We investigated elementary school children's use of direct subtraction (DS) and subtraction by addition (SBA) when mentally solving multi-digit subtractions. Fourth- to sixth-grade children of varying mathematical achievement levels were offered subtractions in one choice condition (choice between DS or SBA) and two no-choice conditions (mandatory use of either DS or SBA). Results showed that children solved slightly less than half of the subtractions in the choice condition with the untaught SBA strategy, and used this strategy more efficiently compared to DS, especially on subtractions with a small (e.g., 504 − 476 =?) difference between minuend and subtrahend. Children were adaptive for the numerical characteristics of the subtractions and their individual strategy speed, and sixth-graders were also adaptive for their individual strategy accuracy. Our results concerning the frequent, efficient, and adaptive use of SBA, even in younger and mathematically lower achieving children, challenge mathematics instruction practices that focus heavily on DS.

我们调查了小学生在心理解决多位数减法时使用直接减法 (DS) 和加法减法 (SBA) 的情况。不同数学成绩水平的四到六年级儿童在一种选择条件（DS 或 SBA 之间的选择）和两种无选择条件（强制使用 DS 或 SBA）中进行减法。结果表明，在未教过的 SBA 策略下，儿童在选择条件下解决了略少于一半的减法，并且与 DS 相比，使用该策略的效率更高，尤其是在被减数之间具有很小（例如，504 - 476 =？）差异的减法上和减法。孩子们适应了减法的数字特征和他们个人的策略速度，六年级学生也适应了他们个人策略的准确性。我们关于 SBA 的频繁、高效和适应性使用的结果，即使是在更年轻和数学成绩较低的儿童中，也挑战了严重关注 DS 的数学教学实践。