Publications

Books

Barrett, J., Cullen, C., Behnke, D., & Klanderman, D. (2017). A pleasure to measure: tasks for teaching measurement in the elementary grades. Reston, VA: National Council of Teachers of Mathematics.

Book Chapters

Jeune, M., Cullen, C.J. (2024). Mathematics Education for Children with Critical and Terminal Illness. In: Clements, M.(., Kaur, B., Lowrie, T., Mesa, V., Prytz, J. (eds) Fourth International Handbook of Mathematics Education. Springer International Handbooks of Education. Springer, Cham. https://doi.org/10.1007/978-3-031-51474-6_20

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.

Clements, D. H., Barrett, J. E., Sarama, J., Cullen, C. J., Van Dine, D. W., Eames, C. L., Kara, M., Klanderman, D., & Vukovich, M. (2017). Length – A summary report. 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.

Journal Articles

Martin, T. S., Cullen, C.J., Chávez, O, & Kimball, K., (2024). Developing directed-length definitions for the tangent and secant functions. In Editors, Proceedings of the forty-sixth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 887 – 896). Cleveland, OH: Publisher. https://doi: 10.51272/pmena.46.2024

Cullen, C. J., Ssebaggala, L., & Chávez, Ó. (2024). Rate of change: Degrees vs. radians. North American GeoGebra Journal, 12(1): 25-31.

Cullen, C. J., & Hertel, J. T. (2023). Improving our criticism of technology in mathematics education. Mathematics Teacher: Learning & Teaching PK–12, 116(5), 314–321. https://doi.org/10.5951/mtlt.2023.0004

Hertel, J. T., & Cullen, C. J. (2023). Technology: Reflecting and Moving Forward. Mathematics Teacher: Teaching and Learning PK–12, 116(5), 310–311. https://doi.org/10.5951/MTLT.2023.0053

Rupnow, T. J., 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. The Journal of Mathematical Behavior, 67, 1-20. doi: 10.1016/j.jmathb.2022.100998.

Sarama, J., Clements, D. H., Barrett, J. E., Cullen, C. J., & Hudyma, A. (2022). Length measurement in the early years: Teaching and learning with learning trajectories. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2020.1858245

Eames, C. L., Barrett, J. E., Cullen, C. J., et al. (2020) Examining and developing fourth grade children’s area estimation performance. School Science and Mathematics.  120: 67– 78. https://doi.org/10.1111/ssm.12386

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

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.

Kelley, T., Nickels, M., Bush, S. B., Taylor, M. S., & Cullen, C. (2019). Robotics in mathematics: Engaging students in perimeter. The Elementary STEM Journal.23(3), 10-13. 

Clements, D. H., Sarama, J., Van Dine, D. W., Barrett, J. E., Cullen, C. J., Hudyma, A., . . . [Cullen, A. L.], Eames, C. L. (2018). Evaluation of three interventions teaching area measurement as spatial structuring to young children. Journal of Mathematical Behavior, 50, 23–41. doi:10.1016/j.jmathb.2017.12.004

Cullen, A. L., Cullen, C. J., & O’Hanlon, W. A. (2018). Effects of an intervention on children’s conceptions of angle measurement. International Journal of Research in Education and Science, 4(1), 136–147. doi:10.21890/ijres.382941

Cullen, A. L., Eames, C. L., Cullen, C. J., Barrett, J. E., Sarama, J., Clements, D. H., & Van Dine, D. W. (2018). Effects of three interventions on children’s spatial structuring and coordination of area units. Journal for Research in Mathematics Education, 49(5), 533–574.

Cullen, A. L., Eames, C. L., Cullen, C. J., Barrett, J. E., Sarama, J., Clements, D. H., & Van Dine, D. W. (2018). Effects of three interventions on children’s spatial structuring and coordination of area units. Journal for Research in Mathematics Education, 49(5), pp. 533–574.

Cullen, C. J., & Martin, T. S. (2018). Discovering trig identities in geometric representations. The Mathematics Teacher, 112(3), p. 260.

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.

Cullen, A. L., Cullen, C. J., & O’Hanlon, W. A. (2017). Elementary students’ reasoning about angle constructions. 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. 347–354). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

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.

Nickels, M., & Cullen, C. J., (2017). Mathematical Thinking and Learning Through Robotics Play for Children with Critical Illness: The Case of Amelia. Journal for Research in Mathematics Education, 48(1), 22 – 77.

Nickels, M. (with Cullen, C. J., Cullen, A. L., & Joe, R.). (2017). Separate and unequal: Students with HIV/AIDS and mathematics education. Journal of Urban Mathematics Education, 10(2), 39–51.

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.

Barrett, J. E., Cullen, C. J., Sarama, J., & Clements, D. H. (2016). Investigating the intersection of spatial measurement and school mathematics. A paper presented to the Topic Study Group 9 on Measurement, in Gabriele Kaiser & Rudolf vom Hofe (Eds.), the Proceedings of the 13^th International Congress on Mathematics Education. Hamburg, Germany, July 2016.

