Stability and change in markers of core numerical competencies.

Abstract

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental signatures, is unknown. To investigate these issues, the DE and NC RT signatures of 159 children were assessed 7 times over 6 years. Cluster analyses identified within-task and across-age subgroups. DE signatures comprised 4 parameters: (a) the RT slope within the subitizing range, (b) the RT slope for the counting range, (c) the subitizing range (indicated by the point of slope discontinuity), and (d) the overall average DE RT response. NC RT signatures comprised 2 parameters (NC intercept and slope) derived from RTs comparing numbers 1 to 9. Analyses yielded 3 distinct DE and NC profiles at each age. Within-age subgroup profiles reflected differences in 3 of the 4 DE parameters and only 1 NC parameter. Systematic changes in parameters were observed across ages for both tasks, and both tasks broadly identified the same subgroups. Sixty-nine percent of children were assigned to the same subgroup across age, even though parameters themselves changed across age. Subgroups did not differ in processing speed or nonverbal reasoning, suggesting that DE and NC do not tap general cognitive abilities but reflect individual differences specific to the domain of numbers. Indeed, both DE and NC subgroup membership at 6 years predicted computation ability at 6 years, 9.5 years, and 10 years.

Symbolic magnitude processing in elementary school children: A group administered paper-and-pencil measure (SYMP Test)

“…It also allows for the quick assessment of children's symbolic magnitude knowledge in large-scale classroom-based studies on other more complex aspects of children's mathematical knowledge, such as rational number understanding (e.g., Van Hoof, Verschaffel, & Van Dooren, 2015), to which The two-digit subtest was not administered in Grade 1 symbolic magnitude knowledge might be related (Siegler & Lortie-Forgues, 2015). This will help us to more fully understand the various developmental trajectories of different mathematical abilities and their individual differences and different profiles (e.g., Reeve et al, 2012). Such research inevitably requires large sample sizes in which short, reliable and valid assessments are required to measure different cognitive variables in an efficient way.…”

“…Indeed, other studies have emphasized the roles of other early numerical competencies, such as counting (Geary et al, 1992;Reeve et al, 2012), subitizing (Schleifer & Landerl, 2011), spontaneous focusing on numbers (Hannula & Lehtinen, 2005) and number line estimation (Booth & Siegler, 2008). Future studies should carefully investigate how these early numerical competencies are related to symbolic number comparison and to each other and how each of these variables uniquely predicts subsequent mathematics achievement in school.…”

Preventive Support for Kindergarteners Most At-Risk for Mathematics Difficulties: Computer-Assisted Intervention

“…There is also evidence that fluency in object counting is rather stable between different fluency-level groups (e.g., Reeve et al, 2012). In previous CAI studies, positive effects on object counting accuracy in low-performing children have been reported (Ortega-Tudela & Gómez-Ariza, 2006; Table 1).…”

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study

“…This should be considered when comparing the present findings to previous results and in future training studies. Thirdly, the present study mainly focused on the field of numerical magnitude processing; the other factors, which were also considered as markers of mathematical competence such as dot enumeration (Reeve et al, 2012), should also be investigated in future studies.…”