Liping Ma Multi-Strategy Math Explorer

Minuend:

Subtrahend:

Preset:

Strategy:

Drag Tens blocks to decompose into 10 Ones

Step 1 / 4

1. Initial Setup

Represent minuend 52 with 5 Tens blocks and 2 Ones blocks. Subtrahend 27 requires taking away 2 Tens and 7 Ones.

PUFM Strategy Analytics

Active Strategy: Standard Regrouping

Conceptual Connectedness: 92 / 100

Cognitive Efficiency: Medium (3 Steps)

Decomposition State: 5 Tens, 2 Ones

Computed Result: 52 − 27 = 25

Liping Ma Research Insight

Liping Ma's landmark study highlights that teachers with a Profound Understanding of Fundamental Mathematics (PUFM) perceive standard algorithms as one path among several. Multiple flexible strategies (such as compensation or place-value decomposition) build deeper spatial place-value flexibility rather than memorized procedures.

Strategy Profiles

Standard Regrouping: Decomposes 1 Ten into 10 Ones when minuend ones are smaller than subtrahend ones.

Compensation: Adds +3 to subtrahend (27➔30) and minuend (52➔55) to eliminate regrouping.

Place-Value Splitting: Subtracts Tens first (52 - 20 = 32), then subtracts Ones (32 - 7 = 25).