Robinson Katherine M, Ninowski Jerilyn E, Gray Melissa L
Department of Psychology, Campion College at the University of Regina, Regina, Sask., Canada S4S 0A2.
J Exp Child Psychol. 2006 Aug;94(4):349-62. doi: 10.1016/j.jecp.2006.03.004. Epub 2006 May 3.
Previous studies have shown that even preschoolers can solve inversion problems of the form a+b-b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e/e was also examined. Grade 6 and 8 students solved inversion problems of both types as well as standard problems of the form a+b-c and d x e/f. Students in both grades used the inversion concept on both types of inversion problems, although older students used inversion more frequently and inversion was used most frequently on the addition/subtraction problems. No transfer effects were found from one type of inversion problem to the other. Students who used the concept of associativity on the addition/subtraction standard problems (e.g., a+b-c=[b-c]+a) were more likely to use the concept of inversion on the inversion problems, although overall implementation of the associativity concept was infrequent. The findings suggest that further study of inversion and associativity is important for understanding conceptual development in arithmetic.
先前的研究表明，即使是学龄前儿童也能通过运用加法和减法是逆运算这一知识来解决a + b - b形式的反演问题。在本研究中，还考察了一种新型的d × e / e形式的反演问题。六年级和八年级的学生解决了这两种类型的反演问题以及a + b - c和d × e / f形式的标准问题。两个年级的学生在两种反演问题上都运用了反演概念，尽管年龄较大的学生更频繁地使用反演，并且在加减法问题上反演的使用最为频繁。未发现从一种反演问题类型到另一种反演问题类型的迁移效应。在加减法标准问题（例如，a + b - c = [b - c] + a）上运用结合律概念的学生，在反演问题上更有可能运用反演概念，尽管结合律概念的整体运用并不常见。研究结果表明，对反演和结合律的进一步研究对于理解算术概念发展很重要。
