# Publications

**Articles in Refereed Journals**

Moore, K. C., Stevens, I. E., Paoletti, T., Hobson, N. L. F., & Liang, B. (2019). Pre-service teachers’ figurative and operative graphing actions. *The Journal of Mathematical Behavior. *Available at https://doi.org/10.1016/j.jmathb.2019.01.008

Moore, K. C., Silverman, J., Paoletti, T., Liss, D. R., & Musgrave, S. (2019). Conventions, Habits, and U.S. Teachers’ Meanings For Graphs. *Journal of Mathematical Behavior, *53, 179-195. Available at https://doi.org/10.1016/j.jmathb.2018.08.002

Lee, H., Moore, K. C., & Tasova, H. I. (2019). Reasoning within quantitative frames of reference: The case of Lydia. *The Journal of Mathematical Behavior, 53, 81-95*. Available at https://doi.org/10.1016/j.jmathb.2018.06.001

Paoletti, T. & Moore, K. C. (2018). A covariational understanding of function: Putting a horse before the cart. *For the Learning of Mathematics*, 38 (3), 37-43. Available at https://flm-journal.org/index.php?do=details&lang=en&vol=38&num=3&pages=37-43&ArtID=1202

Paoletti, T., Stevens, I. E., Hobson, N. L. F., Moore, K. C., & LaForest, K. R. (2018). Inverse function: Pre-service teachers' techniques and meanings. *Educational Studies in Mathematics*., 97(1), 93-109. Available at https://doi.org/10.1007/s10649-017-9787-y

Paoletti, T. & Moore, K. C. (2017). The parametric nature of two students' covariational reasoning. *Journal of Mathematical Behavior*, *48*:137-151. Available at https://doi.org/10.1016/j.jmathb.2017.08.003

Paoletti, T. , Stevens, I. E. & Moore, K. C. (2017). Tricks May Inhibit Students' Reasoning. *The Mathematics Teacher,* *110*(6), 446-453. doi:10.5951/mathteacher.110.6.0446

Moore, K. C., LaForest, K. R., & Kim, H. J. (2016). Putting the unit in pre-service teachers’ unit circle. *Educational Studies in Mathematics*, *92*(2), 221–241. Available at https://doi.org/10.1007/s10649-015-9671-6

Moore, K. C., Silverman, J., Paoletti, T., & LaForest, K. R. (2014). Breaking conventions to support quantitative reasoning. *Mathematics Teacher Educator*, 2(2), 141-157. Available at https://www.jstor.org/stable/10.5951/mathteaceduc.2.2.0141

**Refereed Proceedings**

Moore, K. C., Liang, B., Tasova, H. I., & Stevens, I. E. (in press, 2019). Abstracted quantitative structures. In... (Eds.), *Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. XXX-XXX). St. Louis, MO: PUBLISHER.

Liang, B. (in press, 2019). A radical constructivist model of teachers’ mathematical learning through student-teacher interaction. In... (Eds.), *Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. XXX-XXX). St. Louis, MO: PUBLISHER.

Liang, B. (2019). Construction and application perspective: A review of research on teacher knowledge relevant to student-teacher interaction. In Weinberg, A., Moore-Russo, D., Soto, H., & Wawro, M. (Eds.), *Proceedings of the Twenty-Second Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education *(pp. 35-43)*. *Oklahoma City, OK.

Tasova, H. I., Liang, B., & Moore, K. C. (2019). Generalizing actions of forming: Identifying patterns and relationships between quantities. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), *Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education* (pp. 602–610). Oklahoma City, OK.

Stevens, I. E. (2019). The role of multiplicative objects in a formula*. *In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), *Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education* (pp. 273–281). Oklahoma City, OK.

Stevens, I. E. (2019). Using a dynamic geometric context to support students’ constructions of variables*.** *In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.), *Proceedings of the Twenty-Second Annual Conference on Research in Undergraduate Mathematics Education* (pp. 576–585). Oklahoma City, OK.

