Preschool and Kindergarten Mathematical Patterns: Curriculum Analysis
Article Sidebar
Main Article Content
Abstract
The aim of the present study was to analyze the preschool and kindergarten Ecuadorian curriculum, with a focus on mathematical patterns, in light of the international literature. The method used was a documentary analysis of these curriculums focused on three components, namely what, when and how to teach. The results of the study demonstrate that the Ecuadorian curricula for the analyzed levels, generally include simple mathematical repeating patterns, with more complex patterns such as growing patterns being less evident. It was also found that the curriculums do not include a clear sequence to work with patterns, and that, although the methodological recommendations contemplated in the curricular documents suggest various tasks for working with patterns, the identifying the unity of the pattern task, which is fundamental for the development of the child’s mathematical thinking, is not included. In general, we concluded that these findings point to the need to review the national curriculum in view of improving Ecuadorian children’s patterning competencies in particular, and mathematical competencies in general, from the first years of schooling.
Downloads
Article Details
COPYRIGHT NOTICE
Authors who publish in the INNOVA Research Journal keeps copyright and guarantee the journal the right to be the first publication of the work under the Creative Commons License, Attribution-Non-Commercial 4.0 International (CC BY-NC 4.0). They can be copied, used, disseminated, transmitted and publicly exhibited, provided that: a) the authorship and original source of their publication (magazine, publisher, URL and DOI of the work) is cited; b) are not used for commercial purposes; c) the existence and specifications of this license of use are mentioned.
References
Aunio, P., & Niemivirta, M. (2010). Predicting children´s mathematical perfomance in grade one by early numeracy. Learning and Individual Differences, 20, 427-435.
Autor. (2015).
Bailey, D., Nguyen, T., Jenkins, J. M., Domina, T., Clements, D. H., & Sarama, J. (2016). Fadeout in an early mathematics intervention: Constraining content or preexisting differences? 52(9), 1457-1469.
https://doi.apa.org/doiLanding?doi=10.1037%2Fdev0000188. Obtenido de https://doi.org/10.1037/dev0000188
Baroody, A. (2004). The role of psychological research in the development of early childhood. En D. H. Clements, J. Sarama y A.-M. DiBiase (Eds.). Engaging young children in mathematics: Standards for early childhood mathematics education, 149-172.
Baroody, A., Clements, D., & Sarama, J. (2019). Teaching and learning mathematics in early childhood programs. In C. Brown, M. McMullen, & amp; N. K. File (Eds.). Handbook of early childhood care and education. (Section III of Curriculum in Early Childhood Care and Education). Hoboken, NJ: Wiley Blackwell Publishing.
Björklund, C., & Pramling, N. (2014). Pattern discernment and pseudo-conceptual development in early chidhood matehematics education. 22, 89-104. Obtenido de International Jornal of Early Years Education: https://doi.org/10.1080/09669760.2013.809657
Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. 2. Nueva York, NY, Routledge.
Coburn, T., Bushey, B., Holton, L., Latozas, D., Mortimer, D., & Shotwell, D. (1993). Patterns.Curriculum and evaluation standards for school mathematics. Addenda Series, Grades K-6. Reston, Va.: National Council of Teachers of Mathematics.
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1426-1446.
Economopoulos, K. (1998). What comes next? The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5, 4, 230-233. Obtenido de http://www.jstor.org/stable/41197171
Epstein, Q. (2007). The Intentional Teacher: Choosing the Best Strategies for Young Children´s. National Association for the Education of Young Children. Washington, DC:.
Fyfe, E. R., Rittle-Johnson, B., & DeCaro, M. S. (2012). The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters. Journal of Educational Psychology, 104, 1094-1108.
Griffin, S. (2005). Fostering the development of number sense. Teaching mathematics in the early primary grades. En M. S. Donovan & J. D. Bransford (Eds.). How students learn: History, mathematics and science in the classrooms, 257-308. Washington, D. C.: The National Academies Press.
Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850-867.
Kidd, J. K., Carlson, A. G., Gadzichowski, M., Boyer, C. E., Allington, D., & Pasnak, R. (2013). Effects of patterning instruction on the academic achievement of 1st-grade children. Journal of Research in Childhood Education, 27(2), 224-238.
Kulm, G., & Li, Y. (2009). Curriculum research to improve teaching and learning: National and cross-national studies. ZDM Mathematics Education, 41, 709-715.
Lüken, M. M. (2012). Young children’s structure sense. Journal fur Mathematik-Didaktik. 33(2), 263-268. Obtenido de https://doi.org/10.1007/s13138-012-0036-8
Lüken, M. M. (2018). Repeating pattern competencies in three- to five-year old kindergartners: A closer look at strategies. Contemporary Research and Perspectives on Early Childhood Mathematics Education, 35-54.
