Campbell Jamie I D, Alberts Nicole M
Department of Psychology, University of Saskatchewan, Saskatchewan, Saskatoon, Canada.
Can J Exp Psychol. 2010 Jun;64(2):77-85. doi: 10.1037/a0015720.
Mauro, LeFevre, and Morris (2003) and Campbell (2008) manipulated problem format to assess university students' simple division and subtraction. Large division problems (dividend > 25; e.g., 42 / 6 = _) and large subtraction problems (minuend > 10; e.g., 13 - 6 = _), but not small problems, were solved more quickly when presented in inverse operation format (e.g., 6 x _ = 42 for division; 6 + _ = 13 for subtraction). They concluded that adults often solve large simple division and subtraction problems by reference to the inverse operation but rely on direct memory retrieval for smaller problems. Their findings, however, might have resulted from unequal practice or mixing of the inverse operations. Here, in Experiment 1 (division) and Experiment 2 (subtraction) normal and inverse formats received equal practice and only one operation was practiced (i.e., division or subtraction). Large divisions and subtractions were solved substantially faster when presented in inverse format, but there was also evidence that subtraction ties (e.g., 12 - 6 = 6) and small subtractions (minuend <or=10) benefited from inverse format. The results affirm that inverse reference is an important element in adult's performance of elementary subtraction and division.
毛罗、勒费夫尔和莫里斯（2003年）以及坎贝尔（2008年）通过操控问题形式来评估大学生的简单除法和减法运算能力。当以逆运算形式呈现时（例如，除法：6×_ = 42；减法：6 + _ = 13），大的除法问题（被除数>25；例如，42÷6 = _）和大的减法问题（被减数>10；例如，13 - 6 = _），而非小问题，能被更快地解决。他们得出结论，成年人在解决大的简单除法和减法问题时，常常借助逆运算，但在解决较小问题时则依赖直接的记忆提取。然而，他们的研究结果可能是由于逆运算练习不均衡或两种逆运算混合使用所致。在此，在实验1（除法）和实验2（减法）中，常规形式和逆运算形式的练习量相等，且只练习一种运算（即除法或减法）。当以逆运算形式呈现时，大的除法和减法问题的解决速度大幅提高，但也有证据表明减法等式（例如，12 - 6 = 6）以及小的减法问题（被减数≤10）也从逆运算形式中受益。这些结果证实，借助逆运算参考是成年人进行基本减法和除法运算时的一个重要因素。
