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.…

The Advanced Placement® (AP®) Program offers high school students the opportunity to take rigorous coursework in high school and receive college credit for AP Exam scores that meet or exceed the requirements of their attending institution. Students receiving AP credit are typically exempted from an introductory level course or series of courses…

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…

This dissertation explores the views and experiences of high school calculus teachers and college mathematics professors on the professional development which occurs at the annual national AP Calculus exam grading. This professional development experience comes in several forms: the exam briefing sessions, the actual reading of the exams, the…

This study describes the trends in course credit attainment (CCA) of high school students in required and non-required science and math courses and trends in registration in non-required science and math courses in Texas between 1997 and 2009. Using Texas Public Education Information Management System data between 1997 and 2009, it presents…

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…

The purpose of this action research was to investigate how the use of technology promotes interaction to foster high school students' mathematical understanding. This mixed method study is guided by social-constructivist theory (Vygotsky, 1978) and framed within Moore's (1989) model of learner-content, learner-instructor, and learner-learner…

The goal of the present study was to report an instrument designed to determine students' mathematical performances and preference for visual or analytic thinking for the calculus derivative and antiderivative tasks as well as examine the relationships among students' cognitive style, cognitive ability, and mathematical performance in calculus.…

This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

The purpose of these modules is to provide an introduction to the world of probability and statistics to accelerated mathematics students at the high school level. The modules also introduce students to real world math concepts and problems that property and casualty actuaries come across in their work. They are designed to be used by teachers and…

THE COURSE IS INTENDED TO GO BEYOND THE REQUIREMENTS OF THE ADVANCED PLACEMENT PROGRAM IN MATHEMATICS AS DESIGNED BY THE COLLEGE ENTRANCE EXAMINATION BOARD. THE ADVANCED PLACEMENT PROGRAM CONSISTS OF A 1-YEAR COURSE COMBINING ANALYTIC GEOMETRY AND CALCULUS. PRESUPPOSED HERE ARE--A SEMESTER COURSE IN ANALYTIC GEOMETRY AND A THOROUGH KNOWLEDGE OF…

Two-hundred forty-seven students in AP Calculus BC classes in 15 schools were compared to 229 students in college calculus courses in nine colleges, using a testing instrument valid for both groups. The AP Calculus BC students achieved as well as, or better than, their college counterparts. (MNS)

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…