Dimensionality of preschoolers’ informal mathematical abilities

Abstract

Recent research examining children's early mathematical abilities has focused primarily on number and operations (e.g., counting, addition) with considerably less attention directed to the role of other possible dimensions of early mathematical abilities, such as, measurement, geometry, and patterning. The current study examined the dimensionality of informal mathematical abilities by conducting categorical confirmatory factor analysis (CCFA) using data from a large sample of preschool children from low-income families (N=1630; Mean age = 4.46 years, SD = .37) using the Child Math Assessment (CMA; . The best fitting model consisted of four factors of Number and Operations, Measurement, Geometry, and Patterning, with the Number and Operations factor explaining common variance in three first-order factors of Numbering, Operations, and Relations. These findings support the view that informal mathematical knowledge is a multi-dimensional construct comprised of each of these separable dimensions. Additionally, a Multiple Indicators Multiple Causes model was used to determine if mathematical ability differed for male and female preschoolers on each of the four factors or on each of the 35 items of the CMA. Results showed no differences for mathematical abilities between males and females at this age. Future research and curricular implications are discussed.

The Multifactorial Nature of Early Numeracy and Its Stability

“…Comparing our results with those of previous studies revealed that the basic numerical competences specified in the different models were quite similar indeed. Most obviously, we also found a factor for basic arithmetic operations similar to Purpura and Lonigan (2013) , Milburn et al (2019) , and Hellstrand et al (2020) , and a factor for patterning (which here also included geometry and measurement ) as did Hirsch et al (2018) and Milburn et al (2019) . Although several factors of models reported in other studies did not directly correspond to those observed in the present study, a more detailed comparison of item contents from this and previous studies revealed ( Table 3 ) that they seem to be in part subsumed in our number sense factor.…”

“…Early numeracy has been typically considered a unitary or two-factorial construct in previous studies (e.g., Aunio et al, 2004 ; Jordan et al, 2010 ). However, there is evidence also using large-scale assessment data that early numeracy in preschool years may be constituted by more than two basic numerical competences ( Purpura and Lonigan, 2013 ; Hirsch et al, 2018 ; Milburn et al, 2019 ; Hellstrand et al, 2020 ). In these studies, items from large-scale assessments of early numeracy were used to specify and evaluate multifactorial models by means of confirmatory factor analysis.…”

“…In particular, Purpura and Lonigan (2013) established a three-factor model of early numeracy with factors for numbering , relation , and operation competences. Milburn et al (2019) extended this model by adding another three distinct factors for measurement , geometry , and patterning competences. Another four-factor model with symbolic/non-symbolic number knowledge , numerical relations , basic arithmetic , and counting competences was recently presented by Hellstrand et al (2020) , and Hirsch et al (2018) substantiated a five-factor model reflecting patterning , seriation , non-symbolic comparison , counting , and symbolic number knowledge abilities.…”

“…This three-factor model was recently replicated and expanded based on data from an assessment of early numeracy that covered a broader range of tasks. In particular, Milburn et al (2019) observed a four-factor model consisting of the factors measurement , geometry , patterning , and numeracy —with the latter conceptualized as a second-order factor that was further differentiated into numbering , relations , and operations as proposed by Purpura and Lonigan (2013) . Another four-factor model of early numeracy in kindergarten children was reported by Hellstrand et al (2020) who differentiated the factors of symbolic and non-symbolic number knowledge , understanding mathematical relations , counting , and basic arithmetic (see also Aunio and Räsänen, 2016 ).…”

Preschool Mathematics Performance and Executive Function: Rural-Urban Comparisons across Time

“…Although much of the literature discusses EF-mathematics connections, many studies focused specifically on numerical skills, including knowing, comparing, and ordering numbers and "doing" simple operations rather than aspects of mathematics including number and operations, measurement, patterning, and geometry (Milburn, Lonigan, DeFlorio, & Klein, 2019). One research group (Eden & Potter, 2013) found no relationship between geometry and teacher ratings of children's self-regulation, but to our knowledge, EF-geometry links have otherwise received little attention.…”