Relations between complexity and difficulty on repeating-pattern tasks in early childhood

  1. Pascual D. Diago 1
  2. Dionisio F. Yáñez 1
  3. David Arnau 1
  1. 1 Universitat de València
    info

    Universitat de València

    Valencia, España

    ROR https://ror.org/043nxc105

Revista:
Journal for the Study of Education and Development, Infancia y Aprendizaje

ISSN: 0210-3702,  1578-4126

Año de publicación: 2022

Volumen: 45

Número: 2

Páginas: 311-350

Tipo: Artículo

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Otras publicaciones en: Journal for the Study of Education and Development, Infancia y Aprendizaje

Resumen

La identificación de patrones de repetición, como componente del conocimiento matemático temprano, es una actividad habitual en los primeros niveles escolares en la cual no todos los estudiantes tienen el mismo éxito. Este estudio tiene como objetivo medir diferentes variables que afectan el desempeño en tareas de reconocimiento de patrones en niveles educativos elementales. Para ello, se analiza el éxito en estudiantes de cuatro años (N = 33), cinco años (N = 31) y seis años (N = 33) en la resolución de 14 tareas con patrones repetitivos, que varían en complejidad. Los resultados revelan diferencias no significativas entre las tareas de identificación de patrones de longitud core-2 y core-4; y un mayor éxito en aquellas tareas de reconocimiento de patrones repetitivos que involucran el tamaño. Este estudio también introduce distractores, como elemento innovador, en las actividades de identificación de patrones presentando información contradictoria o superflua. Se discuten las relaciones entre complejidad y dificultad en las tareas con patrones reiterativos y el impacto de cada uno de los factores implicados, con el fin de contribuir al diseño de itinerarios para su enseñanza.

