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 40thannual 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 40thannual 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.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 709-716). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

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 41st 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.