We delineate some types of structured practice (modeling, requests, feedback, and space-making) that help students learn to pose appropriate questions and to initiate exploration of those questions. Developing skills requires practice, so we suggest ways to embed structured practice into existing class sessions. Including structured practice is…

Throughout the school year, AP Calculus teachers strive to teach course content comprehensively and swiftly in an effort to finish all required material before the AP Calculus exam. As early May approaches and the AP Calculus test looms, students and teachers nervously complete lessons, assignments, and assessments to ensure student preparation.…

There are specific topics in college calculus that can be major stumbling blocks for students. Having taught college calculus for four years to over a thousand students, we observed that even the students who have already taken pre-calculus or calculus during their high school careers had common misunderstandings. Students may remember a technique…

Students at all levels often generate ideas that are not obviously right or wrong, and, when they do, it is productive to take time to explore the ideas as a group. Some of these ideas are really strange. Occasionally, they are so strange that even the teacher might not know what to think of them. This is the story of what Cosby's rule is, how it…

This article describes a partnership involving a college and its surrounding public high schools in order to offer a model for transforming professional development initiatives into collaborative, reciprocal community engagement opportunities. This ongoing partnership addresses the shared goal of improving the mathematical college readiness of…

An advanced placement calculus program is described that incorporates IBM personal computers, conference telephone connections, modems that transmit computer signals over the phone lines, OPTEL graphics that allow the users to "write" on their computer screens, and a sophisticated package of calculus software used for homework…

For many people committed to strong academic standards, the "advanced" high school courses offered through the College Board's Advanced Placement program and, increasingly, the Diploma Programme of the International Baccalaureate Organisation (IBO) represent the curricular gold standard for secondary education. Admissions directors and…