Articles in Refereed Journals

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7. Liang, B. (2023). Mental processes underlying mathematics teachers' learning from student thinking. Journal of Mathematics Teacher Education. Advance online publication. 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

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5. 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. 
 

4. Liang, B., Ng, O., & Chan, Y. (2022). Seeing the continuity behind “double discontinuity”: Investigating Hong Kong prospective mathematics teachers’ secondary–tertiary transition. Educational Studies in Mathematics. Advance online publication. https://doi.org/10.1007/s10649-022-10197-7

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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

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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 

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Published Curricula (Online)

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1. Moore, K. C., Liang, B., Tasova, H. I., & Stevens, I. E. (2019). Advancing reasoning covariationally (ARC Curriculum). Athens, GA. 

 

Book Chapters

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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

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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.

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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

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16. Liang, B. (in press). Unfolding the cognitive processes underlying the interactions between knowledge of content and knowledge of student thinking. Paper submitted to the 15th International Congress on Mathematics Education (ICME). Sydney, Australia.

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15. Chen, Q., Liang, B., Zhang, Y. (in press). Characterizing the role of programming outputs in mediating students’ mathematical learning. Paper submitted to the 15th International Congress on Mathematics Education (ICME). Sydney, Australia.

 

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. 

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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.

 

11. Moore, K. C., Liang, B., Stevens, I. E., Tasova, H. I., Paoletti, T., & Ying, Y. (2020). A quantitative reasoning framing of concept construction. In S. S. Karunakaran, Z. Reed, & A. Higgins (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 743-752). Boston, MA.

 

10. Tasova, H., Liang, B., & Moore, K. C. (2020). The role of lines and points in the construction of emergent shape thinking. In S. S. Karunakaran, Z. Reed, & A. Higgins (Eds.), Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education (pp. 562-570). Boston, MA. 
 

9. Moore, K. C., Liang, B., Tasova, H. I., & Stevens, I. E. (2019). Abstracted quantitative structures. 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. 1879-1883). St. Louis, MO: University of Missouri.

 

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.

 

6. Tasova. H., Liang, B., & Moore, K. C. (2019). Generalizing actions of forming: Identifying patterns and relationships between quantities. 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. 602-610). 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.

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Published Abstracts

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4. Moore, K. C., Stevens, I. E., Liang, B., & Tasova, H. I. (2019). Concept construction and abstracted quantitative structures. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 40(1), 421. 

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3. Tasova, H. I., Liang, B., Stevens, I. E., & Moore, K. C. (2019). Characterizing two undergraduate students’ quantitative comparisons of covarying quantities’ magnitudes. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 40(1), 421.

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2. Liang, B. & Moore, K. C. (2017). Rate of change as a feature of partitioning activity: The case of Lydia. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 38(1), 462. 

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1. Liang, B. & Castillo-Garsow, C. (2017). Pre-service secondary teachers’ understandings of central angle and inscribed angle. In C. D. Savage, G. Benkart, B. D. Boe, M. L. Lapidus, & S. H. Weintraub. Abstracts of Papers Presented to the American Mathematical Society, 38(1), 465.