, the K-12 reform math curriculum does not prepare students for college-level math courses.
An Algebra-2 course in one school may be different in content compared with an Algebra-2 course at another school, even if the same textbook was used. The teachers are different, the grading is different, and the expectations are different, etc. Making an accurate comparison is difficult. An A in one school could be a C in another school.
We should never leave judgment to a computer software program.