Ellis, A.B., Horne, D., Bloodworth, A., Nielsen, A., & Ely, R. (Accepted). Playful math: Modeling students’ engagement in play-based algebra activities. To appear in the Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

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Ely, R., & Ellis, A.B. (Accepted). Playful mathematics and learning. To appear in the Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

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Ellis, A.B. (2022). Generalizing beyond body-supported dimensions. In A. Simpson (chair), C. Williams-Pierce, E. Shokeen, N. Katirci, H. Soto, J. Baker, D. DeLiema, M. Kapur, A. Ellis, E. Lockwodoo, D. Plaxco, M. Alibali, & D. Ramirez, The Nature(s) of Embodied Mathematical Failure. In C. Chinn, E. Tan, C. Chain, & Y. Kali (Eds.), 16th International Conference of the Learning Sciences (ICLS) 2022, ICLS Proceedings, pp. 1787 – 1793.

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Ellis, A.B., Ying, Y., Wawsa, A., Moore, K., Hamilton, M., Tasova, H., & Çelik, A. (2021). Classroom supports for generalizing. In Olanoff, D., Johnson, K., & Spitzer, S. (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1420 – 1429), Philadelphia, PA.

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Tasova, H., Ellis, A.B., Hamilton, M., Moore, K., Wawsa, A., Çelik, A., & Ying, Y. (2021). A serendipitous mistake: How one teacher’s beliefs and knowledge mediated her in-the-moment instruction. In Olanoff, D., Johnson, K., & Spitzer, S. (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1574 – 1579), Philadelphia, PA.

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Hamilton, M., Moore, K., Ellis, A.B., Ying, Y., Tasova, H.I., Çelik, A., & Wawsa, A. (2021). Supporting generalizing in the classroom: One teacher's beliefs and instructional practice. In  Olanoff, D., Johnson, K., & Spitzer, S. (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1536 – 1541), Philadelphia, PA.

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Plaxco, D., Reimer, P.N., Williams-Pierce, C., Ellis, A.B., Molitoris-Miller, S., Simpson, A., Zandieh, M., Mauntel, M., & Dogan, M.F. (2021). Mathematical play: Across ages, context, and content. In Olanoff, D., Johnson, K., & Spitzer, S. (Eds.), Proceedings of the Forty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1913 – 1915), Philadelphia, PA.

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Williams-Pierce, C., Dogan, M.F., & Ellis, A.B. (2021). Multimodal generalizing in a mathematical videogame. In E. de Vries, E., Y. Hod, & J. Ahn (Eds.), Proceedings of the 15th International Conference of the Learning Sciences (pp. 641-644). Bochum, Germany: International Society of the Learning Sciences.

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Ellis, A.B., & Lockwood, E. (2020). Beyond patterns: Making sense of pattern-based generalizations through empirical re-conceptualization. To appear in the Proceedings of the 42nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico. ​Cinvestav / AMIUTEM / PME-NA (pp. 981 - 985). Mazatlan, Mexico.

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Fonger, N., & Ellis, A.B. (2020). Amidst multiple metaphors for learning trajectories research. To appear in the Proceedings of the 42nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico. Cinvestav / AMIUTEM / PME-NA (pp. 2325 - 2329). Mazatlan, Mexico.

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Plaxco, D., Reimer, P.N., Williams-Pierce, C., Ellis, A.B., Molitoris-Miller, S., Simpson, A., Zandieh, M., Mauntel, M., & Dogan, M.F. (2020). Mathematical play: Across ages, context, and content. To appear in the Proceedings of the 42nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Mexico. Cinvestav / AMIUTEM / PME-NA (pp. 178 - 180). Mazatlan, Mexico.

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Ellis, A.B., Lockwood, E., & Lynch, A.G. (2020). Empirical Re-Conceptualization: Bridging from Empirical Patterns to Insight and Understanding. In S. Cook (Ed.), Proceedings of the twenty-third Annual Conference on Research in Undergraduate Mathematics Education, (pp. 1593 - 1596). Boston, MA: Boston University.

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Ellis, A.B., Lockwood, E., & Lynch, A. (2020). Empirical Re-Conceptualization as a Bridge to Insight. In M. Gresalfi & I. Horn (Eds.), The Interdisciplinarity of the Learning Sciences, 14th International Conference of the Learning Sciences (ICLS) 2020, (pp. 159 - 167). Nasheville, TN: Vanderbilt University.

