Mapping the Calculus Curriculum, Part II
March 27–29, 2010
- Guershon Harel, University of California San Diego
- Deb Hughes Hallett (chair), University of Arizona
- Joceline Lega, University of Arizona
- William McCallum, University of Arizona
- Pat Thompson, Arizona State University
- Alejandro Uribe, University of Michigan
A year ago, participants in the Mapping the Calculus Curriculum workshop articulated a set of problems in the learning and teaching of calculus. The goal of this follow-up workshop will be to produce pamphlets to guide instructors dealing with these problems. Each pamphlet will include the following sections.
- A discussion of the issue, based on both research and practical classroom experience.
- A discussion of the teaching of the issue, both at the high school and college levels.
- A set of tasks that could form the basis of a small instructional unit that would help address the issue.
The themes listed below were identified during the Mapping the Calculus Curriculum workshop and will form the basis of the pamphlets.
The role of problem solving in the teaching of calculus
Cognitive, pedagogical, and practical considerations in the use and choice of tasks, from simple calculations that illustrate a procedure to more complex problems that require in-depth understanding of a concept.
The importance and use of symbols in the teaching of calculus
How students' mathematical conceptions and misconceptions are reflected by their use of symbols; how best to teach the language of mathematics; how the ability to use symbols correctly relates to conceptual understanding.
Calculus courses for AP and IB students
Issues related to the design and teaching of high school calculus courses, as well as to the transition from high school to college for students who take AP and IB calculus.
Accumulation and the fundamental theorem of Calculus
Cognitive, pedagogical, and practical considerations in the teaching of the definite integral and the fundamental theorem of calculus.
Understanding rates of change
Conceptual and practical issues related to the teaching of derivatives, rates and related rates, and the chain rule.
Limits, continuity, and approximation
Conceptual and practical (including the use of technology) issues related to the teaching and of limits and continuity; students' understanding of these ideas and the role of approximation in relation to these concepts.
Registration is limited to 35 participants. Applicants are encouraged to attend in pairs consisting of a college or university faculty member and a high school teacher. The Institute for Mathematics and Education will do its best to provide complete support for high school teachers. Each teacher who attends the workshop in its entirety will receive a certificate for 16 hours of professional development credit.
A significant portion of the workshop time will be devoted to group work, including the preparation of a written document, which will discuss the cognitive, pedagogical, and practical aspects of each theme. Interested participants should fill out the application form and indicate which themes they would like to work on.
The workshop will be held at the Institute for Mathematics and Education, Gould-Simpson building, Room 837. Breakfast and/or lunch will be catered at the beginning of each half-day session. The conference dinner will be held on Sunday, March 28.
Lodging will be provided at the Doubletree Hotel Tucson at Reid Park, located 445 S. Alvernon Way, Tucson. Hotel shuttles will transport participants to and from the Institute for Mathematics and Education.
Starts at 12 noon on Saturday, March 27 and ends at 1 pm on Monday, March 29.
- Download the agenda (PDF)
The following articles were produced by the participants and edited by Cody Patterson.
- Mapping the AP / College Calculus Transition (PDF)
- The Fundamental Theorem of Calculus (PDF)
- Limits (PDF)
- Problem Solving (PDF)
- Rates of Change (PDF)
- Cultivating Symbol Sense in Your Calculus Class (PDF)