The manifestation of graph-theoretic methods in mathematics education research

RUME 26, Omaha, NE, February 2024

Background

This project serves as the preliminary literature review for my Ph.D. dissertation project. It has been published in the Proceedings of the 26th Conference on Research in Undergraduate Mathematics Education (Link to Proceedings), and I presented it as a poster at the 26th RUME Conference in Omaha, NE.

Some bullet points:

Inspired by the mathematical definition of a graph, I define a graph-theoretic method as any research method that considers the relationships amongst a set of objects.
I chose to study conference proceedings initially because they represent the raw "grassroots" of research rather than highly polished journal articles. In the near future, I would like to expand this project to include more conference proceedings, and eventually journal articles.
Of the 3,940 publications included in RUME and CERME conference proceedings from 2015-2022, only 80 (about 2%) were considered to meet the criteria for employing graph-theoretic methods.
Six Graph-theoretic methods arose from the analysis:
- Data Visualization: a graph was used to visualize the results of an analysis that was already conducted.
- Flowcharts: directed graphs analyzed without any reference to mathematical digraphs. Used in a visualization capacity.
- Graphs: still used mostly in a visualization capacity. However, some considered the diagrams to have mathematical significance. Additionally, these specifically called the diagrams "graphs" rather than "maps" or "networks".
- Grids: disguised adjacency table/matrix of graphs. These went by various theoretical context-specific names.
- Maps: undirected graphs analyzed without any reference to mathematical graphs. Used in a visualization capacity.
- Network Analysis: specifically referenced the method of network analysis, usually in a social network analysis context.
Despite the rarity of graph-theoretic methods, there is an overwhelming notion that the entire body of mathematics education research looks like a graph. Below are frequencies of specific words that connote mathematical graphs amongst all 3,940 RUME and CERME proceedings from 2015-2022.
- Network appears 1,861 times.
- Connection appears 5,553 times.
- Relationship appears 8,935 times.

This suggests that mathematics education researchers are subconsciously thinking about graphs all the time, even if they don't specifically use graph-theoretic methods in their research.

Because of the relatively small number of publications meeting the criteria for analysis, analyzing trends over time was not feasible.

Figures

These trees present the various graph-theoretic methods below in more detail. The most common method used was to consider graphs as "Maps". While both the "Maps" and "Data Visualization" methods involved visualization without mathematical significance, the difference between the two methods is that "Maps" were directly analyzed in some way, whereas "Data Visualization" was the presentation of an analysis that had already been conducted.

This word cloud visualizes the countries represented by the articles below. In total, 21 countries across 5 continents were represented amongst the 80 publications.

This graph visualizes the relationships among the topics studied by the articles below. Initially, the vertex set was constructed using Open Coding. An edge was drawn between two vertices if a publication involved both topics. The colored vertices are the top seven highest-degree vertices, as determined by Degree Centrality calculations. This gives insight into major themes present amongst topics that have been studied by graph-theoretic methods.

List of Articles Analyzed by Method (SIGMAA-RUME & CERME 2015-2022)

Data Visualization

Choutou, C. & Potari, D. (2022). Boundaries between mathematics and visual art teaching communities. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 3345-3352) Free University of Bozen-Bolzano and ERME.
Harvey, F. & Teledahl, A. (2020). Teacher Professional Development and Collegial Learning: A literature review through the lens of Activity System. 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 (pp. 3331-3338). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Tichá, M. & Hošpesová, A. (2015). Word problems of a given structure in the perspective of teacher training. In K. Krainer & N. Vondrová (Eds.). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9, February 4-8, 2015) (pp. 2916-2922) Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME.
Tuktamyshov, N. (2022). Mathematical picture of the world and understanding. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 3032-3039) Free University of Bozen-Bolzano and ERME.
Van Steenbrugge, H. (2022). Rethinking the notion of textbooks as mediators between the official curriculum and classroom practice. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4050-4057). Free University of Bozen-Bolzano and ERME.

