Assistant Professor @ The University of Hong Kong
PhD in Mathematics Education
Mathematics Education Researcher
Mathematics (Teacher) Educator
Articles in Refereed Journals
11. Moore, K. C.*, Tasova, H. I., Stevens, I. E., & Liang, B. (2026). Competing meanings, perturbation, and engendering shifts in (prospective) teacher meanings. Frontiers in Education. 11, Article 1656163. https://doi.org/10.3389/feduc.2026.1656163
10. Liang, B.*, Chen, Q., Zhang, Y, & Ng, O. (2026). From output to understanding: How programming outputs mediate mathematics learning via perturbation. International Journal of Science and Mathematics Education. Advance online publication. https://doi.org/10.1007/s10763-026-10650-6
9. Zhang, Y., Ng, O.*, & Liang, B. (2026). From pre-ritual to exploration: Young learner’s gestural routine development in manipulative-based number discourse. Educational Studies in Mathematics. 121, 365–385. https://doi.org/10.1007/s10649-025-10457-2
8. Ye, H., Liang, B., & Ng, O.* (2025). A learner‐centred exploration of teachers’ solution pathways in K‐12 programming‐based mathematical problem‐solving. Journal of Computer Assisted Learning, 41(5). https://doi.org/10.1111/jcal.70102
7. Liang, B.* (2025). Mental processes underlying a mathematics teacher’s learning from student thinking. Journal of Mathematics Teacher Education, 28(1), 7–32. https://doi.org/10.1007/s10857-023-09601-7
6. Ye, H., Liang, B., Ng, O., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: A systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10, Article 3. https://doi.org/10.1186/s40594-023-00396-w
5. Liang, B., Ng, O.*, & Chan, Y. (2023). Seeing the continuity behind “double discontinuity”: Investigating Hong Kong prospective mathematics teachers’ secondary–tertiary transition. Educational Studies in Mathematics, 113, 107-124. https://doi.org/10.1007/s10649-022-10197-7
4. Ng, O., Liang, B., Chan, A., Ho, T. C., Lam, L. P., Law, M. H., Li, E. M., Lu, T. Y (2022). A collective reflection on the transition from secondary to university mathematics through the lens of the “double discontinuity” by Felix Klein. EduMath, 45.
3. Liang, B. & Moore, K. C. (2021). Figurative and operative partitioning activity: Characterizing a student’s meanings for amounts of change. Mathematical Thinking and Learning, 23(4), 291-317. https://doi.org/10.1080/10986065.2020.1789930
2. Liang, B. & Castillo-Garsow, C. (2020). Undergraduate students’ meanings for central angle and inscribed angle. The Mathematics Educator, 29(1), 53-84. https://openjournals.libs.uga.edu/tme/article/view/2093/2599
1. 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, 56, Article 100692. http://doi.org/10.1016/j.jmathb.2019.01.008
Published Curricula (Online)
1. Moore, K. C., Liang, B., Tasova, H. I., & Stevens, I. E. (2019). Advancing reasoning covariationally (ARC Curriculum). Athens, GA.
Book Chapters
4. Moore, K. C., Stevens, I., Tasova, H., & Liang, B. (2024). Operationalizing figurative and operative framings of thought. In P. C. Dawkins, A. J. Hackenberg, A. J. Norton (Eds), Piaget’s Genetic Epistemology in Mathematics Education (pp. 89-128). Springer. https://doi.org/10.1007/978-3-031-47386-9_4
3. Ng, O., Sinclair, N., Ferrara, F., & Liang, B. (2023). Transforming arithmetic through digital resources. In B. Pepin, G. Gueudet, & J. Choppin (Eds.), Handbook of Digital Resources in Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-95060-6_17-1
2. Ng, O., Liang, B., & Leung, A. (2023). Using first- and second-order models to characterise in-service teachers’ video-aided reflection on teaching and learning with 3D Pens. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The Mathematics Teacher in the Digital Era: International Research on Professional Learning and Practice (pp. 95-117). Springer. https://doi.org/10.1007/978-3-031-05254-5_4.
1. Moore, K. C., Liang, B., Stevens, I. E., Tasova, H., & Paoletti, T. (2022). Abstracted quantitative structures: Using quantitative reasoning to define concept construction. In G. Karagöz Akar, İ.Ö. Zembat, S. Arslan, & P. W. Thompson (Eds.), Quantitative Reasoning in Mathematics and Science Education (pp. 35-69). Springer. https://doi.org/10.1007/978-3-031-14553-7_31.
Refereed Conference Proceedings (Selected)
16. Liang, B., Liu, R., Wu, Y. (in press). Learning through others: Conceptualizing decentering for mathematical learning across peer, student-teacher, and human-agent interaction. Paper to be presented at the 48th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Brigham Young University.
15. Liang, B. (2025). The coherent and strategic uses of Piaget’s notion of perturbation in mathematics (teacher) education. Proceedings of the 9th ICMI-East Asia Regional Conference on Mathematics Education (Vol. 3) (pp. 708-712). Seoul National University, South Korea.
14. Liang, B. & Moore, K. C. (2021). Theorizing teachers’ learning of students’ mathematical thinking in the context of student-teacher interaction. Paper presented at the 14th International Congress on Mathematics Education (ICME). Shanghai, China.
13. Liang, B. (2020). Theorizing teachers’ mathematical learning in the context of student-teacher interaction: A lens of decentering. In S. S. Karunakaran, Z. Reed, & A. Higgins (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 733-742). Boston, MA.
12. Liang, B., Ying, Y., & Moore, K. C. (2020). A conceptual analysis for optimizing two-variable functions in linear programming. In S. S. Karunakaran, Z. Reed, & A. Higgins (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 374-381). Boston, MA.
8. Liang, B. (2019). A radical constructivist model of teachers’ mathematical learning through student-teacher interaction. In S. Otten, A. G. Candela, Z. de Araujo, C. Haines, & C. Munter (Eds.), Proceedings of the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1814-1819). St. Louis, MO: University of Missouri. [PDF-Short]
7. Liang, B. (2019). Construction and application perspective: A review of research on teacher knowledge relevant to student-teacher interaction. In A. Weinberg, D. Moore-Russo, H. Soto & M. Wawro (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.
5. Liang, B., Stevens, I. E., Tasova. H., & Moore, K. C. (2018). Magnitude reasoning: Characterizing a pre-calculus student’s quantitative comparison of covarying magnitudes. In T. 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. 608-611). Greenville, NC: University of South Carolina & Clemson University.
4. Liang, B. & Moore, K. C. (2018). Figurative thought and a student’s reasoning about “amounts” of change. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, and S. Brown (Eds.), Proceedings of the Twenty-First Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (pp. 271-285). San Diego, CA.
3. Liang, B. & Castillo-Garsow, C. (2018). Themes in undergraduate students’ conceptions of central angle and inscribed angle. In A. Weinberg, C. Rasmussen, J. Rabin, M. Wawro, and S. Brown (Eds.), Proceedings of the Twenty-First Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (pp.549-556). San Diego, CA.
2. 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.
1. 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 Twentieth Annual Special Interest Group of the Mathematical Association of America on Research in Undergraduate Mathematics Education (pp. 928-936). San Diego, CA.