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Demonstrating Understanding in AP Calculus Free Response Questions

Thursday, July 27, 1:00 p.m. – 2:20 p.m., Boulevard A

How do students demonstrate understanding of concepts in calculus? What assessment items provide evidence of what students know and can do relative to the “big ideas” in calculus? Workshop participants will examine actual student work from AP calculus assessments and consider how to ensure that it is scored consistently and accurately in a way that measures student understanding. Through this process, workshop participants will also better understand what AP Calculus students know and are able to do, which informs faculty who teach these students as they transition to mathematics classes at their respective colleges. Participants will also have the opportunity to dialogue with members of the AP Calculus Development Committee – the eight college faculty and high school teachers involved in the AP Calculus exam development process – particularly with respect to item writing and the calculus knowledge targeted, the introduction of the new curriculum framework for AP Calculus, and mathematical skills and practices.

James Sellers, The Pennsylvania State University

Stephen Davis, Davidson College

What’s the Story? A Graduate Student Workshop on Formulating a Research Presentation for an Undergraduate Audience

Thursday, July 27, 2:35 p.m. – 3:55 p.m., Boulevard A

Presenting recent and ongoing research to undergraduate students is fun and rewarding, but frequently challenging. The gory details of mathematical results often require a great deal of specific jargon and background knowledge. Nonetheless, the big idea-the “story”-can almost always be presented at a variety of levels. This workshop is designed to help graduate students formulate a presentation on their research that is appropriate for an audience of undergraduate students, something many colleges and universities require as part of a job interview. Moreover, the ability to communicate complex mathematical ideas is a valued trait in any context. As such, this session aims to develop a framework for creating an engaging and accessible presentation for undergraduates. Graduate students who will be going on the job market in the fall may find this workshop especially useful.

May Mei, Denison University
Aliza Steurer, Dominican University

Examples and Experiences in Teaching a Modeling-Based Differential Equations Course

Friday, July 28, 1:00 p.m. – 2:20 p.m., Boulevard A

This workshop will give participants an opportunity to actively experience what it is like to learn and teach in a modeling-based differential equations environment. We will do this with engaging learning examples, situations in which modeling gives rise to mathematics, and examples of approaches taken by colleagues who have taught this way. The rich Modeling Scenarios from the SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations community at will serve as examples and working opportunities. The examples offered will involve participants generating and collecting data through experiments, building a mathematical model, estimating parameters, validating the model, and creating the need for learning more about differential equations as a direct result of the modeling activity. The collegial narratives which demonstrate the effectiveness of using modeling to motivate the study of differential equations will be taken from a number of different school settings. Workshop participants will leave with a wealth of examples they can use to offer a modeling-based approach in their own teaching of differential equations.

Rosemary Farley, Manhattan College
Therese Shelton, Southwestern University
Patrice Tiffany, Manhattan College
Brian Winkel, SIMIODE