Challenge
Many US students and teachers share a maladaptive view of mathematics as a domain that requires memorization of steps rather than thinking and problem solving (e.g., Stigler at al., 2010; Givvin et al. 2011). This interacts with a cultural belief that there are math people for whom math ability is largely innate (Stevenson & Stigler, 1992). These beliefs work together to prevent students from struggling to understand math. If math as a discipline is about memorizing things that math people have discovered, then if one is not a math person, one cannot figure out math.
A recent study of California’s 11th graders found a majority to be neither ready nor conditionally ready for college-level math (2017 data, https://www.ppic.org/publication/college-readiness-in-california/. Sixty-five percent of California’s entering community college students are similarly identified as underprepared for college level math (data from AY 2009-10, Mejia, Rodriguez, & Johnson, 2016). Attempts to address this problem through developmental mathematics courses – which typically involve teaching students the same content, using the same methods, that they have already been exposed to in high school – have largely failed, leaving students stuck and unable to transfer or graduate.
Students who do get past the math prerequisites still struggle with math, discouraging many from pursuing STEM careers. Among these students, continued disparities exist in performance between URMs and other groups, between first- and later-generation college students, and by socioeconomic status. At UCLA, for example, URMs taking statistics – across a number of different departments – earn significantly lower grades than their non-URM peers, and have lower pass rates. The gap is similar, if not larger, between students receiving PELL grants and others; and between first-generation college students and others, and similar patterns are evident in the Cal State and Community College systems.
Current definitions of success may be impeding the ability to make significant headway against this problem. If success is simply defined as course completion, then the resulting strategies, while increasing rates of completion, may do nothing to solve the fundamental problem, namely, the educational system’s inability to produce deep mathematical understanding in students and to adequately prepare them with the skills and desire to pursue STEM careers.
Design
This project will develop, implement, and continuously improve an online interactive textbook for introductory statistics. The project focuses on statistics for several reasons. Statistics is critical not only for gaining entry into STEM careers, but also for excelling in them. In fact, modern computational statistics is arguably more critical for future STEM careers than are traditional mathematics courses. Additionally, statistics may be the most direct pathway for students seeking to overcome poor mathematical preparation, and, significant from a psychological perspective, the notion that statistics is “not math,” may provide an inroad for students who have been convinced that they can’t learn math.
The project’s design – based on learning science theories of how people develop deep understanding in complex domains – involves repeatedly engaging students with the deep conceptual structure of the domain (in this case, statistical modeling), and includes a heavy emphasis on simulation, randomization, and bootstrapping as tools for both doing data analysis and understanding statistical ideas. The goal is not simply students’ course completion, but the development of flexible and transferable knowledge – i.e., deep understanding – in all students.
The project begins with Version 1.0 of the book, then works to improve the book and its implementation at scale. Through this work, the project will create a replicable R&D model that engages researchers, designers/developers, and instructors in the hard work of scaling the innovation, and of continuous improvement of the book and its implementation. The project team is also building an innovative technology platform to support this work (funded separately).
The goals of this project are to: 1) produce measurable improvements in students’ understanding of statistics; 2) change students’ and instructors’ beliefs about what it means to “do math,” from a view that math is about memorizing rules and facts to one in which math is a set of tools and representations than can be used to help think through problems; 3) reduce gaps that traditionally leave some groups behind; 4) make substantive contributions to the science of learning – especially to the understanding of how learning proceeds in complex domains (such as statistics) over longer periods of time; 5) create a replicable R&D model for producing continuous improvements in online educational resources over time – i.e., “a better book.” Separately, the project team will produce an open-source technology platform designed to support the R&D process.
Preliminary Impact
As of February 2021, the course materials have been used by more than 50 faculty members in higher education, in more than 120 classes, with nearly 5,000 students.
