Publications | Nancy Ruo Ning Qiu

2026

Qiu, R. N., Rasmussen, C., Fortune, N., Carney, D., Santos, J., Ponce, M., Jacome, N. & Stewart, M. (2026)

Connecting university and secondary mathematics: design principles for developing prospective teachers’ content knowledge and critical stance

Mathematics Teacher Education and Development, 28, Article 19.

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In this article, we present the design of Inquiry-oriented Dynamical Systems and Modelling (IODSM), an upper-division mathematics content course that can serve as an elective for prospective secondary teachers (PSTs). The course bridges university and secondary mathematics by combining advanced content with structured opportunities to engage secondary mathematics topics, forward-looking teaching practices, and mathematical practices. Grounded in inquiry-based mathematics education and oriented toward fostering productive dispositions such as students’ embracement of a critical stance, IODSM offers a learning environment where PSTs connect mathematics with future teaching. As an Illustration of Practice article, we outline a typical session, describe the theoretical grounding, and highlight four design principles that underpin classroom activities, course materials, and instructional choices. The article concludes with evidence of PSTs’ willingness to critically reflect on their mathematical beliefs and values, resulting in PSTs embracing a critical stance.
@article{qiu2026connecting, author = {Qiu, R. N. and Rasmussen, C. and Fortune, N. and Carney, D. and Santos, J. and Ponce, M. and Jacome, N. and Stewart, M.}, title = {Connecting university and secondary mathematics: Design principles for developing prospective teachers' content knowledge and critical stance}, journal = {Mathematics Teacher Education and Development}, year = {2026}, volume = {28}, number = {3}, pages = {Article 19}, }
Aniceto, R., Qiu, R. N. & Delaney, V. (2026)

Prospective teachers’ model-building of student thinking on sampling distributions

In Proceedings of the Forty-Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1310–1315.

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Prospective secondary teachers (PSTs) should have opportunities to analyze student work and construct “second-order models” of student thinking—that is, the PSTs’ conceptions of students’ thinking as informed by their observations of student work and verbalizations. We detail a qualitative analysis of group discussions from a teaching experiment in a curriculum course for PSTs, where PSTs constructed second-order models of student thinking in response to two hypothetical students’ statements about the sampling distribution. Results indicate that PSTs can build diverse types of second-order models of students’ statistical thinking but need support to identify a range of evidence of students’ knowledge as embedded within their thinking.
@inproceedings{aniceto2026prospective, author = {Aniceto, R. and Qiu, R. N. and Delaney, V.}, title = {Prospective teachers' model-building of student thinking on sampling distributions}, booktitle = {Proceedings of the Forty-Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education}, editor = {Leatham, K. R. and Peterson, B. E. and Siebert, D. K. and Teuscher, D.}, year = {2026}, pages = {1310--1315}, publisher = {Brigham Young University}, address = {Provo, UT}, }
Qiu, R. N. (2026)

Exploring the relationship between group roles and participation patterns in an inquiry-based mathematics course

In Proceedings of the 28th Annual Conference on Research in Undergraduate Mathematics Education, 100–108.

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This report examines how group roles and instructional practices shaped student participation in an inquiry-oriented undergraduate mathematics course. Using classroom video with thematic analysis and equity analytics, findings indicate alignment with the four pillars of Inquiry-Based Mathematics Education (IBME). The role responsible for reporting to the class (called reporter) most clearly influenced participation, while other roles were taken up more fluidly as students responded to the needs of the group’s mathematical exploration. The results suggest that IBME design fosters collaborative learning while also highlighting opportunities for future research on how group roles and instructional practices can be refined to support equitable participation.
@inproceedings{qiu2026RUME_EQUIP, author = {Qiu, R. N.}, title = {Exploring the relationship between group roles and participation patterns in an inquiry-based mathematics course}, booktitle = {Proceedings of the 28th Annual Conference on Research in Undergraduate Mathematics Education}, editor = {Adiredja, A. P. and Katz, B. P. and Melhuish, K. and Gallagher, K.}, pages = {100--108}, publisher = {Virginia Tech}, year = {2026}, keywords = {Group roles, Equity QUantified in Participation, Inquiry-Based Mathematics Education}, }
Rasmussen, C., Qiu, R. N., Carney, D., Ponce, M., Fortune, N., Jacome, N. & Stewart, M. (2026)

Making upper division math courses more relevant for prospective teachers

In Proceedings of the 28th Annual Conference on Research in Undergraduate Mathematics Education, 72–80.

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In this report we address the longstanding problem of the perceived relevance of upper division math courses for prospective secondary school teachers. Through a multi-year design-based research approach we are reimaging a Dynamical Systems and Modeling course and investigating ways to make the course more relevant to prospective teachers. In this work we report on the impact of these efforts on students’ relational understanding of why a particular function is a horizontal shift to the left of another function, a high school topic that is often only instrumentally taught and understood. Analysis of beginning and mid-semester assessments indicate significant growth in our students’ ability to provide meaningful explanations. We also report on students’ perspectives on classroom activities that influenced their reasoning.
@inproceedings{rasmussen2026, author = {Rasmussen, C. and Qiu, R. N. and Carney, D. and Ponce, M. and Fortune, N. and Jacome, N. and Stewart, M.}, title = {Making upper division math courses more relevant for prospective teachers}, booktitle = {Proceedings of the 28th Annual Conference on Research in Undergraduate Mathematics Education}, editor = {Adiredja, A. P. and Katz, B. P. and Melhuish, K. and Gallagher, K.}, pages = {72--80}, publisher = {Virginia Tech}, year = {2026}, keywords = {Function Translation, University-Secondary Mathematics Connections, Prospective Teachers}, }

2025

Qiu, R. N., Vadaparty, A., Vintha, S. & Dow, S. P. (2025)

Self-reflective crowds: surfacing wisdom through emergent scaffolding

In Proceedings of the ACM Collective Intelligence Conference, 169–187.

