Examining the Effects of Perceptual Cues on Middle School Students’ Online Mathematical Reasoning and Learning

许多学生缺乏超越代数I所需的程序和概念知识，这限制了他们追求STEM兴趣、培训和职业生涯的能力。在这一前景看好的支持学习者的方法中，研究人员将研究如何使用嵌入到中学生在线数学材料中的各种感知线索，努力评估操纵材料中的视觉感知线索，如颜色和间距，是否通过引导学生在解决问题的过程中将注意力集中到关键信息来影响学习和表现。这些结果将使人们了解不同类型的感知线索是否以及如何发挥作用，以便在在线数学学习环境中提供低成本、有效的教学支持，从而更好地为学生学习代数和更高水平的数学做好准备。有人建议，观看突出相关数学结构的线索将有助于立即表现和学习，但观看打破符号模式或结构的线索，结合训练，将有助于更好地保持。本研究旨在实施两项实验研究，考察数学符号中一致和不一致的知觉线索是否以及如何影响中学生的操作顺序成绩、学习和保持，并了解知觉线索如何在数学实践中产生令人满意的困难或生产性斗争。研究一将通过实验操作和检验数学符号中知觉线索对中学生运算顺序问题的个体效应。研究二采用3×3析因设计，系统地检验了一致和不一致知觉线索对学生操作顺序成绩、学习和保持的个体效应和协同效应。此外，这两项研究都将调查学生的先验知识、数学焦虑和知觉处理技能是否会缓和知觉线索的影响。这个项目将提供知觉线索对学生数学成绩、学习和记忆的作用的证据，包括一致和不一致知觉线索的效果是否存在差异的初步证据，以及这些知觉效果的变化是否会协同影响学习。该项目由EDU核心研究(ECR)计划资助，该计划支持关于STEM学习和学习环境的基础研究，扩大对STEM的参与，以及STEM劳动力发展。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Many students lack the necessary procedural and conceptual knowledge to progress beyond Algebra I. This limits their ability to pursue STEM interests, training, and careers. In this promising approach to giving support to learners, investigators will study the use various perceptual cues embedded in online math materials for middle school students in an effort to evaluate whether manipulating the visual perceptual cues in the materials, such as coloring and spacing, influence learning and performance by directing students’ attention towards key pieces of information during problem solving. The outcomes will provide an understanding of whether and how different types of perceptual cues work in order to provide low-cost, and effective instructional support in online math learning environments that will better prepare students for algebra and higher-level mathematics. It is proposed that viewing cues that highlight relevant mathematical structures will support immediate performance and learning, but that viewing cues that break the pattern or structure of the notations, in combination with training, will support greater retention. The purpose of this research is to implement two experimental studies that investigate whether and how congruent and incongruent perceptual cues within math notation influence middle school students’ order-of-operations performance, learning, and retention, and to understand how perceptual cues create desirable difficulties, or productive struggles, in mathematics practice. Study 1 will experimentally manipulate and test the individual effects of perceptual cues in math notation on middle school students’ performance on order-of-operations problems. Study 2 will use a 3×3 factorial design to systematically test the individual and synergistic effects of congruent and incongruent perceptual cues on students’ order-of-operations performance, learning, and retention. Additionally, both studies will investigate whether students’ prior knowledge, math anxiety, and perceptual processing skills moderate the effects of perceptual cues. This project will produce evidence of the roles of perceptual cues on students’ math performance, learning, and retention, including preliminary evidence of any differences in the effects of congruent vs. incongruent perceptual cues, and whether these variations in perceptual effects influence learning synergistically. This project is funded by the EDU Core Research (ECR) program, which supports fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.