Does Counting Count for 3‐ to 4‐year‐olds? Parental Assumptions about Preschool Children's Understanding of Counting and Cardinality

Abstract

Research indicates that children do not typically understand the connection between counting and cardinality for several months after learning to count, yet parents speak to 3-year-olds as though they already understood the significance of counting. The present research was designed to investigate mothers' awareness of the discrepancy between children's procedural and conceptual mastery of counting. In Study 1 mothers of a hundred 3-to 4 1 / 2 -year-olds completed an anonymous questionnaire asking them to anticipate how their child would respond to a series of real-life vignettes based on widely used experimental measures of cardinal understanding. Most anticipated that their child, irrespective of age, would (1) understand the significance of the last word of a count, and (2) be able accurately to give a specified non-subitizable number of objects. Comparison with the performance of 54 children from the same local population supported the hypothesis that parents overestimate children's understanding of the cardinal significance of counting. Mothers reported a range of impromptu numberrelated activities in which their child had recently participated at home; most of these involved simple procedural counting. In Study 2, 35 mothers of 3-to 4 1 / 2 -year-olds completed a modified questionnaire concerning procedural aspects of counting as well as cardinality; their responses were then compared with the performance of their own children. Again, mothers overestimated their children's cardinal understanding, but this was shown not to be a result of a general tendency to overestimate their counting abilities. It is suggested that preschoolers' counting generally occurs during joint activities in which caregivers may be unaware of the support that they provide, and, provided that the jointly executed count procedures are error-free, parents implicitly assume a 'common knowledge' regarding the cardinal significance of counting.

Parents' Estimations of Preschoolers' Number Skills Relate to at-Home Number-Related Activity Engagement

“…In examining the direction of the estimation errors, parents demonstrated a greater tendency to overestimate than underestimate their preschoolers’ number skills, especially children's advanced numeracy and non‐symbolic skills. Previous research has found that overestimation is the predominant direction of error in parents’ conceptions of children's counting abilities, which is consistent with our findings (Fluck et al, ). Previous research has also demonstrated that parents tend to overestimate their children's skills in other domains, such as general cognitive abilities (Hunt & Paraskevopoulos, ; Miller, ; Miller et al, ; Stoiber, ), language (Hunt & Paraskevopoulos, ) and social and motor skills (Stoiber, ).…”

“…For our second goal, we assessed parents' estimations of their preschool‐aged children's number skills on a range of early numeracy measures. Previous work has only reported parents' estimates of their preschoolers' counting abilities (Fluck et al, ). The present study extends this previous research in important ways by also examining parents' estimations of their preschooler's advanced number skills, (i.e.…”

Children's performance on the ‘give x’ task: a microgenetic analysis of ‘counting’ and ‘grabbing’ behaviour

“…This is supported by subsequent research, which confirms that regulatory self-directed speech increases between 2 and 6 years before declining thereafter (Diaz & Berk, 1992;Fernyhough & Fradley, 2005;Fluck, Donnelly & Hicks, 1981;Kohlberg, Yaeger, & Hjertholm, 1968), moreover, in some contexts internalization may be evident as early as 4 years (Conrad, 1971). Since children generally experience counting as a shared activity from an early age (Durkin, 1993;Fluck, 1995;Fluck et al, 2005), the internalization of the count sequence may begin relatively early. The suggestion that combination and correct non-verbal responses reflect the internalization of the count sequence is supported by our observation that children who used these strategies often showed lip movements, as if counting.…”

“…appreciation of Gelman and Gallistel's (1978) 'how to count' principles. However, although caregivers seem unaware of it (Fluck et al, 2005), several months elapse before children understand the relation between counting and quantity (Gelman's Cardinality principle}the last word denotes the quantity), typically after their fourth birthday (Briars & Siegler, 1984;Fuson, 1988;Frye, Braisby, Lowe, Maroudas, & Nicholls, 1989;Wynn, 1990Wynn, , 1992Fluck & Henderson, 1996;Linnell & Fluck, 2001). Furthermore, signs of a principled understanding of cardinality do not appear for another year (Freeman, Antonucci & Lewis, 2000).…”

Some types of parent number talk count more than others: relations between parents’ input and children’s cardinal-number knowledge

“…For example, the vast majority of parents of preschool‐ and kindergarten‐aged children believe that school is primarily responsible for children’s mathematics skill (Evans, Fox, Cremaso & McKinnon, 2004). Further, nearly all parents overestimate their child’s numerical knowledge and fail to realize that their child, who typically can count to 10, does not understand important numerical concepts such as the cardinal principle (Fluck, Linnell & Holgate, 2005). Finally, parents are often unsure about how to promote their child’s numerical development.…”