Relational Notation & Mapping Structures: A Data Analysis Framework

Three main type of Representational Unit Coordination (RUC) arose from various usages by middle and high school preservice teachers (PST) when making growing rectangles for special numbers such as prime and composite numbers, summation expressions for odd, even, and counting numbers as well as polynomials in x and y using magnetic color cubes and tiles. In a Multiplicative type RUC, I used a relational notation of the form (a,b) where a and b stand for the corresponding linear units of the growing rectangle represented by the dimension tiles. I also observed more than one additive type RUC’s which can be described using a functional notation ∑f(i)=g(n) where the areal quantities f(i)'s are being summed from 1 to n (number of addends) and i is the stage number (ordering number for the addends). There is one more type RUC, in between additive and multiplicative which I named Pseudo Multiplicative type RUC. This occurred for the “Area of the boxes of the same color as a product ” in dealing with polynomial rectangles made of color tiles. Moreover, a mapping structure of multiplication and addition operations was spelled out by these PST