Singapore Math Overview
Concrete: Students learn to work with real objects at first, performing tangible operations such as counting blocks, putting groups of blocks together, and taking away blocks. Using natural, everyday language such as "take away 2 apples" instead of "subtract 2" helps firmly ground the meaning of the math before moving on to more formal manipulations.
Pictorial: Pictorial representations such as number lines and bundles of objects representing 10s
Abstract: As students become increasingly comfortable, they can learn and use the formal language of math. Efficiency/power of symbolic math, context-independent abstraction that can be applied to all general situations
Intuitive to specific:
regrouping vs. renaming or borrowing and carrying