数值的认知： 更多或更少
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Overview
资料来源： 实验室的尼古拉 Noles 和朱迪思 Danovitch — — 路易斯维尔大学
现代教育体系的目标之一就是要教孩子们数学识字。他们被教导要添加，减去，乘除，和这方面的基础知识用来支持学习关于几何、 代数、 微积分、 物理和统计。学龄期儿童通常获得这些技能在正式的教育环境，但数学理解的基础开发早得多的生活。
作为婴儿，人类开始形成粗糙的表示形式，允许他们对数量，做出判断和人类发展的第一个数值概念也许是少与更多的想法。然而，探讨这些概念可以很困难，因为即使婴儿有多一些了解，他们有的炫耀他们知道的很少方式。他们能做什么是爬、 吃饭、 哭泣，睡觉。因此，研究人员开发出利用这组有限的反应调查是否婴儿弱智可以表示数量的任务。
本实验演示如何研究人员可以创造性地使用食物来研究婴儿使用的方法 Feigenson，凯里及豪泽的数学认知的概念。1
Procedure
Results
In order to see significant results, researchers would have to test at least 16 infants in each condition, not including infants dropped for failing to complete the task. Infants presented with 1 vs. 2 crackers and 2 vs. 3 crackers typically selected the container containing more crackers (Figure 1). However, infants typically showed no strong preference for the container holding more crackers when presented with 3 vs. 4 crackers.
Infants consistently chose the container containing the greater number of crackers when presented with comparisons of 1 vs. 2 and 2 vs. 3. However, infants failed to represent differences between larger numbers of items. Critically, this result does not rely solely on proportions, because infants also fail to discriminate between 3 vs. 6, which is the same proportion as 1 vs. 2.
Figure 1: Proportion of infants selecting the container with the greater number of crackers.
Applications and Summary
Although infants are limited in the number of objects they can represent at any given time, the fact that they can represent 2 vs. 3, or up to five items, at one time is cited as evidence that even very young infants can represent number and make comparisons between different values. The method described here can also be applied to measuring how other species, such as dogs and chimps, reason about number.
Infants are impressively capable of representing number and making comparisons of more versus less at a very young age. The results reported here show that infants can reason about their environment in sophisticated ways, and this early skill may contribute to the emergence of numerical reasoning and mathematical ability later in development. However, there is an ongoing debate about whether these representational skills indicate true mathematical understanding, or if they are more appropriately considered in terms of visual representations.
References
- Feigenson, L., Carey, S., & Hauser, M. The representations underlying infants’ choice of more: Object files versus analog magnitudes. Psychological Science., 13, 150-156 (2002).
Transcript
Very early in life—before the age of 1—humans develop a foundation in the mathematical understanding of numerical quantities, called numerical cognition.
To build this foundation, infants begin to form rough mental representations that allow them to make judgments about number and develop the concept of less versus more.
However, probing these concepts of numerical cognition can be difficult. Thus, researchers must be creative in designing tasks by using alluring objects, such as toys or food, due to the limited set of responses—like crawling—in infants.
Using the method developed by Drs. Feigenson, Carey, and colleagues, this video demonstrates how to setup and test numerical cognition in infants, as well as how to analyze and interpret the data regarding judgments between quantities of food items.
In this experiment, 12-month-old infants watch the researcher place appealing graham crackers, one at a time, into two different opaque containers. The number of crackers placed into each one varies, depending on the assigned condition: 1 vs. 2, 2 vs. 3, and 3 vs. 4.
The infants are allowed to crawl to one of the two, and the choice of container is the dependent variable.
If infants are able to represent number, they are expected to choose the one with the most crackers by crawling to that container. However, due to their age, there may be a limit in their capacity to discriminate more than five, in which case they would choose a container at random.
Before the arrival of the infant, ensure the proper functioning of the video equipment and collect one empty small bucket and another filled with graham crackers, a toy, and two tall opaque containers.
To begin the experiment, greet the infant and have them sit on the floor while you sit 100 cm away facing them. Once settled, have an assistant start the video camera to record the session.
First acclimate the infant to crawling towards a container: when the infant is looking, place the toy inside the empty bucket and non-verbally encourage them to crawl and retrieve the toy. After they crawl to the toy, remove it and the bucket and place the infant back to the starting position.
To initiate the test phase, simultaneously introduce the two large containers and show the infant that they are empty. Place the containers 70 cm in front of the infant and 35 cm apart, ensuring that they cannot reach both containers at the same time.
Retrieve the small bucket of graham crackers. Hold up one cracker and say “Look at this.” When the infant is looking, place the cracker into a container. Continue this process until both containers have the appropriate number of crackers for the given condition.
After placing all crackers, look down to avoid influencing the infant’s response of choosing a container. Without looking up, verbally encourage them to pick a container after 10 seconds: “Come this way.”
Once the test phase is completed, have two independent coders who are blind to the conditions view the video recordings and make note of the chosen container for each infant.
To analyze the results, count the number of infants that chose the container with the greater number of crackers and graph the resulting percentages for each condition.
Notice that infants were very good at picking the container with the greater quantity for conditions 1 vs. 2 and 2 vs. 3, but performed near chance level in condition 3 vs. 4, suggesting that there is an upper limit to numerical representation at this age of 12 months.
Now that you are familiar with the methods used to test the concept of less vs. more in infants, let’s look at the emergence of numerical reasoning in other species and the importance of numerical cognition in mathematical ability.
A very similar experimental setup can be used to explore numerical cognition in other animals, such as dogs.
Comparisons in numerical abilities between other species—like birds choosing more food and guppies joining larger social groups—add to the understanding of the ontogeny for numerical competence in the absence of language.
Representing number and making comparisons of more versus less show that infants can reason about their environment in sophisticated ways. This early skill may contribute to the emergence later in development of numerical reasoning and mathematical ability such as addition, subtraction, and even calculus.
You’ve just watched JoVE’s introduction to numerical cognition. Now you should have a good understanding of how to design and run an experiment investigating how infants represent number and quantity, as well as how to analyze and assess the results.
Thanks for watching!