'To support the assertion that children do better when they are not taught traditional arithmetic, Anne Goodrow, in her PhD thesis at Tufts University, compared subtraction strategies of students taught traditional methods with those who used constructivist methods with "Investigations curriculum".Although negative numbers are not taught in the 2nd grade, "constructivist" student subtracting 9 from 28 explains that "8 minus 9 equals negative 1" and then argues that "-1 plus 20 is the same as 20-1 and equals 19."