CAREER: Magnitude Biases in Mathematical Cognition, Learning, and Development

这个项目将调查大小偏差在数学认知、学习和发展中的作用。量值偏差指的是心理量值往往与其相应的实际量值不同的想法。这项建议列出了适用于数学教育的经常使用的数值认知研究范式中这些偏见的证据，描述了两组进一步研究这些偏差的研究，并为未来的职业生涯奠定了基础，该职业将通过与教育研究人员和实践者发展伙伴关系来调查教育影响。第一组实验考察了抽象量偏向在儿童学习中的作用，以将他们对数量的直觉理解与语言系统相结合。这项工作对数学认知和学习具有重要的理论意义，并展示了它在数学教育中的应用：所讨论的发展变化与学校数学成绩的变化相关。第二组研究知觉大小偏差在非语言数量思维中的作用。这项工作对儿童数学知识表征基础的性质具有重要的理论意义，并有望在教育应用中应用，因为知觉偏差影响我们对观察项目大小的思考。在某种程度上，像操作器和可视化工具这样的教学材料是为了传达有意义的大小信息，这些偏见很可能会影响数学概念的学习。

This project will investigate the role of magnitude biases in mathematical cognition, learning, and development. Magnitude bias refers to the idea that psychological magnitudes are often different from their corresponding actual magnitudes. This proposal lays out evidence for these biases in oft-used research paradigms in numerical cognition that are applicable to math education, describes two sets of studies to investigate these further, and sets the stage for a future career that will investigate educational implications by developing partnerships with educational researchers and practitioners. The first set of experiments investigates the role of abstract magnitude bias in children's learning to integrate their intuitive understanding of quantity with linguistic systems. This work has important theoretical implications for mathematical cognition and learning, and it has demonstrated applications to math education: the developmental changes in question are correlated with changes in school-based math achievement. The second set investigates the role of perceptual magnitude bias in nonverbal quantitative thinking. This work has important theoretical implications for the nature of the representational foundations of children's math knowledge, and it holds promise for educational applications because perceptual biases affect our thinking about the magnitudes of observed items. To the extent that instructional materials such as manipulatives and visualization tools are meant to convey meaningful magnitude information, these biases are likely to affect math concept learning.