“…Recent studies in mathematics, science, and statistical reasoning have identified the existence of two U-M-R cycles operating within the concrete-symbolic mode (Callingham, 1994;Campbell, Watson, & Collis, 1992;Levins & Pegg, 1993;Pegg, 1992;Pegg & Davey, 1998;Watson, Collis, & Campbell, 1995;. More specifically, these researchers have identified two cycles when students engage in reasoning about fractions, volume measurement, and higher order statistical thinking.…”