As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on students’ automaticity. Research reported observational data regarding strategy-use, but not growth in number sense and understanding of operations. This study investigated the effects of an intervention using the concrete-representational-abstract-integrated (CRA-I) sequence. The purpose of this study was to assess the effects of CRA-I on students’ number knowledge (magnitude, place value, and flexibility in strategy-use) and understanding of addition (commutative property and relation to subtraction). The researchers used a multiple probe across participants design. In addition, the researchers collected descriptive data on students’ automaticity. There was a functional relation between CRA-I and students’ number sense and understanding of addition, and students’ automaticity increased.

随着学生对加法等个位数运算的理解和流利，他们会发展复杂的策略和数感（大小、数字顺序和组成）。数感上的缺陷和对低效方法的依赖会导致数学上的挣扎。该领域的干预研究报告了对学生自动性的影响。研究报告了有关战略使用的观察数据，但没有报告数量感和对操作的理解的增长。本研究调查了使用具体-表征-抽象-整合 (CRA-I) 序列的干预效果。本研究的目的是评估 CRA-I 对学生数字知识（大小、位值和策略使用的灵活性）和加法理解（交换属性和与减法的关系）的影响。研究人员在参与者设计中使用了多重探针。此外，研究人员还收集了有关学生自动性的描述性数据。CRA-I与学生的数感和加法理解之间存在函数关系，学生的自动性增加。