The types of reasoning identified in this standard are fundamental to doing mathematics but cannot always be observed in students' verbal answers or written work. It is natural for students to form conjectures on the basis of the examples they have seen or worked and to develop arguments that are based on what they know to be true.
Students can also have intuitive notions about proportional reasoning and spatial relationships.
All students should have explicit opportunities to engage in such intuitive, informal reasoning and, hence, any assessment of students' reasoning abilities should obtain evidence of these processes. Accordingly, assessment techniques should specifically assess students' use of different types of reasoning. Although some aspects of reasoning might be more appropriate than others at a given grade level, all aspects can be used at any grade level. However, in the early grades, some aspects may be used only in an intuitive sense. The following examples illustrate tasks or activities for assessing students' abilities to reason.