Deductive reasoning Roger doesn't believe that adding the same number of points to each student's test score will increase the average score by that same amount. Write a valid argument to convince Roger that this is true. It is particularly important that advanced students understand that there is an element of arbitrariness in how the rules are selected but that the encompassing system is consistent. The following problems can be given to geometry students, since one of the desired outcomes of teaching geometry is that students develop a sense of what constitutes an axiomatic system. The axiomatic nature of mathematics should be highlighted.
Students can work in small groups to develop an essay, which can then be presented in class.
The student's response should emphasize that the selection of the postulate is arbitrary but that once selected, the second statement can be proved on the basis of the accepted postulate.