People make complex decisions throughout their lives and often seek out evidence to help them understand their options. In areas such as finance and health, some of the most useful information for decision-making is presented numerically and requires mathematical and statistical reasoning to make sense of. For example, it is important in medicine to quantify the risks and benefits of a treatment to help people decide whether to accept it. Related to health and wellness, the decision whether to drink alcohol or how much to exercise also relies on understanding the magnitude of risks and benefits to make decisions aligned with one’s personal values and goals. As a final example drawn from everyday living and financial decision making, deciding to rent or buy a home entails making sense of complex mathematics that is influenced by day-to-day changes. This project will support the public’s quantitative reasoning about critical personal health and finance decisions by (1) designing representations of real-world data that are accessible to people with a wide range of educational backgrounds. The project will (2) expand our knowledge of how adults use mathematical and statistical reasoning by studying how people use the representations of data to make decisions. In turn, this project will (3) support pre-service and in-service mathematics teachers in teaching mathematical and statistical ideas that are critical for decision-making This project will curate quantitative data from published, peer-reviewed research on topics of broad interest that people learn about to make decisions. People are interested in understanding more about the risks and benefits of alcohol, exercise, and various commonly used medicines. People also use tools such as rent versus buy calculators to make decisions. In this study, Quantitative Data Representations (QDRs) will be designed to help make data accessible to people who have a wide-range of mathematics backgrounds. For instance, comparing the relative size of two fractions is difficult for many. This is important when trying to represent the magnitudes of risk visually for activities like drinking alcohol, physical activity, and selecting the best mortgage. This project will explore the use of AI to reduce the cost of coding QDRs and investigate the constraints and affordances of using AI to transform peer-reviewed results into QDRs. The project team will conduct interviews with individuals while engaging them with the QDRs in efforts to iteratively improve them and to create models of mathematical thinking of people engaged in real-world decision making. The interviews will also be used to create hypotheses and design surveys given to representative samples of US residents. Randomized controlled trials will be used to test the understandability of QDR design and hypotheses about mathematical thinking used in decision making. Exploring quantitative reasoning in real-life contexts will provide valuable insights for improving the relationship between what is taught in mathematics classrooms and what knowledge adults use in life. This work will expand the utility of models of mathematical thinking, which were often limited to researchers studying reasoning in classroom contexts, by refining those models via studying quantitative reasoning in real-world contexts. Generating knowledge about how people use data representations to support their reasoning will inform improvements in the design of data representations about critical topics such as health risks and finance. The project will contribute to improving STEM education and educator development by preparing in-service and pre-service mathematics teachers to teach new financial literacy standards. The project will contribute to the lives of all Americans by designing QDRs that are accessible to people with a variety of mathematics, financial, and health backgrounds and support their quantitative reasoning.
Funder: NSF
Amount: $626,531
PI: Cameron Byerley, Mary Frances Early College of Education