Eames, C., Barrett, J. E., Cullen, C. J., & Klanderman, D. (2016). Evaluating a hypothetical learning trajectory for length measurement using a partial credit Rasch model. A paper presented to the Topic Study Group 9 on Measurement, in Gabriele Kaiser & Rudolf vom Hofe (Eds.), the Proceedings of the 13^th International Congress on Mathematics Education. Hamburg, Germany, July 2016. 

O’Dell, J., Cullen, C. J., Rupnow, T. J., Barrett, J. E., Clements, D. H., Sarama, J., & Van Dine, D. W. (2016). Developing an understanding of children’s justifications for the circle area formula. Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tucson, AZ: University of Arizona. 

Rupnow, T. J., Cullen, C. J., Barrett, J. E., Beck, P. S., Clements, D. H., & Sarama, J. (2015). Children’s three-dimensional mental structuring using a dynamic computer environment. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.),Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 304­–307). East Lansing, MI: Michigan State University.

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. Proceedings of the 36^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 105–112). Vancouver, Canada.

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. Proceedings of the 35^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 171–178). Chicago, IL.

Cullen, C. J., Hertel, J. T., & John, S. (2013). Investigating extrema with dynamic geometry software. The Mathematics Teacher, 107(1), 68–72.

Voica, C., Pelczer, I., Singer, F. M., & Cullen C. (2013). When (and How) Does a Posed Problem Become a Problem? Proceedings of the 37^th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, Kiel, Germany: PME, pp. 353 – 360 (ISSN 0771-100X, ISBN 978-3-89088-290-1)

Wickstrom, M. H., Baek, J., Barrett, J. E., Cullen, C. J., & Tobias, J. M. (2012). Teacher’s noticing of children’s understanding of linear measurement. Proceedings of the 34^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 488-494). Kalamazoo, MI: Western Michigan University.

Kara, M., Miller, A. L., Cullen, C. J., Barrett, J. E., Sarama, J., & Clements, D. H. (2012). A retrospective analysis of students’ thinking about volume measurement across grades 2-5. Proceedings of the 34^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1016 – 1023). Kalamazoo, MI: Western Michigan University.

Miller, A. L., Kara, M., Eames, C. L., Cullen, C. J., & Barrett, J. E. (2012). A comparison of three students’ responses to area invariance tasks across grades 2-5. Proceedings of the 34^th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1042). Kalamazoo, MI: Western Michigan University.

Barrett, J., Clements, D., Sarama, J., Cullen, C., McCool, J., Witkowski Rumsey, C., & Klanderman, D. (2011). Evaluating and improving a learning trajectory for linear measurement in elementary grades 2 and 3: A longitudinal study. Mathematical Thinking and Learning, 14(1), 28 – 54.

Barrett, J., Cullen, C., Sarama, J., Clements, D., Klanderman, D., Miller, A. L., & Witkowski Rumsey, C. (2011). Children’s unit concepts in measurement: A teaching experiment spanning grades 2 through 5. ZDM: The International Journal on Mathematics Education, 43(5), 637 – 650.

Cullen, C. J., Miller, A. L., Barrett, J. E., Clements, D. H., & Sarama, J. (2011). Unit eliciting task structures: verbal prompts for comparative measures. In B. Ubuz (Ed.), Proceedings of the 35^th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 249 – 256). Ankara, Turkey: PME.

Hertel, J., & Cullen, C. (2011). Teaching trigonometry: A directed length approach. In L. R., Wiest, & T. Lamberg (Eds.), Proceedings of the 33^rd Annual 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.

Kara, M., Eames, C. L., Miller, A. L., Cullen, C. J., & Barrett, J. E. (2011). Developing and understanding of area measurement concepts with triangular units. In L. R., Wiest, & T. Lamberg (Eds.), Proceedings of the 33^rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1015 – 1023). Reno, NV: University of Nevada, Reno.

Martin, T. S., Cullen, C. J., & Day, R. (2011). What’s 2 got to do with it? Using dynamic geometry environments to find surprising results and motivate proof. New England Mathematics Journal: (Focus Issue: Exploring the Richness of Geometry via Technology). (Invited submission), 43, 49 – 62.

McCool, J. K., & Cullen, C. J. (2011). Promoting growth in measurement knowledge. Wisconsin Teacher of Mathematics, 63(2), 8 – 10.

Cullen, C. J., Witkowski, C., Miller, A. L., Barrett, J. E., Sarama, J. A., & Clements, D. H. (2010). Key components for measurement tasks. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the 32nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 6, pp. 599 – 606). Columbus, OH: Ohio State University.

Cullen, C. J., & Barrett, J. E., (2010) Strategy use indicative of an understanding of units of length. In M. Pinto & T. Kawasaki (Eds.), Proceedings of the 34th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 281 – 288). Belo Horizonte, Brazil: International Group for the Psychology of Mathematics Education. 

Cullen, C., Witkowski, C., Wilder, R., & Maubach, R. (2009). Using communication to motivate measurement precision and the use of standard units. ComMuniCator – The California Mathematics Council, 33, 36 – 39.