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Development of SFON in Ecuadorian Kindergartners

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Abstract

This study explored the development of Ecuadorian Kindergartners’ spontaneous focusing on numerosity (SFON) during the kindergarten year, as well as the contribution of early numerical abilities to this development. One hundred Kindergartners coming from ten classrooms received two SFON tasks, one at the beginning and one at the end of the school year, and an early numerical abilities achievement test at the beginning of the school year. Results first demonstrated limited SFON development during the kindergarten year, with inter-individual differences and intra-individual stability of children’s SFON tendency. Second, both children’s SFON tendency and their early numerical abilities at the start of the kindergarten year were predictively related to their SFON tendency at the end of the year. Our results do not only add to our theoretical understanding of SFON in young children, but also inform educational policy and practices in the domain of early mathematics education in Ecuador, as they provide building blocks for optimizing the educational goals and curricula for kindergarten mathematics.

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Notes

  1. Subitizing is defined as an ability to accurately and immediately recognize a small number of objects in a collection (Kaufman et al. 1949).

    Children’s subitizing skill can be clearly distinguished from their SFON, as the former refers to the ability component of their early numerical competencies (i.e., children’s numerical knowledge and skills; see “Introduction” section of the manuscript), whereas the latter refers to the inclination component (i.e., children’s attentional processes in the domain of number). As defined by Hannula and colleagues, SFON involves children’s spontaneous attention for exact numerosity. To determine this exact numerosity, children can use their subitizing and/or their counting skills. Stated otherwise, after having spontaneously focused on the element of exact numerosity in the environment (SFON), children still have to actually determine the exact number of items and therefore rely on their subitizing and/or counting abilities.

  2. As it is not possible to administer children’s spontaneous focus on numerosity at test 2 via the same task as offered at test 1, we selected to highly similar parallel versions of the SFON Imitation Task. As discussed in Hannula-Sormunen (2015) and in Rathé et al. (in press), the SFON Parrot Imitation Task and the SFON Mail-box Imitation Task are both designed to capture children’s spontaneous attention for exact numerosity in non-mathematically focused situations and are characterized by exactly the same task requirements, procedures, and materials, except from the overall context (namely feeding a parrot with berries versus posting envelopes into a mailbox). As indicated by a recent study (Hannula–Sormunen et al. in preparation), the SFON Parrot Imitation Task and the SFON Mailbox Imitation Task are of equivalent difficulty: A group of 87 4–7-year-old children who were offered both variants of the SFON Imitation Task at one measurement time received an overall mean score of M = 1.98 (SD = 1.54) on the Parrot Imitation Task and of M = 2.15 (SD = 1.64) on the Mailbox Imitation Task, the difference between the two task scores being not statistically significant, t(86) = 1.62, p > .05.

  3. We used the non-parametric Wilcoxon signed-rank test as our SFON data do not follow a normal distribution.

References

  • Anders, Y., Grosse, C., Roßbach, H.-G., Ebert, S., & Weinert, S. (2012). Preschool and primary school influences on the development of children’s early numeracy skills between the ages of 3 and 7 years in Germany. School Effectiveness and School Improvement, 24, 195–211.

    Article  Google Scholar 

  • Berch, D. (2005). Making sense of number sense: implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339.

    Article  Google Scholar 

  • 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, 565–586.

    Article  Google Scholar 

  • Clarke, B., & Shinn, M. R. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review, 33, 234–248.

    Google Scholar 

  • Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461–555). Charlotte: Information Age.

    Google Scholar 

  • Ministerio de Educación (2012). Rendición de cuentas 2011 [Accountability 2011], Quito, Ecuador.

  • De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103, 469–479.

    Article  Google Scholar 

  • Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446.

    Article  Google Scholar 

  • Everitt, B. S., & Dunn, G. (2010). Applied multivariate data analysis (2nd ed.). Wiley: Chichester.

    Google Scholar 

  • Geary, D. (2011). Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Developmental Psychology, 47, 1539–1552.

    Article  Google Scholar 

  • Hannula, M. M. (2005). Spontaneous focusing on numerosity in the development of early mathematical skills. Annales Universitais Turkuensis B, 282. Painosalama: Turku.

    Google Scholar 

  • Hannula, M. M., & Lehtinen, E. (2005). Spontaneous focusing on numerosity and mathematical skills of young children. Learning and Instruction, 15, 237–256.

    Article  Google Scholar 

  • Hannula, M. M., Mattinen, A., & Lehtinen, E. (2005). Does social interaction influence 3 year-old children’s tendency to focus on numerosity? A quasi-experimental study in day-care. In L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds.), Powerful learning environments for promoting deep conceptual and strategic learning (Studia Paedagogica Vol. 41) (pp. 63–80). Leuven: Leuven University Press.

    Google Scholar 

  • Hannula, M. M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9, 51–58.

