Effect of Visualization on Undergraduate Students' Understanding of Fundamental Probability Concepts, Including Bayesian Inference

在NSF改善本科STEM教育计划：教育和人力资源（IUSE：EHR）计划的支持下，该项目旨在为高质量本科STEM教育的国家利益服务。 它将通过开发和研究可视化资源来实现这一目标，这些资源可能会促进本科统计学的学习。 帮助学生理解基本的概率概念对于促进科学素养，以及为STEM专业的学生提供在研究生院，工作场所和其他地方取得成功所需的技能和知识至关重要。本项目将开发和测试一个关于贝叶斯推断所涉概率概念的学习模块，这是一个根据新数据更新概率的程序。该项目还将通过比较学习模块的视觉和非视觉版本来探索视觉化在学习概率概念中的作用。为该项目创建的教学材料可以帮助教育工作者在他们的课程中包括贝叶斯推理。 这种包含很重要，因为贝叶斯推理在许多STEM领域是一个越来越重要的概念，教学模块可以促进广泛的学生STEM成功。更广泛地说，这些发现可能揭示了一些原则，这些原则可以指导未来的教学方法，使学生，特别是那些数学困难的学生更容易理解困难的数学概念。贝叶斯推理学习模块的两个版本都将结合基础研究的创新。 视觉版本还将使用一个显示器，将数学概念与简单的空间关系联系起来。在介绍统计类的讨论部分的学生将完成该模块的视觉或非视觉版本，他们的理解将通过他们对作业的回答和一对一访谈中的定性回答的准确性进行评估。主要的研究问题是：（1）视觉表征是否通过提高学生在直接指导之前应用统计推理的问题上的表现来促进主动学习和直观理解？(2)视觉表征是否能产生更持久的学习效果，这一点可以通过在初始指导后一个月完成的计算问题上的表现来证明？(3)视觉表征是否有助于学生在面试中传达对概率概念的深刻理解？（4）视觉表征是否能缩小数学概念困难或对数学持消极态度的学生的成绩差距？本文将采用定性和定量相结合的方法来寻求这些研究问题的答案。NSF IUSE：EHR计划支持研究和开发项目，以提高所有学生的STEM教育的有效性。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

With support from the NSF Improving Undergraduate STEM Education Program: Education and Human Resources (IUSE: EHR) Program, this project aims to serve the national interest in high-quality undergraduate STEM education. It will do so by developing and researching visualization resources that may promote learning in undergraduate statistics. Helping students understand basic probability concepts is critical to promote science literacy, as well as to equip STEM majors with the skills and knowledge they need to succeed in graduate school, the workplace, and beyond. This project will develop and test a learning module on the probability concepts involved in Bayesian inference, a procedure for updating probability in response to new data. The project will also explore the role of visualization in learning probability concepts by comparing visual and non-visual versions of the learning module. The instructional materials created for the project may help educators include Bayesian inference in their courses. This inclusion is important because Bayesian inference is an increasingly important concept across many STEM fields, and the instructional modules may promote STEM success for a wide range of students. More broadly, the findings may reveal principles that can guide future efforts to create instructional methods that make difficult mathematical concepts more accessible to students, especially those who struggle with math.Both versions of the Bayesian inference learning module will incorporate innovations from basic research. The visual version will also use a display that links mathematical concepts to simple spatial relationships. Students in discussion sections of an introductory statistics class will complete either the visual or non-visual versions of the module, and their understanding will be assessed by the accuracy of their responses on assignments and qualitative responses in one-on-one interviews. The primary research questions are: (1) Does the visual representation facilitate active learning and intuitive understanding by increasing performance on problems that challenge students to apply statistical reasoning before getting direct instruction? (2) Does the visual representation produce more durable learning as evidenced by performance on computational problems completed one month after initial instruction? (3) Does the visual representation help students convey a deep conceptual understanding of probability concepts in interviews? and (4) Does the visual representation reduce the performance gap for students who either struggle with mathematical concepts or who have negative attitudes towards math? Both qualitative and quantitative methods will be used to seek the answers to these research questions. The NSF IUSE: EHR Program supports research and development projects to improve the effectiveness of STEM education for all students.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.