# Interview Tasks

**Instructions: **

Click the images below to view an animation for each task. For access to the animations, please email Dr. Kevin Moore (kvcmoore at uga.edu). Materials for students (Student Version) and interviewers (Protocol Version) can be accessed using the links below each image. The tables at the bottom of the page provide information organized by task. You can click on the citations to read about tasks of interest.

# Articles by Task

## Task

## Article Name (Journal Articles in bold)

### Which One?

Stevens, I. E., Paoletti, T., Moore, K. C., Liang, B., & Hardison, H. (in press). Principles for designing tasks that promote covariational reasoning. *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education. *

### Taking a Ride*

Stevens, I. E., & Moore, K. C. (2016). The Ferris wheel and justifications of curvature. In M. B. Wood, E. E. Turner, M. Civil, & J. A. Eli (Eds.), *Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 644-651). Tucson, AZ: The University of Arizona.

Stevens, I. E., Paoletti, T., Moore, K. C., Liang, B., & Hardison, H. (in press). Principles for designing tasks that promote covariational reasoning. *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education*.

Hobson, N. & Moore, K. C. (in press). Exploring Experts’ Covariational Reasoning*.* *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education*.

### Taking a Square Ride

Hobson, N. & Moore, K. C. (in press). Exploring Experts’ Covariational Reasoning*.* *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education.*

### The Cone Problem

Moore, K. C., Paoletti, T., Stevens, I. E., Hobson, N. L. F. (in press).* *Graphing habits: “I just don’t like that”*. Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education*. Pittsburgh, PA: West Virginia University.

Paoletti, T., Mauldin, K. D., Moore, K. C., Stevens, I. E., Hobson, N. L. F., & LaForest, K. R. (2015).* *Changing cones: Students’ images of a dynamic situation.In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 427). East Lansing, MI: Michigan State University.

Stevens, I. E., Hobson, N. L. F., Moore, K. C., Paoletti, T., LaForest, K. R., & Mauldin, K. D. (2015).* *Changing cones: Themes in students' representation of a dynamic situation*. *In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 363-370). East Lansing, MI: Michigan State University.

### Going Around Gainesville

Paoletti, T., Moore, K. C., & Stevens, I. E. (2016). Task-design principles for covariational reasoning. *Proceedings of the 13th International Congress on Mathematical Education*. Hamburg, Germany.

Moore, K. C. (2016). Graphing as figurative and operative thought. In Csíkos, C., Rausch, A., & Szitányi, J. (Eds.). *Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, *Vol. 3, pp. 323-330. Szeged, Hungary: PME.

Stevens, I. E., Paoletti, T., Moore, K. C., Liang, B., & Hardison, H. (in press). Principles for designing tasks that promote covariational reasoning. *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education*.

Hobson, N. & Moore, K. C. (in press). Exploring Experts’ Covariational Reasoning*.* *Proceedings of the Twentieth Annual Conference on Research in Undergraduate Mathematics Education*.

Moore, K. C., Paoletti, T., Stevens, I. E., Hobson, N. L. F. (in press). Graphing habits: “I just don’t like that”.* Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education. *Pittsburgh, PA: West Virginia University.

### City Travels**

Moore, K. C., Paoletti, T., Stevens, I. E., Hobson, N. L. F. (in press). Graphing habits: “I just don’t like that”*. Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education*. Pittsburgh, PA: West Virginia University.

Paoletti, T., & Moore, K. C. (in press). Covariational and parametric reasoning.* Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education*. Pittsburgh, PA: West Virginia University.

### Conventions

Moore, K. C., & Thompson, P. W. (2016). Ideas of calculus, and graphs as emergent traces. *Paper presented at the 13th International Congress on Mathematical Education*. Hamburg, Germany.

Moore, K. C. (2016). Graphing as figurative and operative thought. In Csíkos, C., Rausch, A., & Szitányi, J. (Eds.). *Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, *Vol. 3, pp. 323-330. Szeged, Hungary: PME.

Paoletti, T., Stevens, I. E., Hobson, N. L. F., Moore, K. C., & LaForest, K. R. (Accepted with revisions). Pre-Service Teachers’ Inverse Function Meanings. *Educational Studies in Mathematics*.

Paoletti, T., Stevens, I. E., & Moore, K. C. (2017). Tricks may inhibit students’ reasoning. *Mathematics Teacher*. 110(6), 447–453.