Tasova, H. I., & Moore, K. M. (2018). Generalization of an invariant relationship between two “quantities.” In T. E. Hodges, G. J. Roy, & A. M. Tyminski, (Eds.), *Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 588–595). Greenville, SC: University of South Carolina & Clemson University.

Stevens, I. E. (2018). The parallelogram problem: Supporting covariational reasoning in the construction of formulas. In Hodges, T. E., Roy, G. J., & Tyminski, A. M.(Eds.)*, Proceedings of the 40 ^{th}annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 624–627). Greenville, SC: University of South Carolina & Clemson University.

Liang, B., Stevens, I. E., Tasova, H. I., & Moore, K. C. (2018). Magnitude reasoning: A pre-calculus student’s quantitative comparison between covarying magnitudes. In Hodges, T. E., Roy, G. J., & Tyminski, A. M. (Eds.)*,Proceedings of the 40 ^{th}annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 608–611). Greenville, SC: University of South Carolina & Clemson University.

Paoletti, T., & Moore, K. C. (2018). A covariational understanding of function: Putting a horse before the cart. In Hodges, T.E., Roy, G.J., Tyminski, A.M. (Eds.), *Proceedings of the 40th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 203–206). University of South Carolina & Clemson University, Greenville, SC,

Hobson, N. (2018). Constant rate of change: The reasoning of a former teacher and current doctoral student. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), *Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education *(pp. 1668-1669). San Diego, CA.

Liang, B. & Moore, K. C. (2018). Figurative thought and a student’s reasoning of “amounts” of change. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), *Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education (pp. 271-285)*. San Diego, CA.

Paoletti, T. (2018). Katlyn’s inverse dilemma: School mathematics versus quantitative reasoning. *Proceedings of the Twenty-First Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (SIGMAA on RUME) Conference (pp. 360-367)*. San Diego, CA.

Paoletti, T., Silverman, J., Moore, K. C., Liss, D. R., Musgrave, S., Vishnubhotla, M., & Rahman, Z. (2018). Conventions or constraints? Pre-service and in-service teachers’ understandings. *Proceedings of the Twenty-First Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (SIGMAA on RUME) Conference (pp. 87-101)*. San Diego, CA.

Paoletti, T., Silverman, J., Moore, K. C., Vishnubhotla, M., Rahman, Z., Monahan, C., & Germia, E. F. (2018). Reasoning about quantities or conventions: Investigating shifts in in-service teachers’ meanings after an on-line graduate course. *Proceedings of the Twenty-First Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (SIGMAA on RUME) Conference (pp. 508-516)*. San Diego, CA.

Stevens, I. E. (2018). Insights into students' images of a geometric object and its formula from a covariational reasoning perspective. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), *Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education (pp. 997-1005)*. San Diego, CA.

Tasova, H., Stevens, I. E., & Moore, K. C. (2018).* *A framework for analyzing written curriculum from a shape-thinking and (co)variational reasoning perspective*. *In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), *Proceedings of the Twenty-First Annual Conference on Research in Undergraduate Mathematics Education (pp. 1527-1533)*. San Diego, CA.

Hardison, H., Stevens, I. E., Lee, H. Y., & Moore, K. C. (2017). Lydia's circle concept: The intersection of figurative thought and covariational reasoning. In E. Galindo & J. Newton (Eds.), *Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 391). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Lee, H. Y., Tasova, H., & Moore, K. C. (2017).* *Reasoning within quantitative frames of reference and graphing: The case of Lydia. In E. Galindo & J. Newton (Eds.), *Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 753-756). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Liang, B. & Moore, K.C. (2017). Reasoning with change as it relates to partitioning activity. In E. Galindo & J. Newton (Eds.), *Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 303-306). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Paoletti, T. (2017). Quantitative reasoning and inverse function: A mismatch. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 973–976). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Paoletti, T., Silverman, J., Monahan, C., Rahman, Z., Vishnubhotla, M., & Germia, E. F. (2017). Graphing rules or understandings? Teachers understandings. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (p. 536). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Stevens, I. E. & Moore, K. C. (2017). The intersection between quantification and an all-encompassing meaning for a graph. In E. Galindo & J. Newton (Eds.),

Stevens, I. E. (2017). A critical examination of the critiques of radical constructivismas an epistemology for education. In Kaur, B., Ho, W. K., Toh T.L., & Choy, B.H. (Eds.). *Proceedings of the 41 ^{st} Conference of the International Group for the Psychology of Mathematics Education*,

*Vol 1, p. 270. Singapore: PME.*

Stevens, I. E., Paoletti, T., Moore, K. C., Liang, B. & Hardison, H. (2017). Principles for designing tasks that promote covariational reasoning. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education (pp. 928-936). San Diego, CA.