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Producing open-ended creative work through crowdsourcing remains a challenge, as workers often lack domain expertise, and requesters struggle to provide scalable guidance. Can the workers themselves create materials that guide subsequent workers? In this paper, we prototype a workflow for emergent scaffolding, where hints, rubrics, and examples are generated by crowd workers after attempting the task. We demonstrate how an iterative Train-Try-Reflect-Synthesize pattern—supported by LLMs—can produce a structured rubric with graded examples to guide subsequent workers on a task to create digital illustrations for scientific papers. To evaluate this strategy, we conducted a between-subjects experiment with three conditions: baseline instructions, generic examples, and emergent scaffolding. Participants in the emergent scaffolding condition created significantly better illustrations, as rated by blind-to-condition judges, compared to generic examples or instructions only. While self-efficacy ratings were mixed across conditions, emergent scaffolding participants provided better feedback during their post-task reflections. We discuss the potential for emergent scaffolding to support and scale up complex, creative tasks in crowdwork.
@inproceedings{qiu2025emergentscaffolding, author = {Qiu, R. N. and Vadaparty, A. and Vintha, S. and Dow, S. P.}, title = {Self-reflective crowds: Surfacing wisdom through emergent scaffolding}, year = {2025}, isbn = {9798400714894}, publisher = {Association for Computing Machinery}, address = {New York, NY, USA}, url = {https://doi.org/10.1145/3715928.3737478}, doi = {10.1145/3715928.3737478}, booktitle = {Proceedings of the ACM Collective Intelligence Conference}, pages = {169--187}, numpages = {19}, keywords = {Crowdsourcing, Learnersourcing, Scaffolding, Creative Work}, series = {CI '25}, }
Qiu, R. N. (2025)

Exploring students’ understanding of a limit of a sequence: using ε-strip activity with realistic mathematics education framework

In Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education, 1404–1405.

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Many studies showed that students find it challenging to develop a proper understanding of the rigorous ε-N definition of a convergent sequence in relation to the concept of limit, a crucial building block to help students make sense of formalized mathematical statements. In the study, I interviewed two students with the ε-strip activity to examine how they reasoned about sequence convergence and analyzed the interview data to inspect whether ε-strip plays the role of defining in student progress from informal to more formal ways of reasoning as a mathematical activity, in other words, to theorize the ε-strip activity with the defining as a mathematical activity (DMA) framework that expands realistic mathematics education (RME). The results reconfirmed the effectiveness of how ε-strip activity scaffolds the rigorous ε-N definition and supported the practicability of DMA and RME to guide instructional task design.
@inproceedings{qiu2025limit, author = {Qiu, R. N.}, title = {Exploring students’ understanding of a limit of a sequence: Using $\epsilon$-strip activity with Realistic Mathematics Education framework}, booktitle = {Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education}, editor = {Cook, S. and Katz, B. P. and Melhuish, K.}, pages = {1404--1405}, year = {2025}, address = {Alexandria, VA}, publisher = {SIGMAA on RUME}, organization = {Virginia Tech}, keywords = {$\epsilon$-strip Activity, Realistic Mathematics Education, Defining as a Mathematical Activity}, }
Qiu, R. N., Rasmussen, C., Carney, D. & Fortune, N. (2025)

The impact of an upper division inquiry-oriented content course on prospective teachers: embracing a critical stance

In Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education, 346–354.

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In this study, we analyze interviews with prospective secondary school teachers focused on how an upper division inquiry-oriented content course influenced their beliefs about learning and teaching mathematics. In particular, we examine how students describe their experiences in this course and the extent to which (and why) students see themselves using an inquiry-oriented instructional approach in their future teaching. Using thematic analysis, we found that the ways prospective teachers described their experiences in the course aligned closely with the four pillars of Inquiry-Based Mathematics Education, and the course empowered students to embrace a critical stance to self-reflect on their experiences and to raise their awareness of their agency to change things (for the better) through their own actions and future forms of instruction.
@inproceedings{qiu2025prospective, author = {Qiu, R. N. and Rasmussen, C. and Carney, D. and Fortune, N.}, title = {The impact of an upper division inquiry-oriented content course on prospective teachers: Embracing a critical stance}, booktitle = {Proceedings of the 27th Annual Conference on Research in Undergraduate Mathematics Education}, editor = {Cook, S. and Katz, B. P. and Melhuish, K.}, pages = {346--354}, year = {2025}, address = {Alexandria, VA}, publisher = {SIGMAA on RUME}, organization = {Virginia Tech}, keywords = {Critical Stance, Inquiry, Prospective Teachers, Beliefs about Teaching}, }