Kyeong Hah Roh’s primary research interest is in undergraduate students’ cognitive development in advanced mathematics with particular attention to mathematical logic and argumentation. She has developed curricular materials and instructional interventions for proof-oriented undergraduate mathematics courses such as advanced calculus, geometry, and mathematical proofs. She has conducted teaching experiments to implement these educational innovations for student-centered, inquiry-based, learning. Her research aims not only to help students have deeper understanding of mathematics and mathematical practice but also to help mathematics teachers support their students’ learning of advanced mathematics topics and mathematical representations.
The overall goals of my research in mathematics education are (1) to better understand undergraduate students intuitive understanding of abstract mathematics concepts, (2) to use the knowledge gained to develop educational innovations for the teaching and learning of proof-oriented mathematics courses, and therefore (3) to bridge gaps between the lower division and upper division of undergraduate mathematics courses. I have conducted research on discovering how undergraduate students develop their intuition and visual reasoning while learning definitions of limits and continuous functions. Using the knowledge gained from my research, I have developed educational innovations for mathematical logic, proving structures, and formal definitions of advanced calculus topics. My current research focuses on (1) students interpretations of conditional statements with multiple quantifiers, which are frequently found in mathematics texts, (2) the role of informal reasoning, including intuitive understanding and visual reasoning, and the logical decision power, in learning the mathematical ideas and constructing mathematical arguments or proofs. I believe that students' development of mathematical intuition and mathematical logic would be foundational to advance undergraduate students' successful transition to the learning of advanced mathematics ideas.
Dawkins, P., & Roh, K. (2019). How do students make meaning for multiply quantified statements in mathematics? To appear to the proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education to be held in Oklahoma City, OK.
David, E., Roh, K., & Sellers, M. (in press). Teaching the representations of concepts in calculus: The case of the intermediate value theorem. To appear to Problems, Resources, and Issues in Mathematics Undergraduate Studies.
David, E., Roh, K., & Sellers, M. (in press). Value-thinking and location-thinking: A framework and a study of two ways students visualize points and think about graphs. Journal of Mathematical Behavior.
Sellers, M., Roh, K., & David, E. (2018). Various meanings a student uses for quantified variables in calculus statement: The case of Zack. Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 580-587). Greenville, SC.
David, E., Roh, K., & Sellers, M. (2018). How do undergraduate students make sense of points on graphs in calculus context? Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 524-531). Greenville, SC.
Roh, K., & Lee, Y. (2018). Cognitive consistency and its relationships to knowledge of logical equivalence and mathematical validity. Proceedings for 21st annual Conference on Research in Undergraduate Mathematics Education. San Diego, CA.
Sellers, M., Roh, K., & David, E. (2017). A comparison of Calculus, Transition-to-Proof, and Advanced Calculus Student Quantifications in complex mathematical statements. Proceedings for 20th annual Conference on Research in Undergraduate Mathematics Education held in San Diego, CA.
David, E., Roh, K., & Sellers, M. (2017). The role of visual reasoning in evaluating complex mathematical statements: A comparison of two advanced calculus students. Proceedings for 20th annual Conference on Research in Undergraduate Mathematics Education held in San Diego, CA.
Roh, K., & Lee, Y. (2017). Designing tasks of introductory real analysis to bridge a gap between students’ intuition and mathematical rigor: The case of the convergence of a sequence. International Journal of Research on Undergraduate Mathematics Education­, 3, 34-68.
Dawkins, P., & Roh, K. (2016). Promoting meta-linguistic and meta-mathematical reasoning in proof-oriented mathematics courses: A method and a framework. International Journal of Research in Undergraduate Mathematics Education, 2, 197-222.
Roh, K., Lee, Y., & Tanner, A. (2016). The King and Prisoner story: A way of introducing the components of logical structures. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 26, 424-436.
Roh, K., & Lee, Y. (2015). Undergraduate students’ construction of existence proofs. Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education held in Pittsburgh, PA.
Zandieh, M., Roh, K., & Knapp, J. (2014). Conceptual blending: Student reasoning when proving "conditional implies conditional" statements. Journal of Mathematical Behavior, 33, 209-229.
Halani, A., Davis, O., & Roh, K. (2013). Critiquing the reasoning of others: Devil’s Advocate and Peer interpretations as instructional interventions. Proceedings of the 16th Annual Conference on Research in Undergraduate Mathematics Education.
Dawkins, P., & Roh, K. (2013). Using metaphors to support students’ ability to reason about logic. Proceedings of the 16th Annual Conference on Research in Undergraduate Mathematics Education.
