ABSTRACT

The development of conceptual multiplication knowledge will assist students in making progress within current mathematics standards. Previous research has shown the concrete-representational-abstract (CRA) sequence to be successful in teaching multiplication with regrouping with an emphasis on conceptual understanding while developing fluency and procedural knowledge. Previous research taught the standard algorithm; however, standards include using multiple strategies. Therefore, the purpose of this study was to use the CRA sequence to teach multiplication using another strategy, partial products algorithm. Three elementary students with disabilities participated in the study. During regularly scheduled instruction, their special education teacher taught multiplication of two 2-digit numbers using the CRA sequence. The researchers employed a multiple probe across students design and demonstrated a functional relation between CRA instruction and accuracy and fluency in multiplication. The researchers also showed that students maintained their performance up to one year after instruction.

摘要

概念乘法知识的发展将帮助学生在当前的数学标准内取得进步。先前的研究表明，具体表示抽象（CRA）序列在教授乘法与重组的过程中是成功的，它着重于概念理解，同时发展了流利性和程序知识。先前的研究讲授了标准算法；但是，标准包括使用多种策略。因此，本研究的目的是使用CRA序列通过另一种策略，即部分积算法来教授乘法。三名残疾小学生参加了研究。在定期安排的教学中，他们的特殊教育老师使用CRA序列教授了两个2位数的乘法。研究人员对学生的设计进行了多次探究，并证明了CRA指令与乘法的准确性和流利性之间的功能关系。研究人员还表明，学生在上课后最多可以保持一年的表现。