How good should a student be at paper and pencil arithmetic and at mental arithmetic in order to move from elementary school into middle school or junior high school? What part of that competence should we expect of the students at the time he or she is graduating from high school?
In math, as well as in other academic areas of study, critics of our educational system like to cite examples of students who don't perform as well as might be expected. Adults draw on various parts of their formal and informal education and schooling. In doing so, they make mistakes from time to time. Some are much better at sensing or finding their errors, and then correcting them. In other cases, errors have few or no consequences. For example, an adult who says, "Lincoln freed the slaves and that started the Civil War," has made an incorrect statement. It may irritate some of the people hearing the incorrect statement, or it may not draw their attention.