University of Arizona
Institute for Mathematics and Education

Mapping the Calculus Curriculum

April 18–20, 2009, Tucson, Arizona

About this workshop

Participants will articulate a set of problems in the learning and teaching of calculus and their conceptual basis (e.g., what are some of the difficulties students encounter in understanding the integral as accumulation of change? How do students' lack of understanding the concept of function affect their understanding of other ideas in calculus?).

In a follow-up workshop in 2010, participants will produce guide pamphlets to help instructors deal with the problems identified at this workshop.


Saturday, April 18

Input from participants
12 – 1 pm: Light lunch and welcome
1 – 3 pm: Brief presentations in which participants describe their own background as researchers and educators, and give illustrative examples of issues encountered in the teaching of calculus.
3 – 3:30 pm: Break
3:30 – 5 pm: Continuation of brief presentations (the time allotted for each presentation will depend on number of participants)
5 - 6 pm: Organizers only: summarize input from brief presentations and organize them into themes related to the papers that will be presented on the next day.

Sunday, April 19

Discussion of research papers in relation to issues raised by the participants
9 – 9:45 am: Inconsistencies in the learning of calculus and analysis, by D. Tall (1990). Presenter: Bill McCallum
9:45 – 10:30 am: Images of rate and operational understanding of the Fundamental Theorem of Calculus, by P.W. Thompson (1994). Presenter: Pat Thompson
10:30 – 11 am: Break
11 – 11:45 am:Conceptual knowledge in introductory calculus, by P. White and M. Mitchelmore (1996). Presenter: Annie Selden
11:45 am – 12:30 pm: The concept of accumulation in calculus, by P.W. Thompson and J. Silverman (2008). Presenter: Jim McClure
12:30 – 2 pm: Lunch break
2 – 3:30 pm: Discussion (moderators: G. Harel & P. Thompson)
3:30 – 4:00 pm: Break
4 – 6 pm: Group work to formulate the teaching and learning issues discussed during the workshop and proposed solutions

Monday, April 20

Presentation (15 minutes) by each group and discussion with the audience (15 minutes)
9 – 10:30 am: Groups 1, 2, and 3
10:30 – 11am: Break
11 am – 11:30 am: Groups 4 & 5
11:30 – 12:00 pm: Concluding remarks

In preparation for the workshop: Participants should prepare a brief presentation describing one or more specific examples of concepts or topics that either the students have difficulties learning, or the teachers have difficulties teaching. In each case, the participant should provide a precise description of the mathematics involved, of the learning and teaching issues encountered, and of why it is important to teach this particular topic/concept.


The Institute for Mathematics and Education in the Gould Simpson Building at the University of Arizona, Room 837.

Lodging provided at the Four Points Sheraton located at 1900 East Speedway Blvd

Organizing Committee


Group 1

Group 2

Group 3

Group 4

Group 5

Group 6

Report on “Inconsistencies in the Learning of Calculus and Analysis”

“Conceptual Knowledge in Introductory Calculus”