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

这个项目将研究数量偏差在数学认知，学习和发展中的作用。量值偏差指的是心理量值通常与其对应的实际量值不同的想法。该提案为适用于数学教育的数字认知中经常使用的研究范式中的这些偏见提供了证据，描述了两组研究以进一步调查这些偏见，并为未来的职业生涯奠定了基础，该职业生涯将通过与教育研究人员和实践者建立伙伴关系来调查教育影响。第一组实验探讨了抽象数量偏差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，并且已经证明了它在数学教育中的应用：问题中的发展变化与学校数学成绩的变化相关。第二组调查的作用，知觉的数量偏见在非言语定量思维。这项工作具有重要的理论意义的儿童的数学知识的代表性基础的性质，它持有的教育应用程序的承诺，因为知觉偏见影响我们的思维观察项目的大小。在某种程度上，教学材料，如操纵和可视化工具是为了传达有意义的数量信息，这些偏见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.