来源:Jonathan Flombaum 实验室——约翰斯·霍普金斯大学
一种常见的游乐场游戏是让参与者猜测装满一罐的软糖数量。猜中确切数字的可能性极低。但猜17或147,000的概率又如何呢?可能比猜中正确答案的概率还要低;因为17和147,000这两个数字看起来明显不合理。为什么呢?毕竟,如果不…
1. 刺激与试验

近似数量感测试是一种用于研究支持“估算”能力的潜在机制的实验范式。
估数能力是指在不知道确切数量的情况下,直观地识别数量多少的能力。例如,在一种常见的游乐场游戏中,参与者需要猜测一个罐子里装有的 jellybeans 软糖数量。几乎没有人能准确猜中确切的数目。
然而,每个人都能给出一个大致接近的估计值,因为当明显超过100时,没有人会猜测为20。因此,估计能力被认为是一种与生俱来的基本能力,个体无需依赖数学计算即可具备。
本视频演示了研究非语言数值估计的实验流程,包括如何设计刺激材料、实施实验,以及如何分析和解释数据。
在本实验中,大小和颜色各异的刺激物会随机且短暂地呈现在计算机屏幕上。每次试验期间,会显示两组图形:一组包含多个蓝色圆圈,另一组包含多个黄色圆圈。
要求参与者猜测哪一组的数量更多。因变量为准确率百分比,即在不同试验比例下记录的正确反应次数所占的百分比。
当圆圈数量比例非常接近(接近1:1)时,表现准确率预计接近随机水平;随着比例差异增大,准确率将提高。
换句话说,区分八和四比区分十二和八更容易。在这两种情况下,相减的差值均为四,但比值差异却不同,分别为 2:1 和 1.5:1。
为了创建刺激材料,生成蓝色和黄色的若干组不同大小的圆形。对于每组,确保蓝色和黄色圆形的数量始终不同,并代表六种比例。
每次试验中,编写程序将显示画面分割,在灰色背景上同时呈现每种颜色组的一组图形,持续 500 毫秒。需注意,数量较多的一组所对应的颜色和圆圈大小应随机选择,并且每种比例应进行 20 次试验。
实验开始时,在实验室中向参与者打招呼,并讲解任务的说明。待参与者理解任务规则后,启动程序。
每次试验中当圆圈消失后,要求参与者若认为看到的黄色点更多,则按“Y”键;若认为看到的蓝色点更多,则按“B”键。
每次试验后,通过声音提供即时反馈,以表明参与者的反应是否正确。
为分析数据,需按每次试验中的比率计算正确响应次数的平均值。绘制不同比率差异下的平均准确率百分比图。注意,随着比率差异的增大,参与者的表现在逐步提升。
即使算术能力并不涉及估算,但数感的近似能力与标准化测试所衡量的算术能力呈正相关。
此外,即使是幼儿也能运用数感来识别熟悉物体组中是否有东西缺失。
您刚刚观看了 JoVE 关于近似数感测试的介绍。现在,您应该已经很好地掌握了如何设计和实施该实验,以及如何分析结果并应用数量估计现象。
感谢观看!
View the full transcript and gain access to JoVE Science Education videos
Q1: What is approximate number sense and how does it differ from counting?
Approximate number sense is a hardwired mental ability to estimate quantities without exact calculation or verbal counting. Unlike learned counting skills, it allows people to intuitively recognize quantity and make reasonable guesses. For example, someone can estimate that a jar contains more than 100 jellybeans without counting each one, demonstrating this innate guesstimating ability.
Q2: How does ratio affect performance accuracy in the approximate number sense test?
Performance accuracy improves as ratio differences between compared sets increase. When ratios are similar, like 1:1, accuracy approaches chance level. As ratios diverge—such as 2:1 versus 1.5:1—participants correctly identify the larger set more often. This demonstrates that the visual system relies on proportional differences rather than absolute numerical differences.
Q3: What stimuli are used in the approximate number sense test procedure?
The test uses blue and yellow circles of varying sizes, randomly presented on a computer screen for 500 milliseconds per trial. Each trial displays two sets with different quantities representing six different ratios. Color and circle size for the larger amount are randomized, with 20 trials conducted for each ratio to ensure reliable data collection.
Q4: How do participants respond during the approximate number sense test?
Participants press the 'Y' key if they believe they saw more yellow circles or the 'B' key for more blue circles. After each response, immediate feedback is provided through a tone indicating correctness. This real-time feedback helps participants understand task performance and maintains engagement throughout the experimental session.
Q5: What does data analysis reveal about approximate number sense performance?
Researchers average correct responses as a function of ratio and graph mean accuracy percentages across ratio differences. Results consistently show that performance improves as ratio differences increase, confirming that approximate number sense operates on proportional rather than absolute differences. This pattern validates the underlying mechanisms supporting nonverbal numerical estimation.
Q6: How does approximate number sense relate to mathematical abilities?
Approximate number sense positively correlates with arithmetic abilities measured by standardized tests, despite arithmetic involving precise calculation rather than estimation. Young children also apply number sense to identify missing objects from familiar groups. This suggests that the foundational estimation ability supports broader numerical competence and mathematical development.
Q7: Why is the approximate number sense test considered an important experimental paradigm?
The test investigates underlying mechanisms supporting guesstimation through controlled stimuli and measurable dependent variables like percent accuracy. By systematically varying ratios and analyzing performance patterns, researchers uncover the computational and neural processes enabling nonverbal numerical estimation. This paradigm bridges cognitive psychology with neuroscience to understand fundamental quantitative abilities.