## 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.

## Program

#### 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.