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Ellis, A.B., Fonger, N.F., & Dogan, M.F. (2019). Articulating links between student conceptions and instructional actions in learning trajectories research. In S. Otten, Z. de Araugo, A. Candela, C. Munter, & C. Haines (Eds.), Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1803 – 1808). St. Louis, MO: University of Missouri.​

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Williams-Pierce,C., Plaxco, D., Reimer, P.N., Simpson, A., Orrill, C.H., Burke, J.P. Sinclair, N., Guyevskey, V., & Ellis, A.B. (2019). Mathematical play: Across ages, context, and content. In In S. Otten, Z. de Araugo, A. Candela, C. Munter, & C. Haines (Eds.), Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1979 – 1990). St. Louis, MO: University of Missouri.

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Fonger, N.F., Ellis, A.B., & Dogan, M.F. (2019). Epistemological and methodological foundations of creating a learning trajectory of children’s mathematics. In U.T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6-10, 2019). Utrech, Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

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Ellis, A.B., Ely, R., Singleton, B., & Tasova, H. (2018). Scaling continuous covariation: Supporting middle school students’ algebraic reasoning. In T. Hodges, G. Roy, & A. Tyminski (Eds.), Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 147 – 154). Greenville, SC: University of South Carolina & Clemson University.

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Ellis, A.B., Tasova, H., & Singleton, B. (2018). How quantitative reasoning can support graph understanding in algebra. In T. Hodges, G. Roy, & A. Tyminski (Eds.), Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 195 – 198). Greenville, SC: University of South Carolina & Clemson University.

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Williams-Pierce, C., Plaxco, D., Reimer, P., Ellis, A.B., & Dogan, M.F. (2018). Mathematical play: Across ages, context, and content. 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. 1507 – 1514). Greenville, SC: University of South Carolina & Clemson University.

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Ely, R., & Ellis, A.B. (2018). Scaling-continuous variation: A productive foundation for calculus reasoning. 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. 1180 - 1188. San Diego, CA: San Diego State University.

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Ellis, A.B., Fonger, N., & Dogan, M.F. (2017). Developing function understanding through dependency relations of change. 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. x-y). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

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Fonger, N., Dogan, M.F., & Ellis, A.B. (2017). Students’ clusters of concepts of quadratic functions. . 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. x-y). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

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Ellis, A.B., Tillema, E., Lockwood, E., & Moore, K. (2017). Generalization across domains: The relating-forming-extending framework. . 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. x-y). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

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Fonger, N.L., Ellis, A.B., & Dogan, M.F. (2016). Students’ conceptions supporting their symbolization and meaning of function rules. 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. 156 - 163). Tucson, AZ: The University of Arizona.

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Singleton, B.K., & Ellis, A.B. (2016). Area units without borders: Alternatives to tiling for determining area change in dynamic figures. 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. 294-297). Tucson, AZ: The University of Arizona.

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Ozgur, Z., Reiten, L., & Ellis, A.B. (2015). On framing teacher moves for supporting student reasoning. In T. Bartell & K. Bieda (Eds.), Proceedings of the 37th annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1062 – 1069). East Lansing, MI: Michigan State University.

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Lockwood, E., Lynch, A., Ellis, A.B., & Knuth, E. (2015). Exhaustive example generation: mathematicians’ uses of examples when developing conjectures. In T. Fukawa-Connelly, N. Infante, K. Keene, and M. Zandieh (Eds.), Proceedings of the eighteenth Annual Conference on Research in Undergraduate Mathematics Education, pp. 216 - 230. Pittsburgh, PA: West Virginia University.

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Ellis, A.B., Weber, E., & Lockwood, E. (2014). The case for learning trajectories research. In Oesterle, S., Liljedahl, P., Nicol, C., & Allan, D. (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 3, pp. 1 – 8. Vancouver, Canada: PME.

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Lockwood, E., Lynch, A.G., Ellis, A.B., & Knuth, E. (2014). Mathematicians’ example-related activity in formulating conjectures. In Oesterle, S., Liljedahl, P., Nicol, C., & Allan, D. (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36, Vol. 4, pp. 129 – 136. Vancouver, Canada: PME.

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Ellis, A.B. (2014). What if we built learning trajectories for epistemic students? In L. Hatfield, K. Moore, & L. Steffe (Eds.), Epistemic Algebraic Students: Emerging Models of Students’ Algebraic Knowing, WISDOMe Monographs (Vol. 4, pp. 199 – 207).  Laramie, WY: University of Wyoming.