Hobson, N. L. F. & Moore, K. C. (2017). Exploring experts’ covariational reasoning. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro & S. Brown (Eds.), Proceedings of the 20th Annual Conference on Research in Undergraduate Mathematics Education (pp. 664-672). San Diego, CA.

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.

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 Groups for the Psychology of Mathematics Education, Vol. 3, pp. 323-330. Szeged, Hungary: PME.

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

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.

Stevens, I. E., & Moore, K. C. (2016). Undergraduate students' graphing habits. *Proceedings of the 13th International Congress on Mathematical Education*. Hamburg, Germany.

Moore, K. C., Stevens, I. E., Paoletti, T. & Hobson, N. L. F. (2016). Graphing habits: “I just don’t like that”. In (Eds.) T. Fukawa-Connelly, N. Infante, M. Wawro, and S. Brown, *Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education*, Pittsburgh, Pennsylvania.

Paoletti, T., & Moore, K. C. (2016). Covariational and parametric reasoning.* 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 MathematicsEducation *(pp. 518–525). East Lansing, MI: Michigan State 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.,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.

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.,& 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.

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.

Paoletti, T.** **(2015)** **Students’ reasoning when constructing quantitatively richsituations. 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.

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.

**Published Abstracts**

Tasova, H. I., Liang, B., Stevens, I. E., & Moore, K. C. (2019). Undergraduate students’ quantitative comparisons of covarying quantities’ magnitudes. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 40(1), 421.

Moore, K. C., Stevens, I. E., Liang, B., & Tasova, H. I. (2019). Concept construction and abstracted quantitative structures. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 40(1), 421.

Hobson, N. L. F. (2018). "The slope is increasing"--Students' takeaways from Calculus. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 39(1), 464-465.

Moore, K. C. (2018). Visualization: Constructing what is "out there". In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 39(1),362.

Stevens, I. E. (2018). How a pre-calculus student was able to reason about rates of change using magnitudes. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 39(1), 466-467.

Tasova, H. & Moore, K. C. (2018). Justification of an invariant relationship between two quantities: Coordinating quantities vs. steepness of tangent lines. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 39(1), 462.

Hobson, N. & Moore, K. C. (2017). Exploring Experts’ Reasoning in Modeling Dynamic Situations. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 38(1), 462.

Liang, B. & Moore, K. C. (2017). Rate of change as a feature of partitioning activity: The case of Lydia. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 38(1), 462.

Moore, K. C. (2017). Graphing and fostering operative thought. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 38(1), 463.

Stevens, I. E. & Moore, K. C. (2017). A case study: When graphs contain everything. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. *Abstracts of Papers Presented to the American Mathematical Society*, 38(1), 461-462.

Moore, K. C.(2016). Graphing habits and students’ thinking about graphs emergently. *Abstracts of Papers Presented to the American Mathematical Society*, 37(1),434.

**UnPublished Thesis**

Maudldin, K. D. (2018) Characterizing preservice teachers' quantitative reasoning evident in graphing activity (Unpublished master's thesis). University of Georgia, Athens, GA.

Hobson, N. L. F. (2017). Quantities and covariation: An inquiry into the reasoning of experts engaged in graphically representing dynamic situations (Unpublished master's thesis). University of Georgia, Athens, GA.

**UnPublished Dissertation**

Paoletti, T. (2015). Pre-service teachers' development of bidirectional reasoning (Unpublished dissertation). University of Georgia, Athens, GA.