Flowcharts

Anwar, L. & Goedhart, M. (2020). Understanding geometric proofs: scaffolding pre-service mathematics teacher students through dynamic geometry system (dgs) and flowchart proof. 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 (pp. 104-111). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

Graphs

Andrà, C., Magnano, G., Brunetto, D., & Tassone, M. (2022). Mathematical views: a preliminary analysis on undergraduate mathematics students. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 1303-1310) Free University of Bozen-Bolzano and ERME.
Bock, W., Bracke, M., Capraro, P., & Lantau, J. (2020). On the positive influence of product-orientation in mathematical modeling: A research proposal. 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 (pp. 1162-1163). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Brunetto, D., Tassone, M., & Cravero, E. (2022). Community detection for undergraduate mathematical views. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 1327-1328) Free University of Bozen-Bolzano and ERME.
Capone, R. & Lepore, M. (2022). Fuzzy cognitive analysis in undergraduate mathematics class on engagement, motivation, and participation during covid-pandemic. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 1329-1336) Free University of Bozen-Bolzano and ERME.
Datzmann, A. & Brandl, M. (2020). Evaluation of a connecting teaching format in teacher education. 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 (pp. 2462-2463). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Gosztonyi, K. (2020). Conceiving teaching trajectories in the form of series of problems: a step for the theoretical reconstruction of the Hungarian Guided Discovery approach. 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 (pp. 3130-3137). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Johns, G., Nakamura, C., & Grosse, C. (2016). Using the effect sizes of subtasks to compare instructional methods: A network model. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.). Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education (pp. 901-908). Pittsburgh, PA.
Kanwar, P. & Mesa, V. (2022). Mapping student real-time viewing of dynamic textbooks to their utilization schemes of questioning devices. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4002-4003) Free University of Bozen-Bolzano and ERME.
Mamolo, A., Ruttenberg-Rosen, R., & Whiteley, W. (2015). Conceptualizing the notion of a task network. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.). Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 704-711) Pittsburgh, PA.
Przybilla, J., Brandl, M., Vinerean, M., & Liljekvist, Y. (2022). Digital mathematical maps - results from iterative research cycles. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4793-4800) Free University of Bozen-Bolzano and ERME.
Ricca, B.P. & Green, K.H. (2015). Analyzing data from student learning. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.). Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 904-907) Pittsburgh, PA.
Schwarz, A., Brandl, M., Kaiser, T., & Datzmann, A. (2017). Interactive mathematical maps for de-fragmentation. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 2292-2293). Dublin, Ireland: DCU Institute of Education and ERME.

Grids

Aguilar, M.S., Castañeda, A., & González-Polo, R.I. (2017). Research findings associated with the concept of function and their implementation in the design of mathematics textbook tasks. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 3776-3783). Dublin, Ireland: DCU Institute of Education and ERME.
Aoki, M. & Winsløw, C. (2022). How to map larger parts of the mathematics curriculum? The case of primary school arithmetic in Japan. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 328-335) Free University of Bozen-Bolzano and ERME.
Hahn, T. & Eichler, A. (2017). Changes in beliefs of teachers on a PD course after reflecting on students' learning results. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 2884-2891). Dublin, Ireland: DCU Institute of Education and ERME.
Henriksen, B. (2022). Didactic transposition of natural numbers in the first year of compulsory schooling: a case of comparative curricula analysis. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 2192-2199) Free University of Bozen-Bolzano and ERME.
Klöpping, P.M. & Kuzle, A. (2020). Design of repertory grids for research on mathematics teacher conceptions of process-related mathematical thinking. 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 (pp. 3947-3954). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Utsch, N. (2022). Interplay between Concept Image and Concept Definition in Students' Work on Convergence of Sequences. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4837-4844) Free University of Bozen-Bolzano and ERME.
Watson, K.L. & Jones, S.R. (2015). Adding explanatory power to descriptive power: Combining Zandieh’s derivative framework with analogical reasoning. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.). Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 1041-1047). Pittsburgh, PA.