Roh, K., & Lee, Y. H. (2011). The Mayan activity: A way of teaching multiple quantifications in logical contexts. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 21, 1-14.
Roh, K. & Lee, Y. H. (2011) Development of students' understanding of the logic in the epsilon-N definition of limit. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education.
Zandieh, M., Roh, K., & Knapp, J. (2011). Using conceptual blending to analyze student proving. Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
Dawkins, P., & Roh, K. (2011). Mechanisms for Scientific Debate in Real Analysis Classrooms. Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education.
Roh, K. (2010). An empirical study on students’ understanding of a logical structure in mathematics: The relationship between epsilon and N in the definition of the limit of a sequence. Educational Studies in Mathematics, 73, 263-279.
Roh, K. (2010). How to help students conceptualize the rigorous definition of the limit of a sequence. Problems, Resources, and Issues in Mathematics Undergraduate Studies, 20, 473-487.
Roh, K. (2010). College students’ reflective activity in advanced mathematics. Proceedings of the 32nd Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education.
Roh, K. (2010). Why does the order of variables matter in logical contexts? A case of the limit of a sequence. Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education.
Roh, K. (2009). Students' understanding and use of logic in evaluation of proofs about convergence. Proceedings of ICMI Study 19: Proof and proving in mathematics education.
Choi, H., Choi, S., Han, C., Kim, T.-W., Kwon, S., Moon, H., Roh, K., & Wee. N. (2008). Two-dimensional offsets and medial axis transform. Advances in Computational Mathematics, 28, 171-199.
Roh, K. (2008). Students’ images and their understanding of definitions of the limit of a sequence. Educational Studies in Mathematics, 69, 217-233.
Choi, H., Han, C. Moon, H., Roh, K., & Wee. N. (1999). Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves, Computer-Aided Design, 31, 59-72.
Carlson,Marilyn P*, Boggess,Albert, Gardner,Carl L, Jackiewicz,Zdzislaw, Milner,Fabio Augusto, Roh,Kyeong Hah, Saldanha,Luis, Thompson,Patrick W, Van De Sande,Carla. Pathways to Preparing Future Mathematics Faculty to Transform Undergraduate Mathematics Teaching and Learning. NSF-EHR-DUE(9/1/2013 - 8/31/2018).
Roh,Kyeong Hah*, Spielberg,John Samuel. The Design of Research Based Curriculum for Real Analysis. NSF-EHR-DUE(7/15/2009 - 6/30/2013).
Carlson,Marilyn P*, Atkinson,Robert Kenneth, Baker,Dale Rose, Bauer II,Richard C, Bauer II,Richard C, Birk,James Peter, Bloom,Irene, Burns,Hillary Dockser, Burrows,Veronica Ann, Buskirk,Trent David, Carpenter,Ray W, Chizmeshya,Andrew V, Chizmeshya,Andrew V, Clark,Douglas B, Culbertson,Robert John, Gomez,Luanna Soledad, Haag,Susan G, Halloun,Ibrahim, Horan,John Joseph, Horan,John Joseph, Hurlbert,Glenn Howland, Judson,Eugene E, Krause,Stephen, Krause,Stephen, Kuang,Yang, Lawson,Anton Eric, Lohr,Sharon Lynn, Mckelvy,Michael J, Mckelvy,Michael J, Middleton,James Arthur, Middleton,James Arthur, Oehrtman,Michael, Pizziconi,Vincent B, Ramirez,Nora G, Ramirez,Nora G, Reynolds,Stephen James, Roh,Kyeong Hah, Rutowski,Ronald L, Semken,Steven, Sloane,Finbarr, Smith,Hal L, Thompson,Patrick W, Wilcox,Kristine, Wilcox,Kristine, Wyckoff,Susan, Zandieh,Michelle Jeanette. Project Pathways: Opening Routes to Math and Science Success for all Students. NSF-EHR(9/15/2004 - 6/30/2008).
Paul Dawkins & Kyeong Hah Roh. Using metaphors to support students ability to reason about logic. The 16th Annual Conference on Research in Undergraduate Mathematics Education (RUME) (Feb 2013).
Aviva Halani, Owen Davis, & Kyeong Hah Roh. Critiquing the reasoning of others: Devils Advocate and Peer interpretations as instructional interventions. The 16th Annual Conference on Research in Undergraduate Mathematics Education (RUME) (Feb 2013).
Kyeong Hah Roh. Design experiment for developing instructional intervention for inquiry-based learning. Department of Mathematics Education, Korean National Education University, Cheong Ju, Korea (Oct 2011).