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Ellis, A.B., Ozgur, Z., Kulow, T., Dogan, M.F., Williams, C., & Amidon, J. (2013). Correspondence and covariation: Quantities changing together. In M. Martinez & A. Superfine (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 119 – 126). Chicago, IL: University of Illinois at Chicago.

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Ellis, A.B., Ozgur, Z., Kulow, T., Williams, C.C.,, & Amidon, J. (2013). An exponential growth learning trajectory. In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 273-280. Kiel, Germany: PME.

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Lockwood, E., Ellis, A.B., Knuth, E., Dogan, M.F., & Williams, C. (2013). Strategically chosen examples lead to proof insight: A case study of a mathematician’s proving process. In M. Martinez & A. Superfine (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 245 – 252). Chicago, IL: University of Illinois at Chicago.

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Ellis, A.B., Lockwood, E., Dogan, M.F., Williams, C.C., & Knuth, E. (2013). Choosing and using examples: How example activity can support proof insight. In Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 265-272. Kiel, Germany: PME.

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Ellis, A.B. (2013). Teaching ratio and proportion in the middle grades. Research Briefs and Clips, National Council of the Teachers of Mathematics.

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Lockwood, E., Ellis, A.B., & Knuth, E. (2013). Mathematicians’ example-related activity when proving conjectures. In S. Brown, G. Karakok, K.H. Roh, and M. Oehrtman (Eds.) Proceedings of the 16th Annual Conference on Research in Undergraduate Mathematics Education (Vol. 1) (pp. 16 – 30). Denver, CO: Northern Colorado University.

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Ellis, A.B., Lockwood, E., Williams, C., Dogan, M.F., & Knuth, E. (2012). Middle school students’ example use in conjecture exploration and justification. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky (Eds.), Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 135 - 142). Kalamazoo, MI: Western Michigan University.

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Lockwood, E., Ellis, A.B., Dogan, M.F., Williams, C., & Knuth, E. (2012). A framework for mathematicians’ example-related activity when exploring and proving mathematical conjectures. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky (Eds.), Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 151 – 158). Kalamazoo, MI: Western Michigan University.

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Ellis, A.B., Ozgur, Z., Kulow, T., Williams, C., & Amidon, J. (2012). Quantifying exponential growth: The case of the jactus. In R. Mayes & L. Hatfield (Eds.), Quantitative Reasoning and Mathematical Modeling: A Driver for STEM Integrated Education and Teaching in Context. (pp. 93 – 112). Laramie, WY: University of Wyoming.

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Ellis, A.B. (2011). Middle school algebra from a functional perspective: A Conceptual analysis of quadratic functions. In L. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 79 – 87). Reno, NV: University of Nevada, Reno.

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Williams, C., Akinsiku, O., Walkington, C., Cooper, J.L., Ellis, A.B., Kalish, C., & Knuth, E. (2011). Understanding students’ similarity and typicality judgments in and out of mathematics. In L. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1180 – 1189). Reno, NV: University of Nevada, Reno.

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Williams, C., Akinsiku, O., Walkington, C., Cooper, J.L., Ellis, A.B., Kalish, C., & Knuth, E. (2011). Understanding students’ similarity and typicality judgments in and out of mathematics. In L. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1180 – 1189). Reno, NV: University of Nevada, Reno.

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Cooper, J., Walkington, C., Williams, C., Akinsiku, O., Kalish, C., Ellis, A.B., & Knuth, E. (2011). Adolescent reasoning in mathematics: Exploring middle school students’ strategic approaches in empirical justifications. In L. Carlson, C. Hölscher, & T. Shipley (Eds.), Proceedings of the 33rd Annual Conference of the Cognitive Science Society (pp. 2188 – 2193). Austin, TX: Cognitive Science Society.

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Ellis, A.B. (2007). Unexpected connections across function families: Students’ generalizations about quadratic data. In Lamberg, T., & Wiest, L.R. (Eds.), Proceedings of the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.

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Ellis, A.B. (2005). Justification as a support for generalizing: Students’ reasoning with linear relationships. In G.M. Lloyd, M.R. Wilson, J.L.M. Wilkins, & S.L. Behm (Eds.), Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education [CD-ROM]. Eugene, OR: All Academic.

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Ellis, A. B. (2001).  An examination of the interaction patterns of a single-gender mathematics class. In R. Speiser, C. Maher, & C. Walter (Eds.), Proceedings of the twenty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 609 - 616). Columbus, OH:  ERIC Clearinghouse for Science, Mathematics, and Environmental Education, SE 065 164.