Book, Authored
Barrett, J. E., Cullen, C. J., Klanderman, D., & Behnke, D. (2017). A Pleasure to Measure. (National Council of Teachers of Mathematics): Reston, VA.
Book, Chapter
Barrett, J. E., Wickstrom, M. H., Tobias, J. M., Cullen, C. J., Cullen, A. L., & Baek, J. M., (2019), Chapter 3: Children’s Measurement Project. In P. Sztajn, P. H. Wilson (Eds.), Learning Trajectories for Teachers: Designing Effective Professional Development for Math Instruction. (pp. 48-74). New York, NY: Teachers College Press.
Barrett, J. E., Clements, D. H., Sarama, J., Miller, A. L., Cullen, C. J., Van Dine, D. W., . . . Klanderman, D. (2017). Integration of results: A new learning trajectory for area. In J. E. Barrett, D. H. Clements, & J. Sarama (Eds.), Children’s measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume. Journal for Research in Mathematics Education monograph series (Vol. 16, pp. 129–148). Reston, VA: National Council of Teachers of Mathematics.
Barrett, J. E., Cullen, C. J., Miller, A. L., Eames, C. L., Kara, M., & Klanderman, D. (2017). Area in the middle and later elementary grades. In J. E. Barrett, D. H. Clements, & J. Sarama (Eds.), Children’s measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume. Journal for Research in Mathematics Education monograph series (Vol. 16, pp. 105–127). Reston, VA: National Council of Teachers of Mathematics.
Cullen, C. J., Barrett, J. E., Kara, M., Eames, C. L., Miller, A. L., & Klanderman, D. (2017). Integration of results: A new learning trajectory for volume. In J. E. Barrett, D. H. Clements, & J. Sarama (Eds.), Children’s measurement: A longitudinal study of children’s knowledge and learning of length, area, and volume. Journal for Research in Mathematics Education monograph series (Vol. 16, pp. 181–201). Reston, VA: National Council of Teachers of Mathematics.
Hertel, J., & Cullen, C. (2011). Teaching trigonometry: A directed length approach. In L. R., Wiest, & T. Lamberg (Eds.), Proceedings of the 33rdAnnual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1400 - 1407). Reno, NV: University of Nevada, Reno.
Conference Proceeding
Cullen, C. J., & Martin, T. S. (2018). Exploring trigonometric relationships: Is it a function? In Editors, Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 259–262). Greenville, SC: Publisher.
Dimmel, J., Nickels, M., Cullen, C., & Bock, C. (2018). Mathematical making in immersive virtual environments working group. In Editors, Proceedings of the 40th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1422–1428). Greenville, SC: Publisher.
O’Dell, J. R., Barrett, J. E., Cullen, C. J., Rupnow, T. J., Clements, D. H., Sarama, J., Rutherford, G., & Beck, P. S. (2017). Using a Virtual Manipulative Environment to Support Students’ Organizational Structuring of Volume Units. 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. 1329–1336). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
Beck, P. S., Eames, C. L., Cullen C. J., Barrett, J. E., Clements, D. H., & Sarama, J. (2014). Linking children’s knowledge of length measurement to their use of double number lines. In Liljedahl, P., Nicol, C., Oesterle, S., & Allan, D. (Eds.). Proceedings of the 38th Annual Conference of the International Group for the Psychology of Mathematics Education. (Vol. 2) (pp. 105-112). Vancouver, Canada: PME
Eames, C. L., Miller, A. L., Kara, M., Cullen, C. J., & Barrett, J. E. (2013). The longitudinal development of unit concepts in area and volume measurement contexts: A case study. In M. Martinez & A. Castro Superfine (Eds.), Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 171–178). Chicago, IL. Retrieved from http://pmena.org/2013/files/PMENA2013_Conference_Proceedings.pdf
Journal Article
Rupnow, T., O’Dell, J. R., Barrett, J. E., Cullen, C. J., Clements, D. H., Sarama, J., Rutherford, G. (2022). Children’s Construction of a Volume Calculation Algorithm for a Rectangular Prism with a Dynamic Virtual Manipulative, Journal of Mathematical Behavior, 67. https://doi.org/10.1016/j.jmathb.2022.100998
Sarama, J., Clements, D. H., Barrett, J. E., Cullen, C. J., Hudyma, A., & Vanegas, Y. (2022). Length measurement in the early years: teaching and learning with learning trajectories, Mathematical Thinking and Learning, 24:4, 267-290, DOI: 10.1080/10986065.2020.1858245
Eames, C., Barrett, J. E., Cullen, C., Ruthersford, G., Klanderman, D., Clements, D. H., Sarama, J., & Van Dine, D. (2020). Examining and Developing Fourth Grade Children’s Area Estimation Performance, School Science and Mathematics, 120 (2), 67-78. https://doi.org/10.1111/ssm.12386
Cullen, A. L., Lawton, C. A., Patterson, C. S., & Cullen, C. J. (2020). All the way around a circle. Mathematics Teacher: Mathematics Learning and Teaching PreK–12, 113(8), 637–642.
Cullen, C. J., Hertel, J. T., & Nickels, M. (2020). The Roles of Technology in Mathematics Education. The Educational Forum, 84(2), 166-178. doi:10.1080/00131725.2020.1698683
Other
Kara, M., Eames, C., Miller, A., Cullen, C., & Barrett, J. Developing and understanding of area measurement concepts with triangular units. In L. R., Wiest, & T. Lamberg (EDs), Proceedings of the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. University of Nevada, Reno (2011): 1015-1023.
Cullen, C., Witkowski, C., Miller, A., Barrett, J., Sarama, J., & Clements, D. Tasks and Design of Assessment with a Learning Trajectory for Length. Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Ohio State University (2010)
Cullen, C. J. (2023). Sine, Cosine, Tangent → Sine, Secant, Tangent. Presented at the The 37th Annual Illinois Council of Teachers of Mathematics Conference - Southern Section, February 16, 2023.
Cullen, C. J. (2022). Respecting the Transcendental Functions. Presented at the Illinois Council of Teachers of Mathematics 72nd Annual Meeting, October 29, 2022.
Cullen, C. J., Ssebaggala, L., & Chávez, O. (2022, March). Why Do we Really Need Radians? Presented at the 2022 Regional Conference of the National Council of Teachers of Mathematics, Indianapolis, IN.
Isaacson, K. J., Cullen, C. J., Betz-Cahill, C. (2022). Supporting Equity with Technology. Council of Teachers of Mathematics 72nd Annual Meeting, October 29, 2022.
Creative Mathematical Reasoning and Key Curricular Content as an Evaluative Framework for Preservice Task Engagement.. 24th Annual AMTE Conference. Association of Mathematics Teacher Educators. (2020)
Clarkson, K. A., Lawton, C. A., Azimi, K., Martin, T. S., & Cullen, C. J. (2019, November). The role of creative reasoning in a technology-based task for preservice secondary teachers. Poster presented at the 41st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, St. Louis, MO.
Framing and revising a hypothetical learning trajectory for area measurement.. Annual Research PreSession. National Council of Teachers of Mathematics Meeting. (2013)
Teachers' Noticing of Children's Understanding of Linear Measurement. Association of Mathematics Teacher Educators Annual Conference. (2013)
The Longitudinal Development of Children’s Conceptions of Spatial Measurement. Annual Meeting of the Jean Piaget Society. Jean Piaget Society. (2013)
The effects of learning trajectory based professional development on teachers' noticing. North American Chapter of the International Group for the Psychology of Mathematics Education. (2013)