    Article  Google Scholar 

  • Hannula, M. M., Lepola, J., & Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107, 394–406.

    Article  Google Scholar 

  • Hannula–Sormunen, M. M. (2015). Spontaneous focusing on numerosity and its relation to counting and arithmetic. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of mathematical cognition (pp. 275–290). Oxford: University of Oxford.

    Google Scholar 

  • Hannula–Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Children’s preschool subitizing, spontaneous focusing on numerosity and counting skills as predictors of mathematical performance 6-7 years later at school. Mathematical Thinking and Learning, 17, 155–177.

    Article  Google Scholar 

  • Hannula–Sormunen, M. M., Torbeyns, J., Kyttälä, M., Simms, V., De Smedt, B., & Batchelor, S. (in preparation). Action and verbally based measures of spontaneous focusing on numerosity.

  • Hayes, A. F. (2006). A primer on multilevel modeling. Human Communication Research, 32, 385–410.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. Journal of American Psychology, 62, 498–525.

    Article  Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington: National Academy Press.

    Google Scholar 

  • Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: findings from a four-year longitudinal study. Learning and Instruction, 19, 513–526.

    Article  Google Scholar 

  • Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS ONE, 6(9), e23749.

    Article  Google Scholar 

  • Rathé, S., Torbeyns, J., Hannula-Sormunen, M. M., De Smedt, B., & Verschaffel, L. (in press). Spontaneous focusing on numerosity: a review of recent research. Mediterranean Journal for Research in Mathematics Education.

  • Sarama, J., & Clements, D. H. (2009). Manual for classroom observation (COEMET)—version 3. Unpublished version.

  • UNESCO. (2008). Los aprendizajes de los estudiantes de América Latina y el Caribe 2011 [Students’ learning from Latin America and the Caribbean 2011]. Santiago: Salesianos Impresiones.

    Google Scholar 

  • United Nations (2016). World economic situation and prospects 2016. New York

  • van de Rijt, B. A. M., van Luit, J. E. H., & Pennings, A. H. (1999). The construction of the Utrecht early mathematical competence scales. Educational and Psychological Measurement, 59, 289–309.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Ecuadorian Secretary of Higher Education, Science, Technology and Innovation (SENESCYT). The authors thank the Ecuadorian Ministry of Education, the schools’ personnel and the students who made this research possible.

Author information

Authors and Affiliations

  1. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post Box 3773 B-3000, Leuven, Belgium

    Gina Bojorque, Joke Torbeyns & Lieven Verschaffel

  2. Facultad de Filosofía, Universidad de Cuenca, Av. 12 de Abril s/n y Av. Loja, Cuenca, Ecuador

    Gina Bojorque

  3. Turku Institute for Advanced Studies and Department of Teacher Education, University of Turku, Opettajankoulutuslaitos, Turun yliopisto, FI-20014, Turku, Finland

    Minna Hannula-Sormunen

  4. Center for Educational Effectiveness and Evaluation, KU Leuven, Dekenstraat 2, Post Box 3773, 3000, Leuven, Belgium

    Daniël Van Nijlen

Authors
  1. Gina Bojorque
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  2. Joke Torbeyns
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  3. Minna Hannula-Sormunen
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  4. Daniël Van Nijlen
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  5. Lieven Verschaffel
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Corresponding author

Correspondence to Gina Bojorque.

Additional information

Gina Bojorque. 1. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773 B-3000 Leuven, Belgium. 2. Facultad de Filosofía, Universidad de Cuenca, Av. 12 de Abril s/n y Av. Loja, Cuenca, Ecuador. Tel: ++593 07 4051000 ext. 4127, Email: gina.bojorque@ucuenca.edu.ec

Current themes of research:

Gina Bojorque is a PhD student of the Center for Instructional Psychology and Technology at KU Leuven. She is a lecturer at the University of Cuenca. Her current themes of research focus on early mathematics learning and instruction, and spontaneous focusing on numerosities.

Most relevant publications in the field of Psychology of Education:

Bojorque, G., Torbeyns, J., Moscoso, J., Van Nijlen, D., & Verschaffel L. (in press). Early number and arithmetic performance of Ecuadorian 4-5-year olds. Educational Studies.

Bojorque, G., Torbeyns, J. (2015). Preliminary assessment of the numerical competencies of children from a public preschool and kindergarten in Cuenca. Maskana, 6, 39-52.

Dr. Joke Torbeyns. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773 B-3000 Leuven, Belgium. Tel: ++32 16 32.57.18, Email: Joke.Torbeyns@ppw.kuleuven.be

Current themes of research:

Joke Torbeyns is a Postdoctoral Fellow of the Center for Instructional Psychology and Technology at KU Leuven. Her current themes of research are as follows: early numeracy, number sense, strategy choice in the domain of elementary arithmetic, and strategy development in the domain of elementary arithmetic

Most relevant publications in the field of Psychology of Education:

Torbeyns, J., Schneider, M., Xin, Z., Siegler, R. (2014). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction (in press).

