Quantifying stimulus, response, and numerical biases

描述（由申请人提供）：尽管人们无法对比例做出直觉判断（回顾，见Rothman & Kiviniemi， 1999）已被证明会导致对健康相关问题的判断不佳（Kaplan, Hammel, & Schimmel, 1985），但针对理解比例认知表征的研究相对较少。目前的建议将通过以下方式填补这一空白：(1)提供关于比例内部表示的广泛数据，以及(2)生成类似于整数认知表示模型的比例认知表示模型。目前的建议还涉及经验在数字偏差形成和维持中的作用。了解这些符号是如何以及为什么会被误解的，将有助于找到减少这些偏见的方法，从而产生更有效的数学教学方法。提出的方法结合了实证研究、数值统计程序、探索性分析和计算建模。特别地，本研究将评估三种数字格式和三种数量固有刺激的距离效应，评估六种刺激的跨模态匹配相关偏差，并使用数值统计模型估计数值偏差的参数。一旦数值偏差的功能形式被识别和描述，我将研究经验在这些偏差的形成和维持中的作用。

DESCRIPTION (provided by applicant): Although people's inability to make intuitive judgments about proportions (for a review, see Rothman & Kiviniemi, 1999) has been shown to lead to poor judgments about health related issues (Kaplan, Hammel, & Schimmel, 1985), relatively little research has been directed at understanding the cognitive representation of proportions. The current proposal will fill this gap by (1) providing extensive data on the internal representation of proportions, and (2) generating models of the cognitive representation of proportions similar to the models that exist for the cognitive representation of integers. The current proposal also addresses the role of experience in the formation and maintenance of numerical biases. Learning how and why these symbols are misinterpreted will lead to techniques to reduce these biases, which in turn will lead to more effective methods of teaching mathematics. The proposed approach combines empirical research, numerical statistical procedures, exploratory analysis, and computational modeling. In particular, the proposed research will assess the distance effect for three numerical formats and three stimuli in which quantity is inherent, assess the biases associated with cross-modality matching for the six stimuli, and use numerical statistical models to estimate the parameters of the numerical biases. Once the functional form of numerical biases are identified and described, I will study the role of experience in the formation and maintenance of these biases.