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：教育和人力资源计划(IUSE：EHR)的支持下，该项目旨在为高质量的本科STEM教育服务于国家利益。它将通过开发和研究可视化资源来实现这一点，这些资源可能会促进本科生统计学的学习。帮助学生理解基本的概率概念对于促进科学素养至关重要，也是让STEM专业的学生掌握在研究生院、工作场所和其他地方取得成功所需的技能和知识的关键。该项目将开发和测试一个关于贝叶斯推理所涉及的概率概念的学习模块，贝叶斯推理是一种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可视和非可视版本，探讨可视化在学习概率概念方面的作用。为该项目制作的教学材料可能有助于教育工作者在他们的课程中加入贝叶斯推理。这一纳入很重要，因为贝叶斯推理在许多STEM领域是一个越来越重要的概念，而教学模块可能会促进STEM对广泛范围的学生的成功。更广泛地说，这些发现可能会揭示一些原则，这些原则可以指导未来创造教学方法的努力，使学生更容易接触到困难的数学概念，特别是那些在数学上有困难的学生。这两个版本的贝叶斯推理学习模块都将纳入基础研究的创新。视觉版本还将使用一个将数学概念与简单的空间关系联系起来的显示器。在统计学入门课程的讨论部分，学生将完成本单元的视觉或非视觉版本，他们的理解将通过他们在一对一访谈中对作业的回答和定性回答的准确性来评估。主要的研究问题是：(1)视觉表征是否通过提高学生在接受直接指导之前对问题的统计推理的表现来促进主动学习和直觉理解？(2)视觉表征是否能产生更持久的学习，这一点在最初教学一个月后完成的计算问题上得到了证明？(3)视觉表征是否有助于学生在访谈中传达对概率概念的深刻概念理解？以及(4)对于数学概念有困难或对数学持负面态度的学生，视觉表征是否缩小了成绩差距？我们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STEM教育对所有学生的有效性。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.