Maps

Andrews-Larson, C. & McCrackin, S. (2018). The Next Time Around: Shifts in Argumentation in Initial and Subsequent Implementations of Inquiry-Oriented Instructional Materials. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 932-940). San Diego, CA.
Barquero, B., Bosch, M., & Wozniak, F. (2020). Modelling praxeologies in teacher education: the cake box. 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 (pp. 1144-1151). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Benölken, R. (2017). Developing student teachers' professional knowledge of low attainments' support by "learning-teaching-laboratories". In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 3264-3271). Dublin, Ireland: DCU Institute of Education and ERME.
Boscolo, A. (2022). Active, bodily experience mathematics learning activites. Looking at implementation from the teachers' perspective. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4103-4110) Free University of Bozen-Bolzano and ERME.
Christensen, W., Farlow, B., Vega, M., & Loverude, M. (2018). Student Resources for Unit and Position Vectors in Cartesian and Non-Cartesian Coordinate Systems. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 1742-1743). San Diego, CA.
Courtney, S.A., Austin, C.K., & Glasener, K.C. (2022). Exploring Teachers' Affective Schemes through a Networking of Theories Approach. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 1337-1344) Free University of Bozen-Bolzano and ERME.
de Moraes Rocha, K. & Trouche, L. (2017). Documentational trajectory: A tool for analyzing the genesis of a teacher's resource system across her collective work. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 3732-3739). Dublin, Ireland: DCU Institute of Education and ERME.
Díez-Palomar, J., Hoogland, K., & Geiger, V. (2020). Numeracy in adult education: discussing related concepts to enrich the Numeracy Assessment Framework. 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 (pp. 1309-1316). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Earls, D., Gates, M., Sager, L., Gaultier, G., Tata, J., Glasmacher, K., & Hunter, K. (2022). Concept Maps of Sequences and Series. In S.S. Karunakaran & A. Higgins (Eds.). Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (pp. 1212-1213) Boston, MA.
Ekici, C. (2019). Building coherence in circular and complex trigonometry with inquiry-based modeling. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.). Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education (pp. 1101-1102) Oklahoma City, OK.
Findley, K. & Kaplan, J. (2018). Cognitive Resources in Student Reasoning about Mean Tendency. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 1345-1351) San Diego, CA.
Florensa, I., Bosch, M., Gascón, J., & Ruiz-Munzon, N. (2017). Teaching didactics to lecturers: A challenging field. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 2001-2008). Dublin, Ireland: DCU Institute of Education and ERME.
Hamann, T. & Schmidt-Thieme, B. (2020). Cross-linking maths: Using keynotes to structure a curriculum for future teachers. 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 (pp. 3321-3322). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Horsman, R. (2022). Collaborative knowledge creation of teacher subject knowledge using concept maps. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 3606-3613) Free University of Bozen-Bolzano and ERME.
Huget, J. (2020). The development of a domain map in probability for teacher education. 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 (pp. 964-971). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Jameson, E., Macey, D., & McClure, L. (2022). Implementing research in the practice of curriculum designers: Barriers and an example approach. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4153-4160) Free University of Bozen-Bolzano and ERME.
Johansson, M., Tossavainen, T., Faarinen, E., & Tossavainen, A. (2020). Student teachers' definitions of the concept "teaching mathematics in preschool". 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 (pp. 2277-2284). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Katona, D. (2020). Web of problem threads (WPT) - a frame and task design tool for inquiry-based learning 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 (pp. 4260-4261). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Lankeit, E. & Biehler, R. (2020). Students' work with a task about logical relations between various concepts of multidimensional differentiability. 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 (pp. 2570-2577). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Lefcourt Ruby, T. & Hadar, L. (2018). Beliefs About Mathematics and Curriculum Goals in the Cognitive Domain: a Case Study of Preservice Secondary Mathematics Teachers. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 677-686) San Diego, CA.
Lefcourt Ruby, T. & Solomon, S. (2017). A Topological Approach to Formal Limits Supported by Technology: What Concept Images do Students Form? 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. 1667-1668) San Diego, CA.
Lyublinskaya, I. & Du, X. (2022). Preservice mathematics teacher's learning trajectories of Technological Pedagogical Content Knowledge (TPACK) in an online educational technology course. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 2578-2585) Free University of Bozen-Bolzano and ERME.
Møller, M. (2022). What characterizes STEM professionalism? In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4631-4638) Free University of Bozen-Bolzano and ERME.
Nakash-Stern, G. & Cohen, A. (2020). Developing MAP for integrating mathematical applets in teaching sequence. 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 (pp. 2723-2730). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Nøhr, L.L., Gregersen, M.O., Tamborg, A.L., Dreyøe, J., & Allsopp, B.B. (2020). Ability maps in the context of curriculum research. 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 (pp. 4292-4293). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Pinkernell, G., Düsi, C., & Vogel, M. (2017). Aspects of proficiency in elementary algebra. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 464-471). Dublin, Ireland: DCU Institute of Education and ERME.
Real, R. & Figueras, O. (2015). A network of notions, concepts, and processes for fractions and rational numbers as interpretation of Didactical Phenomenology. In K. Krainer & N. Vondrová (Eds.). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9, February 4-8, 2015) (pp. 346-353) Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME.
Reit, X. (2017). Towards an empirical validation of mathematics teachers' intuitive assessment practice exemplified by modelling tasks. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 3588-3595). Dublin, Ireland: DCU Institute of Education and ERME.
Rodriguez, J., Stricker, A, & Becker, N. (2020). When covariational reasoning does not "work". In S.S. Karunakaran, Z. Reed, & A. Higgins (Eds.). Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 922-929) Boston, MA.
Schermerhorn, B.P. & Wawro, M. (2022). Students' Conceptual Understanding of Normalization of Vectors from R^2 to C^2. In S.S. Karunakaran & A. Higgins (Eds.). Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (pp. 545-553) Boston, MA.
Solano, S., Gómez, P., & González, M.J. (2020). Alignment of mathematics curriculum to standards at high schools in Colombia. 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 (pp. 4334-4335). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Stephens Serbin, K. (2020). A Prospective Teacher's Mathematical Knowledge for Teaching of Inverse Functions. In S.S. Karunakaran, Z. Reed, & A. Higgins (Eds.). Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 1066-1071) Boston, MA.
Tamborg, A.L., Allsopp, B.B., & Fougt, S.S. (2017). Mapping the logics in practice oriented competence development. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 3873-3880). Dublin, Ireland: DCU Institute of Education and ERME.
van de Weerd, L. & Verhoef, N. (2015). The link between the cognitive structure and modelling to improve mathematics education. In K. Krainer & N. Vondrová (Eds.). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9, February 4-8, 2015) (pp. 930-936) Prague, Czech Republic: Charles University in Prague, Faculty of Education and ERME.
VanDieren, M. & Moore-Russo, D. (2019). Critical features and representations of vectors in student-generated mindmaps. In A. Weinberg, D. Moore-Russo, H. Soto, & M. Wawro (Eds.). Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education (pp. 629-637) Oklahoma City, OK.
Verbisck, J.T., Bittar, M., & Bosch, M. (2022). Learning to teach statistics through study and research paths. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 982-989) Free University of Bozen-Bolzano and ERME.
Wallach, M.N., Heyd-Metzuyanim, E., & Band, R. (2022). Explorative potential of linear algebra tasks. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.). Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 4857-4864) Free University of Bozen-Bolzano and ERME.
Wang, C., Salinas-Hernández, U., & Trouche, L. (2020). From teacher's naming system of resources to teacher's resource system: Contrasting a Chinese and a Mexican case. 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 (pp. 4346-4353). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

