Reasoning and sense making in statistics and probability

Reasoning and sense making are inextricably linked in the realm of both statistics and probability, just as they are in other parts of the mathematics curriculum. In this chapter, we start with sense making because no statistics problem can be meaningful without context (Rao 1975); a statistical question must make sense in context before a student can begin to investigate it. All through a statistical investigation, when tools are being applied, patterns explored, uncertainty considered, and conclusions drawn, the question of making sense of the underlying context must be kept in mind. It is also necessary to make sense of the connections among these stages of an investigation. Next we turn to reasoning, a function of the intellect defined as the "process of drawing conclusions on the basis of evidence or stated assumptions" (NCTM 2009, p. 4), which is an apt ·description of a statistical investigation itself. Throughout this chapter sense making and reasoning provide the structure for the procedures and tools used, the modeling carried out, the assumptions made, and the clear communication of results. In this investigative process the importance of connections cannot be overemphasized. There are links within the investigation itself and links to other parts of mathematics, such as, for example, percentage, fraction, measurement, and basic graphing, as well as links across the curriculum in the contexts where statistical questions are found.