Referencias bibliográficas

  • Baroody, A. J., Purpura, D. J., Eiland, M. D., & Reid, E. E. (2015). The impact of highly and minimally guided discovery instruction on promoting the learning of reasoning strategies for basic add-1 and doubles combinations. Early Childhood Research Quarterly, 30, 93–105. https://doi.org/10.1016/j.ecresq.2014.09.003 [Crossref], [Web of Science ®], [Google Scholar]
  • Bull, R., Espy, K. A., & Wiebe, S. A. (2008). Short-term memory, working memory, and executive functioning in Preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology, 33(3), 205–228. https://doi.org/10.1080/87565640801982312 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Callejo, M. L., Fernández, C., & García-Reche, Á. (2019). Cognitive apprehension in visual pattern generalization problems. Infancia y Aprendizaje, 42(4), 783–828. https://doi.org/10.1080/02103702.2019.1652447 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Clements, D. H., & Sarama, J. (2009). Learning and teaching early math. the learning trajectories approach. Routledge. [Crossref], [Google Scholar]
  • Collins, M. A., & Laski, E. V. (2015). Preschoolers’ strategies for solving visual pattern tasks. Early Childhood Research Quarterly, 32, 204–214. https://doi.org/10.1016/j.ecresq.2015.04.004 [Crossref], [Web of Science ®], [Google Scholar]
  • Du Plessis, J. (2018). Early algebra: Repeating pattern and structural thinking at foundation phase. South African Journal of Childhood Education, 8(2), a578. https://doi.org/10.4102/sajce.v8i2.578 [Crossref], [Web of Science ®], [Google Scholar]
  • Economopoulos, K. (1998). What comes next? The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5(4), 230–233. https://doi.org/10.5951/TCM.5.4.0230 [Crossref], [Google Scholar]
  • English, L. D., & Warren, E. A. (1998). Introducing the variable through pattern exploration. The Mathematics Teacher, 91(2), 166–170. https://doi.org/10.5951/MT.91.2.0166 [Crossref], [Google Scholar]
  • Fyfe, E. R., Evans, J. L., Matz, L. E., Hunt, K. M., & Alibali, M. W. (2017). Relations between patterning skill and differing aspects of early mathematics knowledge. Cognitive Development, 44, 1–11. https://doi.org/10.1016/j.cogdev.2017.07.003 [Crossref], [Web of Science ®], [Google Scholar]
  • Fyfe, E. R., Mcneil, N. M., & Rittle-Johnson, B. (2015). Easy as ABCABC: Abstract language facilitates performance on a concrete patterning task. Child Development, 86(3), 927–935. https://doi.org/10.1111/cdev.12331 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
  • Gadzichowski, K. M. (2012). Patterning abilities of first grade children: Effects of dimension and type. Creative Education, 3(5), 632–635. https://doi.org/10.4236/ce.2012.35092 [Crossref], [Google Scholar]
  • Hendricks, C., Trueblood, L., & Pasnak, R. (2006). Effects of teaching patterning to 1st-Graders. Journal of Research in Childhood Education, 21(1), 79–89. https://doi.org/10.1080/02568540609594580 [Taylor & Francis Online], [Google Scholar]
  • Inchaustegui, Y. A., & Alsina, Á. (2020). Learning patterns at three years old: Contributions of a learning trajectory and teaching itinerary. Australasian Journal of Early Childhood, 45(1), 14–29. https://doi.org/10.1177/1836939119885310 [Crossref], [Web of Science ®], [Google Scholar]
  • Kaput, J. J., Carraher, D. W., & Blanton, M. L. (2008). Algebra in the Early Grades. Routledge. [Google Scholar]
  • Kaufman, A. S., & Kaufman, N. L. (1983). Examiner manual. Kaufman assessment battery for children. American Guidance Service. [Google Scholar]
  • Kieran, C. (Ed). (2018). Teaching and learning algebraic thinking with 5- to 12-Year-Olds. ICME-13 Monographs. Springer International Publishing. https://doi.org/http://doi.org/10.1007/978-3-319-68351-5 [Crossref], [Google Scholar]
  • Klein, A.& Starkey, P. (2004). Fostering preschool children’s mathematical knowledge: Findings from the berkeley math readiness project. In D. Η. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. pp. 343–360). Lawrence Erlbaum Associates Publishers. [Google Scholar]
  • Krutestkii, V. A. (1976). The Psychology of Mathematical Abilities in School Children Mathematics. University of Chicago Press. [Google Scholar]
  • Lee, K., Ng, S. F., Pe, M. L., Ang, S. Y., Hasshim, M. N. A. M., & Bull, R. (2012). The cognitive underpinnings of emerging mathematical skills: Executive functioning, patterns, numeracy, and arithmetic. British Journal of Educational Psychology, 82(1), 82–99. https://doi.org/10.1111/j.2044-8279.2010.02016.x [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
  • Liljedahl, P. (2004). Repeating pattern or number pattern: The distinction is blurred. Focus on Learning Problems in Mathematics, 26(3), 24–42. [Google Scholar]