(Springer, Ed.) Hamburg: In C. B. Iliada Elia, Joanne Mulligan, Ann Anderson, Anna Baccaglini-Frank .
Lüken, M. M., Peter-Koop, A., & Kollhoff, S. (2014). Influence of early repeating patterning ability on school mathematics learning. Proceedings of the 38th conference of the International Group for the Psychology of Mathematics Education and the 36th Conference of the North American Chapter of the Psychology of Mathematics education, In D. Allan, P. Liljedahl, C. Nicol, & S. Oesterle, 137-144. Vancouver, Canada.
Ministerio de Educación. (2014). Currículo Educación Inicial. Quito, Ecuador. Recuperado el 10 de enero de 2019, de https://educacion.gob.ec/wpcontent/uploads/downloads/2016/03/CURRICULO-DE-EDUCACION-INICIAL.pdf
Ministerio de Educación. (2015). Guía metodológica para la implementación del currículo de educación inicial. Recuperado el 19 de enero de 2019, de https://educacion.gob.ec/wp-content/uploads/downloads/2016/03/Guia-Metodologicapara-la-Implementacion-del-Curriculo.pdf
Ministerio de Educación. (2016). Currículo de los niveles de educación obligatoria. Quito, Ecuador. Recuperado el 10 de enero de 2019, de https://educacion.gob.ec/wpcontent/uploads/downloads/2016/08/Curriculov2.pdf
Ministerio de Educación. (2017). Guía para el docente para Preparatoria de Educación General Básica. Quito, Ecuador. Recuperado el 10 de enero de 2019, de https://educacion.gob.ec/wp-content/uploads/downloads/2018/04/curriculo/GuiaPreparatoria-1er-Grado.pdf
Ministerio de Educación. (2018). Relaciones lógico matemáticas. Preparatoria. Cuaderno de trabajo 2. Quito, Ecuador: Santillana. Recuperado el 10 de enero de 2019, de https://educacion.gob.ec/wp-content/uploads/downloads/2018/08/RelacionesMatematicas-cuaderno-1ro-PRE-EGB.pdf
Mulligan, J., & Mitchelmore, M. (2009). Awareness of Pattern and Structure in Early Mathematical Development. Mathematics Education Research Journal, 21(2), 33-49.
Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematicas competencies are most predictive of fifth grade achievement? Early Childhood Research Quaterly, 36, 550-560. Obtenido de https://doi.org/10.1016/j.ecresq.2016.02.003
Papic, M., & Mulligan, J. (2007). Mathematical patterning in early childhood: an intervention study. Mathematics: Essential Research, Essential Practice, 2, 591-600. Recuperado el 10 de enero de 2019, de http://oatd.org/oatd/record?record=%22handle:1959.14/215381%22
Piccolo, D. L., & Test, J. (2010). Preschoolers’ thinking during block play. Teaching Children Mathematics, 17(5), 310-316.
Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2017). Early math trayectories: Low-income children´s mathematics knouledge from ages 4 to 11. Child Development, 88(5), 1727-1742. Obtenido de https://doi.org/10.1111/cdev.12662
Rittle-Johnson, B., Fyfe, E. R., Loehr, A. M., & Miller, M. R. (2015). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31, 101-112. Obtenido de https://doi.org/10.1016/j.ecresq.2015.01.005
Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14(3), 376-396. Obtenido de https://doi.org/10.1080/15248372.2012.689897
Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quaterly, 46, 166-178. Obtenido de https://doi.org/10.1016/j.ecresq.2018.03.006
Sarama, J., Clements, D. H., Starkey, P., Klein, A., & Wakeley, A. (2008). Scaling up the implementation of a pre-Kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1, 89-119.
Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T., & Wiley, D. E. (1997). Many Visions, Many Aims: A Cross-National Investigation of Curricular Intensions in School Mathematics. Dordrecht, The Netherlands: Kluwer.
Seo, K. H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? lessons from new research. . In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging Young Children in Mathematics (pp. 91–104). Hillsdale,NJ: Erlbaum.
Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99-120.
Stein, M., Remillard, J., & Smith, M. (2007). How curriculum influences student learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Gweenwich, CT: Information Age.
Verschaffel, L., Torbeyns, J., & De Smedt, B. (2017). Young children’s early mathematical competencies: analysis and stimulation. Plenure Lecture Presented at the Congress of European Research in Mathematics Education (CERME). Dublin, Ireland.
Wijns, N., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Young children’s patterning competencies and mathematical development: A review. In K. Robinson, H. Osana, & D. Kotsopoulos (Eds.). New York: Springer.