Torbeyns, J., De Smedt, B., Peters, G., Ghesquière, P., Verschaffel, L. (2011). Use of indirect addition in adults’ mental subtraction in the number domain up to 1,000. British Journal of Psychology, 102 (3), 585-597.

Torbeyns, J., De Smedt, B., Stassens, N., Ghesquière, P., Verschaffel, L. (2009). Solving subtraction problems by means of indirect addition. Mathematical Thinking and Learning, 11 (1-2), 79-91.

Torbeyns, J., Ghesquière, P., Verschaffel, L. (2009). Efficiency and flexibility of indirect addition in the domain of multi-digit subtraction. Learning and Instruction, 19 (1), 1-12.

Torbeyns, J., De Smedt, B., Ghesquière, P., Verschaffel, L. (2009). Acquisition and use of shortcut strategies by traditionally schooled children. Educational Studies in Mathematics, 71 (1), 1-17.

Minna Hannula-Sormunen. Turku Institute for Advanced Studies and Department of Teacher Education, University of Turku, Opettajankoulutuslaitos, FI-20014 Turun yliopisto, Turku, Finland. Tel: ++358 2 333 8649, Email: Minna.Hannula-Sormunen@utu.fi

Current themes of research:

Minna M. Hannula-Sormunen is a collegium researcher in educational sciences at the University of Turku. Her major research interest is educational psychology of mathematics education, with special attention to attentional processes, such as spontaneous focusing on numerosity and quantitative relations and development of mathematical skills in addition to learning environments aimed at promoting early and later mathematical skills.

Most relevant publications in the field of Psychology of Education:

Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Children’s preschool subitizing, spontaneous focusing on numerosity and counting skills as predictors of mathematical performance 6-7 years later at school. Mathematical Thinking and Learning. Advance online publication.

Hannula-Sormunen, M. M. (2014). Spontaneous focusing on numerosity and its relation to counting and arithmetic. Invited book chapter for Dowker, A. & Cohen Kadosh, R. (Eds.) Oxford Handbook of Mathematical Cognition. doi: 10.1093/oxfordhb/9780199642342.013.018

McMullen, J., Hannula-Sormunen, M.M. & Lehtinen, E. (2014). Spontaneous focusing on quantitative relations in relation to children’s mathematical skills. Cognition and Instruction, 32, 198–218.

McMullen, J., Laakkonen, E., Hannula-Sormunen, M.M., & Lehtinen, E. (2014). Modeling the developmental trajectories of rational number concept(s): A latent variable approach. Learning and Instruction, 37, 14–20.

Hannula, M. M., Lepola, J. Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills. Journal for Experimental Child Psychology. 107, 394-406.

Dr. Daniël Van Nijlen. Center for Educational Effectiveness and Evaluation, KU Leuven, Dekenstraat 2, Post box 3773, 3000 Leuven, Belgium. Tel: ++32 16 32.61.81, Email: Daniel.VanNijlen@ppw.kuleuven.be

Current themes of research:

Daniel Van Nijlen is with the Centre for Educational Effectiveness and Evaluation at the KU Leuven and is involved in the national assessments of educational standards in Flanders, Belgium. His primary research interests lie within the field of educational measurement and psychometrics.

Most relevant publications in the field of Psychology of Education:

Aesaert, K., Van Nijlen, D., Vanderlinde, R., Tondeur, J., Devlieger, I., & van Braak, J. (2015). The Contribution of Pupil, Classroom and School Level Characteristics to Primary School Pupils’ ICT Competences: A Performance-based Approach. Computers and Education, 87, 55-69.

Aesaert, K., Van Nijlen, D., Vanderlinde, R., & van Braak, J. (2014). Direct measures of digital information processing and communication skills in primary education: Using Item Response Theory for the development and validation of an ICT competence scale. Computers and Education, 76, 168-181.

Van Nijlen, D., & Janssen, R. (2011). Measuring mastery across grades: An application to spelling ability. Applied Measurement in Education, 24 (4), 367-387.

Prof. Dr. Lieven Verschaffel. Center for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Post box 3773, B-3000 Leuven, Belgium. Tel: ++ 32 16 32.62.58, Email: Lieven.Verschaffel@ppw.kuleuven.be

Current themes of research:

Lieven Verschaffel is a full professor in educational sciences at the KU Leuven. 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.

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Bojorque, G., Torbeyns, J., Hannula-Sormunen, M. et al. Development of SFON in Ecuadorian Kindergartners. Eur J Psychol Educ 32, 449–462 (2017). https://doi.org/10.1007/s10212-016-0306-9

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