  • Miller, M. R., Rittle-Johnson, B., Loehr, A. M., & Fyfe, E. R. (2016). The influence of relational knowledge and executive function on preschoolers’ repeating pattern knowledge. Journal of Cognition and Development, 17(1), 85–104. https://doi.org/10.1080/15248372.2015.1023307 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Morales, R., Cañadas, M. C., Brizuela, B. M., & Gómez, P. (2018). Functional relationships and strategies of first graders in a functional context. Enseñanza de las Ciencias, 36(3), 59–78. https://doi.org/10.5565/rev/ensciencias.2472 [Web of Science ®], [Google Scholar]
  • Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. https://doi.org/10.1007/BF03217544 [Crossref], [Google Scholar]
  • National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence. Library of Congress Cataloging-in-Publication Data. [Google Scholar]
  • Nesher, P., & Teubal, E. (1975). Verbal cues as an interfering factor in verbal problem-solving. Educational Studies in Mathematics, 6(1), 41–51. https://doi.org/10.1007/BF00590023 [Crossref], [Google Scholar]
  • Ontario Ministry of Education. (2007). A guide to effective instruction in mathematics. kindergarten to grade 3. patterning and algebra. Queen’s Printer for Ontario. [Google Scholar]
  • Orton, A. (Ed). (1999). Pattern in the teaching and learning of mathematics. Cassell. [Google Scholar]
  • Paige, J. M., & Simon, H. A. (1979). Cognitive processes in solving algebra word problems. In H. A. Simon (Ed.), Models of thought (pp. 201–229). Yale University Press. [Google Scholar]
  • Papic, M. (2015). An early mathematical patterning assessment: identifying young australian indigenous children’s patterning skills. Mathematics Education Research Journal, 27(4), 519–534. https://doi.org/10.1007/s13394-015-0149-8 [Crossref], [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), 237–269. https://doi.org/10.5951/jresematheduc.42.3.0237 [Crossref], [Web of Science ®], [Google Scholar]
  • Puchalska, E., & Semadeni, Z. (1987). Children’s reactions to verbal arithmetic problems with missing, surplus or contradictory data. For the Learning of Mathematics, 7(3), 9–16. [Google Scholar]
  • Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26(2), 257–277. https://doi.org/10.1007/s13394-013-0087-2 [Crossref], [Google Scholar]
  • Raven, J. C., Court, J. H., & Raven, J. (1992). Manual for raven’s progressive matrices and mill hill vocabulary scales. Oxford Psychologists Press. [Google Scholar]
  • Rittle-Johnson, B., Fyfe, E. R., Hofer, K. G., & Farran, D. C. (2017). Early math trajectories: Low-Income children’s mathematics knowledge from ages 4 to 11. Child Development, 88(5), 1727–1742. https://doi.org/10.1111/cdev.12662 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
  • 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. https://doi.org/10.1016/j.ecresq.2015.01.005 [Crossref], [Web of Science ®], [Google Scholar]
  • 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. https://doi.org/10.1080/15248372.2012.689897 [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
  • Rittle-Johnson, B., Zippert, E. L., & Boice, K. L. (2019). The roles of patterning and spatial skills in early mathematics development. Early Childhood Research Quarterly, 46, 166–178. https://doi.org/10.1016/j.ecresq.2018.03.006 [Crossref], [Web of Science ®], [Google Scholar]
  • Rivera, F. (Ed). (2013). Teaching and learning patterns in school mathematics. psychological and pedagogical considerations. Springer Netherlands. https://doi.org/http://doi.org/10.1007/978-94-007-2712-0 [Crossref], [Google Scholar]
  • Rustigian, A. (1976). The ontogeny of pattern recognition: Significance of colour and form in linear pattern recognition among young children. University of Connecticut. [Google Scholar]
  • Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge. [Crossref], [Google Scholar]
  • Skoumpourdi, C. (2013). Kindergartners’ performance levels on patterning. International Journal for Mathematics in Education, HMS IJME, 5, 108–131. [Google Scholar]
  • Steen, L. A. (1988). The Science of Patterns. Science, 240(4852), 611–616. https://doi.org/10.1126/science.240.4852.611 [Crossref], [PubMed], [Web of Science ®], [Google Scholar]
  • Threlfall, J. (1999). Repeating patterns in the early primary years. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. pp. 18–30). Cassell. [Google Scholar]
  • Warren, E., & Cooper, T. (2006). Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom, 11(1), 9–14. [Google Scholar]
  • Wechsler, D. (1991). Examiner manual. Wechsler intelligence scale for children (3rd ed.) ed.). The Psychological Corporation. [Google Scholar]
  • Wijns, N., Torbeyns, J., De, S. B., & Verschaffel, L. (2019). Young children’s patterning competencies and mathematical development: A review. In K. M. Robinson, H. P. Osana, & D. Kotsopoulos (Eds.), Mathematical learning and cognition in early childhood (pp. 139–161). Springer. https://doi.org/10.1007/978-3-030-12895-1 [Crossref], [Google Scholar]
  • Zazkis, R., & Liljedahl, P. (2002). Generalization of Patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379–402. https://doi.org/http://doi.org/10.1023/A:1020291317178 [Crossref], [Google Scholar]
Fuente de los datos: Dialnet