Let’s Draw a Picture

Abstract

In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let’s draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their impact on student work are presented.

Keywords:

• Number lines
• analysis
• visual representations

ACKNOWLEDGEMENTS

The authors would like to thank the reviewers whose detailed and thoughtful comments significantly improved the clarity of the final version.

Additional information

Notes on contributors

Christine A. Herrera

Christine A. Herrera earned her Ph.D. in mathematics education from Texas State University in 2016 and is now an assistant professor at California State University, Chico.

Terrance McCabe

Terrance McCabe earned a Ph.D. in functional analysis in 1988 at University of North Texas. He learned the Moore Method studying under John Neuberger and William Mahavier, which he now employs as assistant professor at Texas State University.

Sharon Strictland

Sharon Strickland, an associate professor at Texas State University, received her Ph.D. from Michigan State University in 2008. Her research seeks to better understand and strengthen the pedagogical experiences of students in undergraduate mathematics, especially those that seek to become teachers and/or mathematics majors.

Alexander White

Alexander White graduated with a Ph.D. in statistics from Michigan State in 1999. He developed an interest in visualizing functions while at American University and now is an associate professor at Texas State University.