美国早期代数教科书中的“负负得正”解释方式研究

An Examination of the Methods Performing the Multiplication with Two Negative Numbers in Early Algebra Textbooks in the USA

选取1820—1939年间出版的200种美国早期代数教科书,研究发现:书中"负负得正"的解释方式共有7类,即利用分配律、连减法、利用相反数、归纳法、几何方法、物理模型和生活模型.1880年以前,教科书中多采用利用分配律和连减法;1880年后,多种方法并存,利用分配律解释呈逐渐下降趋势,物理模型和生活模型占比逐渐上升,相反数法和连减法占比普遍较高.了解"负负得正"的多种解释方式和历史演变,有助于教科书编写者和教师深刻理解符号法则的合理性,选择易于学生理解的解释方式.

About 200 algebra textbooks,published between 1820 and 1939 in the USA,were selected to analyze their explanation of the Multiplication of two Negative numbers.It was found that there were seven types of interpretation methods in the books:distribution law,repeated subtraction,opposite number,induction,geometric method,physical model,and life model.Before 1880,many textbooks adopted the distributive law and repeated subtraction.After 1880,a variety of methods coexisted,and interpretation using the distributive law showed a gradually declining trend.The proportion using the physical model and life model methods increased gradually,and the proportion using the opposite number method and repeated subtraction method were generally higher.It is helpful for textbook writers and teachers to have a deep understanding of the rationality of the sign rules and choose the interpretation method that is easiest for students to understand.