Department of Psychology, University of Wisconsin-Madison, Madison, WI 53706, USA.
Department of Psychology, University of Wisconsin-Madison, Madison, WI 53706, USA.
J Exp Child Psychol. 2024 Nov;247:106041. doi: 10.1016/j.jecp.2024.106041. Epub 2024 Aug 21.
The concept of zero is challenging for many children. This study investigated conceptions of zero in fifth- through seventh-grade children (N = 72) in the United States and examined how children's conceptions of zero related to other aspects of their integer knowledge. At the outset of the study, many participants held a null conception of zero (i.e., zero as "nothing"), and some participants held a conception of zero as the symmetry point between the positive and negative integers. Participants in higher grades were more likely to hold a symmetry conception. We hypothesized that participants' conceptions of zero would be related to other aspects of their integer knowledge. Relative to participants who held a null conception of zero, participants who held a symmetry conception demonstrated greater knowledge of the additive inverse principle (for every number x, there exists an inverse, -x, such that the two numbers sum to zero) and greater integer arithmetic skill. Conceptions of zero were not related to integer magnitude understanding. We also examined whether a brief lesson focusing on zero as the symmetry point would lead to shifts in participants' conceptions of zero and gains in understanding of the additive inverse principle. Participants were randomly assigned to receive a lesson about zero as null or zero as the symmetry point between positive and negative integers. Relative to the lesson about zero as null, the lesson about zero as the symmetry point did not lead to substantial changes in conceptions of zero or additive inverse knowledge.
零的概念对许多孩子来说具有挑战性。本研究调查了美国五至七年级儿童（N=72）对零的概念的理解，并考察了儿童对零的概念如何与整数知识的其他方面相关。在研究开始时，许多参与者持有零的空概念（即零是“无”），而一些参与者将零视为正整数和负整数之间的对称点。较高年级的参与者更有可能持有对称概念。我们假设参与者对零的概念将与他们整数知识的其他方面相关。与持有零的空概念的参与者相比，持有对称概念的参与者对加法逆原理（对于每个数 x，都存在一个逆数 -x，使得这两个数相加等于零）有更深入的了解，并且整数运算技能也更强。对零的概念与整数大小理解无关。我们还检查了专注于将零视为对称点的简短课程是否会导致参与者对零的概念发生转变，并提高他们对加法逆原理的理解。参与者被随机分配接受关于零为空或零为正负数之间的对称点的课程。与关于零为空的课程相比，关于零为对称点的课程并没有导致对零的概念或加法逆知识的实质性改变。