Network Analysis

Allsopp, B.B., Dreyøe, J., Tamborg, A.L., Eagan, B., Tabatabai, S., Shaffer, D.W., & Misfeldt, M. (2020). Exploring teachers' assignment of mathematical competencies to planned lessons using Epistemic Network Analysis. 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 (pp. 4162-4169). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.
Apkarian, N. (2015). Social networks among communities of undergraduate mathematics instructors at PhD granting universities. In T. Fukawa-Connelly, N. Infante, K. Keene, & M. Zandieh (Eds.). Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 369-372) Pittsburgh, PA.
Apkarian, N. (2016). Talking about teaching: Social networks of instructors of undergraduate mathematics. In T. Fukawa-Connelly, N. Infante, M. Wawro, & S. Brown (Eds.). Proceedings of the 19th Annual Conference on Research in Undergraduate Mathematics Education (pp. 515-517) Pittsburgh, PA.
Apkarian, N. (2018). Emerging Instructional Leadership in a New Course Coordination System. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, & S. Brown (Eds.) Proceedings of the 21st Annual Conference on Research in Undergraduate Mathematics Education (pp. 1414-1419) San Diego, CA.
Apkarian, N., Rasmussen, C., & Progress Through Calculus Team (2017). Mathematics instruction leadership in undergraduate departments. 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. 485-493) San Diego, CA.
Fetzer, M. & Tiedemann, K. (2017). Talking with objects. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 1284-1291). Dublin, Ireland: DCU Institute of Education and ERME.
Funk, R., Moore-Russo, D., Uhing, K., & Williams, M. (2022). Studying the Potential for Pedagogical Change Based on Perceptions and Proposed Initiatives using the Four Frames. In S.S. Karunakaran & A. Higgins (Eds.). Proceedings of the 24th Annual Conference on Research in Undergraduate Mathematics Education (pp. 970-975) Boston, MA.
Hannula, M.S. & Moreno-Esteva, E.G. (2017). Identifying subgroups of CERME affect research papers. In T. Dooley & G. Gueudet (Eds.). Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME 10, February 1-5, 2017) (pp. 1098-1105). Dublin, Ireland: DCU Institute of Education and ERME.
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