Abstract:

This paper describes a four-year project in the U.S., funded by the National Science Foundation, to design, develop, and evaluate Transition to College Mathematics and Statistics (TCMS), a high school senior-level course to help meet the diverse quantitative needs of students in a technological, information-laden, and data-driven global society whose intended undergraduate programs do not require calculus. For students intending to enroll in non-calculus-based undergraduate programs, many schools in the U.S. have little to offer as a transition to college-level mathematics and statistics other than precalculus or narrow Advanced Placement courses. Consequently, many students opt out of mathematics their senior year or study mathematics that is inappropriate for their undergraduate and career aspirations.

TCMS focuses on broadly useful topics, including mathematical modeling, data analysis and inference, informatics, financial mathematics, decision-making under constraints, enumeration, and mathematical visualization and representations. Development and use of important mathematical habits of mind, including visual thinking, recursive thinking, reasoning abstractly, searching for and explaining patterns, making and checking conjectures, exploiting use of multiple representations and connections among them, providing convincing explanations and valid arguments and evaluating those of others, and a disposition toward strategic use of technological tools are integrated throughout the eight units comprising the course.

Transition to College Mathematics and Statistics is a problem-based, inquiry-oriented, and technology-rich fourth-year high school mathematics course designed for students who have successfully completed a conventional single-subject sequence of algebra, geometry, and advanced algebra or a three-year unified (international-like) mathematics sequence. The course has been carefully field tested in a wide range of high schools with students using conventional mathematics curricula and with students using a unified mathematics program. Both print and interactive digital versions of the TCMS text have been developed.

Key mathematical themes and content, innovative design features of the print and digital versions of the text, and the accompanying suite of curriculum-embedded software tools, including a spreadsheet, a computer algebra system (CAS), data analysis and discrete modeling tools, and dynamic geometry are described and illustrated. A summary of key evaluation findings regarding the use and efficacy of TCMS is discussed. In the case of classroom use of the interactive digital version, how students engaged with other students and the teacher while synchronously interacting with the accessibility features, open-ended problems linked to learner-controlled scaffolding, embedded audio and video clips, embedded mathematical and statistical software tools, and digital collaborative notebooks are highlighted.