Moore, K. C., Paoletti, T., Stevens, I. E., Hobson, N. L. F. (in press). Graphing habits: “I just don’t like that”. *Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education*. Pittsburgh, PA: West Virginia University.

Moore, K. C., & Silverman, J. (2015). Maintaining conventions and constraining abstraction. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (*pp. 518-525). East Lansing, MI: Michigan State University.

Moore, K. C., & Thompson, P. W. (2015). Shape thinking and students' graphing activity. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.), *Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education *(pp. 782-789). Pittsburgh, PA: West Virginia University.

Paoletti, T. (2015). Reasoning quantitatively to develop inverse function meanings. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.),* Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 780-787). *East Lansing, MI: Michigan State University.

Paoletti, T., Stevens, I. E., Hobson, N. L. F., Moore, K. C., & LaForest, K. R. (2015). Pre-service teachers' inverse function meanings. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.),* Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education* (pp. 853-867). Pittsburgh, PA: West Virginia University.

Stevens, I. E., LaForest, K. R., Hobson, N. L. F., Paoletti, T., & Moore, K. C. (2015). Undergraduate students’ inverse strategies and meanings. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(p. 262). East Lansing, MI: Michigan State University.

**Moore, K. C., Silverman, J., Paoletti, T., & LaForest, K. R. (2014). Breaking conventions to support quantitative reasoning. Mathematics Teacher Educator, 2(2), 141-157.**

### Bottle Problem***

Paoletti, T., & Moore, K. C. (in press). Covariational and parametric reasoning. *Proceedings of the Nineteenth Annual Conference on Research in Undergraduate Mathematics Education. *Pittsburgh, PA: West Virginia University.

Moore, K. C., & Paoletti, T. (2015). Bidirectionality and covariational reasoning. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.), *Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education *(pp. 774-781). Pittsburgh, PA: West Virginia University.

### Power Tower****

Paoletti, T., Stevens, I. E., & Moore, K. C. (2017). Tricks may inhibit students’ reasoning. *Mathematics Teacher*. 110(6), 447–453.

Paoletti, T.** **(2015)** **Students’ reasoning when constructing quantitatively rich situations. In T. Fukawa-Connolly, N. E. Infante, K. Keene, & M. Zandieh (Eds.), *Proceedings of the Eighteenth Annual Conference on Research in Undergraduate Mathematics Education *(pp. 845-852). Pittsburgh, PA: West Virginia University.

**Moore, K. C., Silverman, J., Paoletti, T., & LaForest, K. R. (2014). Breaking conventions to support quantitative reasoning. Mathematics Teacher Educator, 2(2), 141-157.**

*

Thank you to Desmos for giving permission to use their animation for this study. (Click here to see Demos animations and related tasks.)

**

Saldanha, L. A., & Thompson, P. W. (1998). Re-thinking co-variation from a quantitative perspective: Simultaneous continuous

variation. In S. B. Berensen, K. R. Dawkings, M. Blanton, W. N. Coulombe, J. Kolb, K. Norwood, & L. Stiff (Eds.), *Proceedings of the 20th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics *

*Education* (Vol. 1, pp. 298-303). Columbus, OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

***

Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. *Journal for Research in Mathematics Education, 33*(5), 352-378.

Carlson, M. P., Larsen, S., & Lesh, R. A. (2003). Integrating a models and modeling perspective with existing research and practice. In R. Lesh & H. M. Doerr (Eds.), *Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching.* (pp. 465-478). Mahwah, NJ: Lawrence Erlbaum Associates.

Heid, M. K., Lunt, J., Portnoy, N., & Zembat, I. O. (2006). Ways in which prospective secondary mathematics teachers deal with mathematical complexity. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. Méndez (Eds.), 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 2-9). Mérida, Mexico.

Johnson, H. L. (2015). Together yet separate: Students' associating amounts of change in quantities involved in rate of change. *Educational Studies in Mathematics, 89*(1), 89-110. doi: 10.1007/s10649-014-9590-y

Shell Centre for Mathematical Education (University of Nottingham). (1985). The language of functions and graphs: An examination module for secondary schools: Nottingham, UK: JMB/Shell Centre for Mathematical Education.

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Thank you to Patrick W. Thompson for inspiring this task. The task is an adaptation of a task he used for professional development with teachers. (Click here for more task ideas.)