Quantyfying stimulus, response, and numerical biases.

尽管人们无法对比例做出直观的判断(有关评论，请参阅Rothman& Kiviniemi，1999)已被证明会导致对健康相关问题的错误判断(Kaplan，Hammel，& Schimmel，1985)，相对较少的研究针对理解认知表征 比例。目前的提案将通过以下方式填补这一空白：(1)提供关于内部 比例表征，以及(2)比例认知表征的生成模型 类似于现有的整数认知表示模型。目前的提案还包括 阐述了经验在数字偏差的形成和维持中的作用。了解如何以及如何 为什么这些符号被曲解将导致减少这些偏见的技术，这反过来将导致 更有效的数学教学方法。建议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。尤其是， 拟议的研究将评估三种数字格式和三种刺激的距离效应，其中 数量是固有的，评估与六个刺激的跨通道匹配相关的偏差，并使用 用数值统计模型估计参数的数值偏差。一旦函数形式为 数字偏差被识别和描述，我将研究经验在形成和 维持这些偏见。

Although peoples 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 maintanance of these biases.