My math instruction follows a Concrete-Representational-Abstract (CRA) sequence to facilitate a thorough understanding of the concept/skills that are being taught. The concrete stage of instruction involves the use of concrete materials or manipulatives such as base ten blocks, pattern blocks, fraction bars or pieces, counters, clocks, play money etc. Once students have a concrete understanding we move to the representational stage of learning. The representational stage sometimes called the semi-concrete stage facilitates student imagery of the concept or skill through drawings using dots, tallies, arrays, positional constructions etc. These pictorial representations supported by previous learning during the concrete stage are translated into conventional (or not so conventional) mathematics notation to arrive at the correct answer.
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." William Paul Thurston
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." William Paul Thurston