Mathematics is crucial to the educational and vocational success of students. The concrete-representational-abstract (CRA) approach is a method to teach students mathematical concepts. The CRA involves instruction with manipulatives, representations, and numbers only in different lessons (i.e., concrete lessons include manipulatives but not pictures or numbers only). Researchers are exploring integrating the phases of CRA referred to as concrete-representational-abstract–integrated (CRA-I) because it may be a more efficient method of instruction. The CRA-I integrates all phases starting with the first lesson (e.g., Lesson 1 includes manipulatives, pictures, and numbers only) and then fades concrete and representational instruction. The purpose of this article is to provide information about a CRA-I Tier 2 mathematics intervention on additive reasoning for second-grade students in a rural school in the southeastern United States. The researchers describe CRA-I, the lessons implemented, and implications for teacher use.

中文翻译：

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具体 - 代表性 - 抽象 - 集成为第 2 层指令来教授加法

数学对于学生的教育和职业成功至关重要。具体-表征-抽象（CRA）方法是一种教授学生数学概念的方法。CRA 仅在不同课程中涉及操作、表示和数字的教学（即，具体课程包括操作，但不包括图片或数字）。研究人员正在探索整合 CRA 的各个阶段，称为具体-代表性-抽象-综合 (CRA-I)，因为它可能是一种更有效的教学方法。CRA-I 整合了从第一课开始的所有阶段（例如，第 1 课仅包括操作、图片和数字），然后淡化具体和代表性的教学。本文的目的是为美国东南部一所乡村学校的二年级学生提供有关加法推理的 CRA-I Tier 2 数学干预的信息。研究人员描述了 CRA-I、实施的课程以及对教师使用的影响。