Abstract
Young children’s early repeating patterning abilities are important foundations for their later mathematical development. Prior studies on young children’s repeating patterning abilities have been conducted exclusively in developed countries differing in economic, societal, and educational characteristics from developing countries. In this study, we analyzed the performance and the errors of 4- to 5-year-olds on three repeating patterning tasks, and we investigated the association between children’s repeating patterning abilities and their early mathematical abilities in a developing country, Ecuador. A total of 60 preschoolers and 56 kindergartners completed a repeating patterning test and an early mathematics test at the end of the school year. Results first indicated rather low repeating patterning performances of both preschoolers and kindergartens, with large inter-individual differences in these performances. Kindergartners had significantly better patterning abilities than preschoolers. Second, error analyses indicated that children made different types of errors when solving the patterning tasks. The majority of errors were pattern-related errors, with preschoolers making more errors that were not pattern related than kindergarteners. Third, children’s patterning abilities were positively associated with early mathematical abilities in both grades. These results complement current theoretical models of young children’s mathematical development and inform educational policy and practices in this domain for developing countries.
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Funding
This work was supported by the Research Office of the University of Cuenca (DIUC), proyecto DIUC_XVI_2018_23_BOJORQUE_GINA.
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Gina Bojorque. Facultad de Filosofía, Universidad de Cuenca, Av. 12 de Abril, Cuenca, Ecuador. E-mail: gina.bojorque@ucuenca.edu.ec
Current themes of research
Her current themes of research focus on early mathematics learning and instruction, spontaneous focusing on numerosities, and early mathematical patterns.
Most relevant publications in the field of Psychology of Education
Bojorque, G., Torbeyns, J., Van Hoof, J., Van Nijlen, D., & Verschaffel, L. (2018). Effectiveness of the building blocks program for enhancing Ecuadorian kindergartners’ numerical competencies. Early Childhood Research Quarterly, 44, 231–241.
Torbeyns, J., Bojorque, G., Van Hoof, J., Van Nijlen, D., & Verschaffel, L. (2018). Unique contribution of Ecuadorian kindergartners’ spontaneous focusing on numerosity to their early numerical abilities. British Journal of Developmental Psychology, 36, 299–312.
Bojorque, G., Torbeyns, J., Van Nijlen, D., & Verschaffel, L. (2018). Ecuadorian Kindergartners’ numerical development: contribution of SES, quality of early mathematics education and school type. Educação e Pesquisa, 44,1–21.
Bojorque, G., Torbeyns, J., Hannula-Sormunen, M., Van Nijlen, D., & Verschaffel, L. (2017). Development of SFON in Ecuadorian kindergartners. European Journal of Psychology of Education. 32:3, 449–462. doi: 10.1007/s10212-016-0306-9
Bojorque, G., Torbeyns, J., Moscoso, J., Van Nijlen, D., & Verschaffel, L. (2015). Early number and arithmetic performance of Ecuadorian 4-5-year-olds. Educational Studies 41:5, 565–586. doi: 10.1080/03055698.2015.1090302
Neli Gonzales. Facultad de Filosofía, Universidad de Cuenca, Av. 12 de Abril s/n, Cuenca, Ecuador. E-mail: neli.gonzales@ucuenca.edu.ec
Current themes of research
Her current research focuses on mathematics learning and instruction.
Most relevant publications in the field of Psychology of Education
Gonzales, N., Trelles, C., Mora, J., 2017. Manejo Docente de las Tecnologías de la Información y Comunicación. Innova Research Journal. Cuenca, Ecuador, 61-72.
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Nore Wijns. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773 B-3000 Leuven, Belgium. Email: nore.wijns@kuleuven.be
Current themes of research
Her current themes of research focus on early mathematics learning and instruction, with specific attention for the development and stimulation of early mathematical patterning competencies.
Most relevant publications in the field of Psychology of Education
Bakker, M., Torbeyns, J., Wijns, N., Verschaffel, L., & De Smedt, B. (2019). Gender equality in 4- to 5-year-old preschoolers’ early numerical competencies. Developmental Science, 22(1), e12718. 10.1111/desc.12718
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Wijns, N., Torbeyns, J., Bakker, M., De Smedt, B., & Verschaffel, L. (2019). Four-year olds’ understanding of repeating and growing patterns and its association with early numerical ability. Early Childhood Research Quarterly, 49, 152–163. 10.1016/j.ecresq.2019.06.004
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.), Mathematical learning and cognition in early childhood (pp. 139–161). Cham: Springer International Publishing. 10.1007/978-3-030-12895-1_9
Verschaffel, L., Wijns, N., De Smedt, B., & Torbeyns, J. (2019, August). Four-year olds’ spontaneous focusing on patterns. In J. McMullen (Chair), Beyond SFON: expanding examinations of spontaneous mathematical focusing tendencies. Symposium conducted at the Earli conference, Aachen, Germany.
Lieven Verschaffel. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773 B-3000 Leuven, Belgium. Email: lieven.verschaffel@kuleuven.be
Current themes of research
His major research interest is psychology of mathematics education, with special attention to number sense and estimation, mental and written arithmetic, arithmetic word problem solving, and rational number knowledge
Most relevant publications in the field of Psychology of Education
Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335-359.
Dewolf, T., Van Dooren, W., & Verschaffel, L. (2011). Upper elementary school children’s understanding and solution of a quantitative word problem inside and outside the mathematics class. Learning and Instruction, 21, 770-780.
Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., Verschaffel, L. (2012). The development of students' use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, 27, 421-438.
Obersteiner, A., Van Dooren, W., Van Hoof, J., & Verschaffel, L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64-72.
Linsen, S., Verschaffel, L., Reynvoet, B., & De Smedt, B. (2015). The association between numerical magnitude processing and mental versus algorithmic multi-digit subtraction in children. Learning and Instruction, 35, 42-50.
Joke Torbeyns. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773 B-3000 Leuven, Belgium. Email: joke.torbeyns@kuleuven.be
Current themes of research
Her current research focuses on the development and stimulation of young children’s early numeracy and patterning competencies, the efficient and adaptive use of strategies in the domain of elementary arithmetic, and preschool teachers’ professional competencies in the domain of mathematics.
Most relevant publications in the field of Psychology of Education
Torbeyns, J., Verbruggen, S., & Depaepe, F. (in press). Pedagogical content knowledge in preservice preschool teachers and its association with opportunities to learn during teacher training. ZDM Mathematics Education.
Torbeyns J., Peters G., De Smedt B., Ghesquière P., & Verschaffel L. (2018). Subtraction by addition strategy use in children of varying mathematical achievement level: a choice/no-choice study. Journal of Numerical Cognition, 4, 215-234.
Torbeyns J., Hickendorff M., & Verschaffel L. (2017). The use of number-based versus digit-based strategies on multi-digit subtraction: 9-12-year-olds' strategy use profiles and task performance. Learning & Individual Differences, 58, 64-74.
Torbeyns J., Peters G., De Smedt B., Ghesquière P., & Verschaffel L. (2016). Children’s understanding of the addition/subtraction complement principle. British Journal of Educational Psychology, 86, 382-396.
Torbeyns J., Schneider M., Xin Z., & Siegler R. S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13.
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Bojorque, G., Gonzales, N., Wijns, N. et al. Ecuadorian children’s repeating patterning abilities and its association with early mathematical abilities. Eur J Psychol Educ 36, 945–964 (2021). https://doi.org/10.1007/s10212-020-00510-4
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DOI: https://doi.org/10.1007/s10212-020-00510-4