Young Children’s Early Mathematical Competencies: The Role of Mathematical Focusing Tendencies

Abstract

In this paper we review and discuss a relatively new line of research in the domain of early mathematical development that addresses the dispositional rather than the ability aspect of children's early mathematical competence, namely their tendencies to attend to and focus on various mathematical elements in their environment and its relation with (later) mathematical development in school. So far, most of this research has been done on young children's spontaneous focusing on numerosity (SFON), but to a much lesser extent, similar efforts have been made for Arabic number symbols (SFONS), quantitative relations (SFOR), and mathematical patterns (SFOP). Our review and discussion of these four mathematical focusing tendencies are organized around the following four themes: definition, measurement, development, and stimulation.

Research on early childhood mathematics teaching and learning

“…Bjørnebye and Sigurjonsson (2020) observed them in teacher-led outdoor games, while Lossius and Lundhaug (2020) observed child-initiated play activities. Some researchers used their observations of children's encounters with mathematical content for theoretical discussions on how to understand children's meaning-making, for example by taking the semiotic mediation perspective (e.g., Bartolini Bussi 2020) or through the lens of attentional processes (Verschaffel et al 2020).…”

“…For example, there was a study about children's enumeration skills when making lists for designating and representing collections of objects (Dorier and Coutat 2016). Also, attention was paid to the use of numerical finger gestures and other bodily-based communication in order to facilitate the learning process (Rinvold 2016), children's spontaneous focusing on numerosity (SFON) (Rathé et al 2018;Bojorque et al 2018), and the link between writing skills and number development (Adenegan 2016). Furthermore, an exploration of children's ability to operate with numbers revealed that 5-year-olds were able to solve multiplication and division problems when they were presented in familiar contexts (Young-Loveridge and Bicknell 2016).…”

Are preschoolers who spontaneously create patterns better in mathematics?

“…A growing body of research addresses young children's tendency to spontaneously attend to mathematical elements in their environment (Hannula-Sormunen, 2015;Verschaffel, Rathé, Wijns, De Smedt, & Torbeyns, 2018). This research distinguishes between children's spontaneous tendency to think and behave mathematically, and their mathematical ability, i.e., the mathematical knowledge and skills they demonstrate when explicitly guided towards mathematical elements (Mulligan et al, 2018;Verschaffel et al, 2018;Verschaffel, Torbeyns, & De Smedt, 2017). Hannula and Lehtinen (2005) described one such tendency as Spontaneous Focusing On Numerosities (SFON), which is "a separate mental process, one which refers to the child's tendency to spontaneously focus on the aspect of numerosity and utilize his or her enumeration skills in various activity situations" (p. 239).…”

Spontaneous mathematical focusing tendencies in mathematical development

“…The past twenty years have seen an exponential growth in investigations into children's selfdirected, spontaneous, mathematical activities. In particular, examinations of spontaneous mathematical focusing tendencies have led to an extensive accounting of how children attend to different mathematical aspects of non-explicitly mathematical situations (for recent reviews, see, McMullen, Chan, et al, 2019;Verschaffel et al, 2020). These investigations suggest that these tendencies may have important implications for mathematical thinking, learning, and instruction.…”

“…We do not aim to provide a comprehensive overview of the field in this introduction text for two reasons. First, several contributors to this special issue, including the three guest editors, have recently produced two reviews that provide a comprehensive look at the current state of the field (McMullen, Chan, et al, 2019;Verschaffel et al, 2020). Second, the individual papers in the enclosed issue will provide a much more detailed account of the most relevant aspects of the literature for the particular contribution.…”