Acknowledgement
This work has been supported in part by the National Science Foundation DRL 2010269.
References
- Aguirre, J. M., Turner, E. E., Bartell, T. G., Kalinec-Craig, C., Foote, M. Q., Roth McDuffie, A., & Drake, C. (2013). Making connections in practice: How prospective elementary teachers connect to children's mathematical thinking and community funds of knowledge in mathematics instruction. Journal of Teacher Education, 64(2), 178-192. doi:10.1177/0022487112466900
- Arleback, J. B., & Bergsten, C. (2013). On the use of realistic Fermi problems in introducing mathematical modelling in upper secondary mathematics. In Lesh, R., Galbraith, P. L., Haines, C., and Hurford, A. (Eds.), Modeling students' mathematical modeling competencies (pp. 597-609). Dordrecht.
- Bartell, T., Wagner, A, Edwards, A., Battery, D., Foote, M., & Spencer, J. (2017). Toward a framework for research linking equitable teaching with the standards for mathematical practice. Journal for Research in Mathematics Education, 48(1), 7-21. https://doi.org/10.5951/jresematheduc.48.1.0007
- Bartell, T. G. (2011). Caring, race, culture, and power: A research synthesis toward supporting mathematics teachers in caring with awareness. Journal of Urban Mathematics Education, 4(1), 50-74. https://doi.org/10.21423/jume-v4i1a128
- Barrett, J. E., Clements, D. H., Sarama, J., Cullen, C. J., Van Dine, D. W. (2022, August 21). Children's measurement project. https://www.childrensmeasurement.org
- Battista, M. T. (2007). The development of geometric and spatial thinking. In Lester, F. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 843-908). National Council of Teachers of Mathematics.
- Battista, M. (2010). Representations of learning for teaching: Learning progressions, learning trajectories, and levels of sophistication. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), Proceedings of the Thirty-Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Vol. pp. 60-71. The Ohio State University.
- Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (1999). Children's mathematics. Cognitively Guided Instruction. Postmourth, NH: Heinemann. Trad. de C. De Castro y M. Linares: Las Matematicas que hacen los ninos.
- Charles A. Dana Center (2019). "What is rigor in mathematics really". https://www.utdanacenter.org/sites/default/files/2019-02/what-is-rigor-inmathematics.pdf
- Civil, M. & Khan, L. (2001). Mathematics instruction developed from a garden theme. Teaching Children Mathematics, 7, 400-405. https://doi.org/10.5951/TCM.7.7.0400
- Clements, D. H., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89. https://doi.org/10.1207/s15327833mtl0602_1
- Clements, D. H., & Sarama, J. (2014). The importance of the early years. Science, Technology & Mathematics (STEM), 5-9, Corwin.
- Cohen, E., Lotan, R., Scarloss, B. & Arellano, A. (1999). Complex instruction: Equity in cooperative learning classrooms. Theory Into Practice, 38, 80-86. doi:10.1080/00405849909543836
- Consortium for Mathematics and Its Applications [COMAP, Inc.]; Society for Industrial and Applied Mathematics [SIAM]. (2019). GAIMME: Guidelines for assessment & instruction in mathematical modeling education. Garfunkel S. A.; Montgomery, M., Eds.
- Cordova, D. I., & Lepper, M. R. (1996). Intrinsic motivation and the process of learning: Beneficial effects of contextualization, personalization, and choice. Journal of educational psychology, 88(4), 715-730. https://doi.org/10.1037/0022-0663.88.4.715
- Driscoll, M. J., DiMatteo, R. W., Nikula, J., & Egan, M. (2007). Fostering geometric thinking: A guide for teachers, grades 5-10. Heinemann.
- Elia, I., Heuvel-Panhuizen, M. V. D., & Gagatsis, A. (2018). Geometry learning in the early years: Developing understanding of shapes and space with a focus on visualization. In Kinnear, V., Lai, M. Y., & Muir, T. (Eds.), Forging connections in early mathematics teaching and learning (pp. 73-95). Springer.
- Featherstone, H., Crespo, S., Jilk, L., Oslund, J, Parks, A., & Woods, M. (2011). Smarter Together! Collaboration and Equity in the Elementary Math Classroom. National Council of Teachers of Mathematics.
- Foglia, L., & Wilson, R. A. (2013). Embodied cognition. Wiley Interdisciplinary Reviews: Cognitive Science, 4(3), 319-325. https://doi.org/10.1002/wcs.1226
- Gay, G. (2002). Preparing for culturally responsive teaching. Journal of Teacher Education, 53(2), 106-116. doi:10.1177/0022487102053002003
- Gutierrez, R., & Irving, S. (2012). Student centered learning: Latino/a, blacks, and mathematics. A white paper commissioned by the Nellie Mae Foundation Boston: Nellie Mae.
