Choreographing complexity: investigation of elementary preservice teachers’ quantitative manipulation in large group formations

References

• An, S. A., Kim, S. J., Tillman, D., Robertson, W., *Juarez, M., & *Guo, C. (2017). It doesn’t feel like a job to learn: Hispanic preservice teachers’ perceptions of dance-themed mathematics education. Journal of Dance Education, 17(4), 138–146.
   Google Scholar
• An, S. A., Tillman, D. A., & Hachey, A. C. (2021). Off the paper and into the dance: Investigating preservice elementary teachers’ experiences with dynamic spatial reasoning choreography tasks. Research in Dance Education, 22(1), 17–37.
   Web of Science ®Google Scholar
• An, S. A., Tillman, D., Kim, S. J., Tinajero, J., & *Wang, J. (2019). Teaching numbers through dance: Developing a choreography-themed mathematics curriculum for early childhood students. Journal of Dance Education, 18(4), 1–10.
   Google Scholar
• Atiyah, M. (2001). Mathematics in the 20th Century. The American Mathematical Monthly, 108(7), 654–666. doi:10.1080/00029890.2001.11919797
   Web of Science ®Google Scholar
• Belcastro, S. M., & Schaffer, K. (2011). Dancing mathematics and the mathematics of dance. Math Horizons, 18(3), 16–20. doi:10.4169/194762111x12954578042939
   Google Scholar
• Bennett, A. B. (2022). A whole new learning space: Exploring classroom variability for teaching mathematics via active learning. International Journal of Mathematical Education in Science and Technology, 53(1), 108–130. doi:10.1080/0020739X.2021.1961033
   Web of Science ®Google Scholar
• Blanton, M. L., & Kaput, J. J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.
   Web of Science ®Google Scholar
• Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J. S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. doi:10.5951/jresematheduc.46.1.0039
   Web of Science ®Google Scholar
• Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. doi:10.1191/1478088706qp063oa
   Google Scholar
• Cai, J., Ng, S. F., & Moyer, J. C. (2011). Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore. In Early algebraization (pp. 25–41). Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-17735-4_3
   Google Scholar
• Carraher, D., & Schliemann, A. D. (2014). Early algebra teaching and learning. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 193–196). Dordrecht: Springer. doi:10.1007/978-94-007-4978-8_54
   Google Scholar
• Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2008). Early algebra is not the same as algebra early. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 235–272). Mahwah, NJ: Lawrence Erlbaum Associates/Taylor & Francis Group. doi:10.4324/9781315097435-12
   Google Scholar
• Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: Exploring their distinguishability and contribution to student learning. Journal of Mathematics Teacher Education, 23(6), 579–613. doi:10.1007/s10857-019-09443-2
   Web of Science ®Google Scholar
• Darling-Hammond, L., & Baratz-Snowden, J. (2007). A good teacher in every classroom: Preparing the highly qualified teachers our children deserve. Educational Horizons, 85(2), 111–132.
   Google Scholar
• Fusch, P. I., & Ness, L. R. (2015). Are we there yet? Data saturation in qualitative research. The Qualitative Report, 20(9), 1408–1416. doi:10.46743/2160-3715/2015.2281
   Web of Science ®Google Scholar
• Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. doi:10.3102/00028312042002371
   Web of Science ®Google Scholar
• Hohensee, C. (2017). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20(3), 231–257. doi:10.1007/s10857-015-9324-9
   Web of Science ®Google Scholar
• Hohenwarter, M., & Jones, K. (2007). Ways of linking geometry and algebra, the case of Geogebra. Proceedings of the British Society for Research into Learning Mathematics, 27(3), 126–131.
   Google Scholar
• Ionescu, T., & Vasc, D. (2014). Embodied cognition: Challenges for psychology and education. Procedia-Social and Behavioral Sciences, 128, 275–280. doi:10.1016/j.sbspro.2014.03.156
   Google Scholar
• Kalpana, I. M. (2015). Bharatanatyam and mathematics: Teaching geometry through dance. Journal of Fine and Studio Art, 5(2), 6–17.
   Google Scholar
• Kieran, C. (2006). Research on the learning and teaching of algebra. In A. Gutierrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 11–49). Rotterdam, Zuid-Holland, The Netherlands: Sense Publishers.
   Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
   Google Scholar
• Knuth, E., Stephens, A., Blanton, M., & Gardiner, A. (2016). Build an early foundation for algebra success. Phi Delta Kappan, 97(6), 65–68. doi:10.1177/0031721716636877
   Web of Science ®Google Scholar
• LaMotte, M. (2018). The integrated approach versus the traditional approach: Analyzing the benefits of a dance and transportation integrated curriculum. Journal of Dance Education, 18(1), 23–32. doi:10.1080/15290824.2017.1336667
   Google Scholar
• Lau, W. W. (2021). Pre-service mathematics teachers’ professional learning in a pedagogy course: Examining changes in beliefs and confidence in teaching algebra. Mathematics Education Research Journal, 33(2), 223–239. doi:10.1007/s13394-019-00285-y
   Web of Science ®Google Scholar
• Luken, M. M., & Sauzet, O. (2021). Patterning strategies in early childhood: A mixed methods study examining 3-to 5-year-old children’s patterning competencies. Mathematical Thinking and Learning, 23(1), 28–48. doi:10.1080/10986065.2020.1719452
   Web of Science ®Google Scholar
• Ma, J., & Hall, R. (2018). Learning a part together: Ensemble learning and infrastructure in a competitive high school marching band. Instructional Science, 46(4), 507–532.
   Web of Science ®Google Scholar
• Moore, C., & Linder, S. M. (2012). Using dance to deepen student understanding of geometry. Journal of Dance Education, 12(3), 104–108. doi:10.1080/15290824.2012.701175
   Google Scholar
• National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Council of Teachers of Mathematics. (2006). Curriculum focal points for pre-k–grade 8 mathematics. Reston, VA: Author.
   Google Scholar
• Nelson, J. (2017). Using conceptual depth criteria: Addressing the challenge of reaching saturation in qualitative research. Qualitative Research, 17(5), 554–570.
   Web of Science ®Google Scholar
• Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9–28. doi:10.1007/s10649-019-09903-9
   Web of Science ®Google Scholar
• Papic, M. M., Mulligan, J. T., & Mitchelmore, M. C. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), 237–268. doi:10.5951/jresematheduc.42.3.0237
   Web of Science ®Google Scholar
• Parsley, J., & Soriano, C. T. (2009). Understanding geometry in the dance studio. Journal of Mathematics and the Arts, 3(1), 11–18.
   Google Scholar
• Presser, A., Clements, M., Ginsburg, H., & Ertle, B. (2015). Big math for little kids: The effectiveness of a preschool and kindergarten mathematics curriculum. Early Education and Development, 26(3), 399–426. doi:10.1080/10409289.2015.994451
   Web of Science ®Google Scholar
• Remillard, J. T., Reinke, L. T., & Kapoor, R. (2019). What is the point? Examining how curriculum materials articulate mathematical goals and how teachers steer instruction. International Journal of Educational Research, 93, 101–117. doi:10.1016/j.ijer.2018.09.010
   Web of Science ®Google Scholar
• Rosenfeld, M. (2013). Making math and making dance: A closer look at integration. Teaching Artist Journal, 11(4), 205–214. doi:10.1080/15411796.2013.815542
   Google Scholar
• Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A systematic review on algebraic thinking in education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), 1–15. doi:10.29333/ejmste/11486
   Google Scholar
• Steinberg, S., Gresalfi, M., Vogelstein, L., & Brady, C. (2022). Coding choreography: Understanding student responses to representational incompatibilities between dance and programming. Journal of Research on Technology in Education, 1–18. doi:10.1080/15391523.2022.2135144
   Web of Science ®Google Scholar
• Temple, B. A., Bentley, K., Pugalee, D. K., Blundell, N., & Pereyra, C. M. (2020). Using dance & movement to enhance spatial awareness learning. Athens Journal of Education, 7(2), 153–167.
   Google Scholar
• Van Amerom, B. A. (2003). Focusing on informal strategies when linking arithmetic to early algebra. Educational Studies in Mathematics, 54(1), 63–75. doi:10.1023/B:EDUC.0000005237.72281.bf
   Google Scholar
• Vogelstein, L., Brady, C., & Hall, R. (2019). Reenacting mathematical concepts found in large-scale dance performance can provide both material and method for ensemble learning. ZDM, 51(2), 331–346. doi:10.1007/s11858-019-01030-2
   Google Scholar
• Wasserman, N. H. (2017). Exploring how understandings from abstract algebra can influence the teaching of structure in early algebra. Mathematics Teacher Education & Development, 19(2), 81–103. doi:10.1080/10986065.2017.1328635
   Google Scholar