The development of computational estimation in the transition from informal to formal mathematics education
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The development of computational estimation in the transition from informal to formal mathematics education Elke Sekeris 1
2
1
& Michaël Empsen & Lieven Verschaffel & Koen Luwel
3,1
Received: 25 March 2020 / Revised: 11 September 2020 / Accepted: 15 September 2020 # Instituto Universitário de Ciências Psicológicas, Sociais e da Vida 2020
Abstract
The transition from informal to formal mathematics is an important episode in children’s mathematical development. The current study investigated how young children’s computational estimation performance and strategy use develops in this transitional period. The computational estimation performance of 350 children was assessed before the start of formal schooling (i.e., third grade of kindergarten) and again after the start of formal schooling (i.e., first grade of primary school) by means of a computational estimation addition task with manipulatives. Both children’s answer construction and their counting behavior while constructing the answer were observed during task administration. Results showed an age-related increase in children’s estimation accuracy as well as in their proportion of exact answers. Age-related changes in strategy use were also observed. Children demonstrated an increase in their counting behavior while constructing the answer, but no changes in the way the answer was constructed. In both grades, the answer was most often constructed by laying down all manipulatives immediately in one group. These results suggested that children can follow two pathways to solve the estimation problems: (1) relying on the visual representation of the addends without using counting and (2) using the verbal labels provided by the experimenters while using counting. More use of counting in first grade positively influenced children’s estimation accuracy in this grade, suggesting that these children strive for more precision compared to children who do not count. Keywords Computational estimation . Kindergarten . First grade . Strategies
* Elke Sekeris [email protected]
1
Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, Box 3773, 3000 Leuven, Belgium
2
Hogeschool PXL Research, Hasselt, Belgium
3
Centre for Educational Research and Development, KU Leuven Campus Brussels, Brussels, Belgium
E. Sekeris et al.
Introduction An important episode in the mathematical development of children is the transition from informal to formal mathematics (Ginsburg et al. 1998; Gueudet et al. 2016; Perry et al. 2015). Already before the start of formal schooling, children develop a basic understanding of number, counting, and arithmetic (Baroody 1987; Ginsburg 1977; Verschaffel et al. 2017). This informal mathematical understanding comprises competencies that are learned before or outside school and is characterized by the use of nonconventional or self-generated symbols and procedures rather than conventional written symbols and procedures (Ginsburg 1977; Purpura et al. 2013). Three overlapping levels of informal mathematics are distinguis
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