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

University Of Massachusetts Amherst, Amherst MA

Investigators

Abstract

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.