I have two main research interest areas. The first is related to students’ development of measurement and quantitative reasoning. My second research area is the role of technology in the teaching and learning of mathematics.

## Measurement and Quantitative Reasoning

I am interested in students’ development of geometric measurement and quantitative reasoning. This includes work in length, area, volume, trigonometry and angle measure. In this research, I have done a lot of work with hypothetical learning trajectories, I have used microgenetic methods, as well as teaching experiments. Some selected works are below.

### Length, Area, Volume

- 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. Examining and developing fourth grade children’s area estimation performance.*School Science and Mathematics*. 2020; 120: 67– 78. https://doi.org/10.1111/ssm.12386

- 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, 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.

### Angle and Trigonometry

- Cullen, A. L.,
*Mathematics Teacher: Mathematics Learning and Teaching PreK–12, 113*(8), 637–642.

- 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, C. J.**, & Martin, T. S. (2018). Discovering trigonometric identities in geometric representations.*Mathematics Teacher, 112*(3), p. 240. https://doi.org/10.5951/mathteacher.112.3.0240

**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.

- 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.,
**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.

- Hertel, J., &
**Cullen, C.**(2011). Teaching trigonometry: A directed length approach. In L. R., Wiest, & T. Lamberg (Eds.),*Proceedings of the 33*(pp. 1400 – 1407). Reno, NV: University of Nevada, Reno.^{rd}Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education

## Technology

My second main area of research interest is the role that technology can plan in the teaching and learning of mathematics. In this area, I focus on using technology to support things that we in the mathematics education field already value. For example, using technology to help students explore, conjecture, test/revise conjectures, and justify those conjectures.

**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: Learning & Teaching PK–12, 116*(5), 310–311. https://doi.org/10.5951/MTLT.2023.0053

**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

- 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.

- 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.

- 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.

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

- Martin, T.,
**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, 43*, 49–62.