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Background/Context Despite advances in the learning sciences, a persistent gap remains between research and practice. Purpose/Objective/Research Question/Focus of Study In this project, we develop and try out a new approach to education research and development in which researchers, designers/ developers, and instructors collaborate to continuously improve an online interactive textbook. Intervention/Program/Practice Using a “learn by doing” strategy, we first created a highly instrumented online textbook for introductory statistics. The design of our online book is based on the practicing-connections hypothesis: Instead of learning individual “bits” of information and then hoping that learners end up with transferable knowledge, we designed a curriculum to engage students in repeated practice of the connections—between core concepts, representations, and the world—that make knowledge transferable. The textbook includes more than 1,200 formative assessments, generating large amounts of data relevant to both the process and outcomes of college students learning of statistics. Using the affordances of technology, we then began working to apply routines and practices from open software development (Git) and improvement science (Toyota Kata) to build an improvement community focused on continuous improvement of the online book. We also are building a technology platform (CourseKata) to publish the book from markdown files stored on GitHub; distribute the book through widely used learning management systems; collect detailed student data and deliver it back to instructors and, in a de-identified form, researchers; and manage experiments that randomly assign different versions of content to different students within a single class, and then assess the effects on students’ learning. Research Design Our research design is a mixed-methods design research and improvement study. We gauge success through measures of process, outcome, and transfer. Conclusions/Recommendations We are at only the beginning of what we see as a lengthy project. We are encouraged, however, by our progress, and invite others—including researchers, designers/developers, and instructors—to join us in our improvement community focused on improving the transferable learning of basic statistical concepts at scale.

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Background. Traditional math instruction that emphasizes procedures and rote memorization is common in math classes, particularly within the United States. Students may be able to perform steps and recite information, but flexible thinking in math is also an important ability. Lay theories assume that extensive experience in math would lead to increased flexibility, but some research has posited a change-resistant account, which argues that experience with traditional instruction may make it difficult to think flexibly about even simple concepts. Aims. The current study explored the mathematical flexibility of college students who completed their K-12 education in the United States, and investigated how affective and cognitive factors contributed to flexible thinking. Sample. Participants were 128 undergraduate students at a competitive U.S. public university. Method. Mathematical flexibility was measured through a novel task that asked participants to generate as many strategies as they could for a simple arithmetic problem. These strategies were coded to create scores of fluency (number of strategies) and flexibility (number of unique strategies). Results and Conclusions. On average, participants were only able to provide little more than three unique strategies beyond the primary strategy taught in K-12 classrooms. Measures of math anxiety, math identity, need for cognition, and working memory were all unrelated to flexibility. However, student perceptions of how many possible solutions exist were significantly related to flexibility. These results provide evidence for a changeresistance account and provide further evidence that math flexibility is a unique construct.