Illumination Through Representation: An Exploration Across the Grades

To support the newest process standard of NCTM (National Council of Teachers of Mathematics), the potential of multiple representations for teaching repertoire is explored through a real-world phenomenon for which full understanding is elusive using only the most common representation (a table of numbers). The phenomenon of "reversal of a comparison when data are grouped" can be explored in many ways, each with their own insights, including: table, platform scale, trapezoidal representation, unit square model, probability (balls in urns), and verbal form. Lesser also commented on this topic in a letter published in The American Statistician (November 2004, p.362).