Abstract
We assessed the degree to which the variability in the time children took to solve single digit addition (SDA) problems longitudinally, predicted their ability to solve more complex mental addition problems. Beginning at 5 years, 164 children completed a 12-item SDA test on four occasions over 6 years. We also assessed their (1) digit span, visuospatial working memory, and non-verbal IQ, and (2) the speed with which they named single numbers and letters, as well the speed enumerating one to three dots as a measure of subitizing ability. Children completed a double-digit mental addition test at the end of the study. We conducted a latent profile analysis to determine if there were different SDA problem solving response time (PRT) variability patterns across the four test occasions, which yielded three distinct PRT variability patterns. In one pattern, labeled a typical acquisition pathway, mean PRTs were relatively low and PRT variability diminished over time. In a second pattern, label a delayed pathway, mean PRT and variability was high initially but diminished over time. In a third pattern, labeled a deficit pathway, mean PRT and variability remained relatively high throughout the study. We investigated the degree to which the three SDA PRT variability pathways were associated with (1) different cognitive ability measures, and (2) double-digit mental addition abilities. The deficit pathway differed from the typical and delayed pathway on the subitizing measure only, but not other measures; and the latter two pathways also differed from each other on the subitizing but not other measures. Double-digit mental addition problem solving success differed between each of the three pathways, and mean PRT variability differed between the typical and the delayed and deficit pathways. The latter two pathways did not differ from each other. The findings emphasize the value of examining individual differences in problem-solving PRT variability longitudinally as an index of math ability, and highlight the important of subitizing ability as a diagnostic index of math ability/difficulties.
Highlights
One goal of early math instruction is to help children acquire the basic arithmetic skills necessary to solve more complex calculation problems
Insofar as different speed trajectories could be identified, we investigated the degree to which different cognitive indices (i.e., visuospatial working memory (VSWM) assessed at 7 years, working-memory span (WM) assessed at 9 years, speed naming numbers/letters, non-verbal IQ, and dot enumeration RTs in the subitizing range assessed at 9 years) were associated with different single digit addition (SDA) problem solving response time (PRT) pathways; and the degree to which different SDA PRT pathways predicted performance on a double-digit mental addition (DDA assessed at 10 years) accounting for other cognitive abilities
The study investigated whether different patterns of change in SDA PRT trajectories in primary/elementary aged children could be identified over a 6 years period, and the degree to which these patterns reflect typical, delayed or deficit math acquisition pathways
Summary
One goal of early math instruction is to help children acquire the basic arithmetic skills necessary to solve more complex calculation problems. While instructional emphases differ (e.g., from a focus on rote learning to reasoning strategies), Typical, Delay, Deficit Math Pathways children tend to use so-called procedural strategies (e.g., counting all items) before so-called conceptual strategies (e.g., decomposition of number facts) to solve SDA problems (Butterworth, 2005; Geary and Hoard, 2005; Siegler, 2016); and, children may use both procedural and conceptual strategies on a single test occasion. While the association between the strategies used to solve SDA problems and problem-solving success varies within and across age, most children solve SDA problems eventually (Paul and Reeve, 2016). This acquisition variability raises the possibility that different SDA acquisition pathways are embedded within a general acquisition pathway. Insofar as different SDA acquisition pathways can be identified, it is possible they lead to a single ability end-point (equifinality); it is possible that different pathways reflect different ability profiles, which would have implications for our understanding of math development
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