- Haviger, J., & Vojkuvkova, I. (2014). The van Hiele geometry thinking levels: Gender and school type differences. Procedia-Social and Behavioral Sciences, 112, 977-981. https://doi.org/10.1016/j.sbspro.2014.01.1257
- Hedges, H., Cullen, J., & Jordan, B. (2011). Early years curriculum: Funds of knowledge as a conceptual framework for children's interests. Journal of Curriculum Studies, 43(2), 185-205. doi:10.1080/00220272.2010.511275
- Hull, T. H., Miles, R. H., & Balka, D. S. (2014). Realizing rigor in the mathematics classroom. Corwin Press.
- Keeton, M. T., & Tate, P. J. (Eds.). (1978). Learning by experience--what, why, how (No. 1). Jossey-Bass.
- Kolb, D. A. (2014). Experiential learning: Experience as the source of learning and development. FT press.
- Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491. doi:10.3102/00028312032003465
- Lewis, C. (2002). Lesson study: A handbook of teacher-led instructional change. Research for Better Schools.
- Mishra, A. (2003). Age and school related differences in recall of verbal items in a story context. Social Science International, 19(2), 12-18.
- Moll, L. C., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 31(2), 132-141. https://doi.org/10.1080/00405849209543534
- National Center for Education Statistics (NCES). 2017. National Assessment of Educational Progress (NAEP), 2017 Mathematics Assessment. Washington, DC: National Center for Education Statistics, U.S. Department of Education. https://nces.ed.gov/nationsreportcard/nqt/
- National Council of Teachers of Mathematics (2020). Catalyzing change in early childhood and elementary mathematics initiating critical conversations. NCTM.
- Peter-Koop, A. (2004). Fermi problems in primary mathematics classrooms: Pupils' interactive modeling processes. Mathematics education for the third millennium: Towards 2010. Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia, Townsville. Putt I, Faragher R, McLean M, Mathematics Education Research Group of Australasia (Eds); Proceedings of the Annual conference of the Mathematics Education Research Group of Australasia (MERGA), 27. Sydney: MERGA: 454-461.
- Piaget, J., Garcia, R., Davidson, P., Davidson, P. M., & Easley, J. (2013). Toward a logic of meanings. Psychology Press.
- Polya, G. (1957). How to solve it. Princeton University Press.
- Sarama, J., & Clements, D. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.
- Schmitt, T., Demary, K., & Wilson-Rich, N. (2021). Urban beekeeping as a tool for STEAM education. In DeCoito, I., Patchen, A., Knobloch, N., and Esters, L. (Eds.), Teaching and learning in urban agricultural community contexts (pp. 179-208). Springer.
- SellarEs, J. A., & Toussaint, G. (2003). On the role of kinesthetic thinking in computational geometry. International Journal of Mathematical Education in Science and Technology, 34(2), 219-237. https://doi.org/10.1080/0020739031000071511
- Seshaiyer, P. & Suh, J. (2019). Mathematical modeling in problem solving: a big idea across the curriculum. In Big Ideas in Mathematics: Yearbook 2019, Association of Mathematics Educators (pp. 167-186).
- Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. https://doi.org/10.2307/749205
- Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129-162. https://doi.org/10.1207/s15327833mtl0602_4
- Suh, J., & Seshaiyer, P. (2015). Examining teachers' understanding of the mathematical learning progression through vertical articulation during lesson study. Journal of Mathematics Teacher Education, 18(3), 207-229. https://doi.org/10.1007/s10857-014-9282-7
- Suh, J. M., & Seshaiyer, P. (2016). Modeling mathematical ideas: Developing strategic competence in elementary and middle school. Rowman & Littlefield.
- Suh, J. M., Matson, K., & Seshaiyer, P. (2017). Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Education Sciences, 7(2), 62. https://doi.org/10.3390/educsci7020062
- Suh, J. M., & Seshaiyer, P. (2019). Promoting Ambitious Teaching and Learning through Implementing Mathematical Modeling in a PBL Environment: A Case Study. The Wiley Handbook of Problem- Based Learning, 529-550.
- Tan Sisman, G., & Aksu, M. (2016). A study on sixth grade students' misconceptions and errors in spatial measurement: Length, area, and volume. International Journal of Science and Mathematics Education, 14(7), 1293-1319. https://doi.org/10.1007/s10763-015-9642-5
- Turner, E., Dominguez, H., Maldonado, L., & Empson, S. (2013). English learners' participation in mathematical discourse: Shifting positioning and dynamic identities. Journal for Research in Mathematics Education, 44(1), 199-234. https://doi.org/10.5951/jresematheduc.44.1.0199
- Van de Walle, J. A. (2004). Elementary and middle school mathematics-Teaching developmentally (5th ed.). Pearson Education.
- Van Hiele, P. M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310-316. https://doi.org/10.5951/TCM.5.6.0310
- Vygotsky, L. (1978). Interaction between learning and development. In Gauvain, M., and Cole, M. (Eds.), Readings on the development of children (pp. 34-41). Scientific American Books.
- Wager, A. A. (2014). Noticing children's participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350. doi:10.5951/jresematheduc.45.3.0312.