Charting the role of the number line in mathematical development

Abstract

Individuals who do well in mathematics and science also often have good spatial skills. However, the predictive direction of links between spatial abilities and mathematical learning has not been firmly established, especially for young children. In the present research, we addressed this issue using a sample from a longitudinal data set that spanned 4 years and which includes measures of mathematical performance and various cognitive skills, including spatial ability. Children were tested once in each of 4 years (Time 1, 2, 3, and 4). At Time 3 and 4, 101 children (in Grades 2, 3, or 4 at Time 3) completed mathematical measures including (a) a number line task (0–1000), (b) arithmetic, and (c) number system knowledge. Measures of spatial ability were collected at Time 1, 2, or 3. As expected, spatial ability was correlated with all of the mathematical measures at Time 3 and 4, and predicted growth in number line performance from Time 3 to Time 4. However, spatial ability did not predict growth in either arithmetic or in number system knowledge. Path analyses were used to test whether number line performance at Time 3 was predictive of arithmetic and number system knowledge at Time 4 or whether the reverse patterns were dominant. Contrary to the prediction that the number line is an important causal construct that facilitates learning arithmetic, no evidence was found that number line performance predicted growth in calculation more than calculation predicted number line growth. However, number system knowledge at Time 3 was predictive of number line performance at Time 4, independently of spatial ability. These results provide useful information about which aspects of growth in mathematical performance are (and are not) related to spatial ability and clarify the relations between number line performance and measures of arithmetic and number system knowledge.

Explaining the relationship between number line estimation and mathematical achievement: The role of visuomotor integration and visuospatial skills

“…It was also observed that there were medium to strong significant correlations between all visuo-spatial and visuo-motor integration measures and number line estimation, barring between R 2 LIN and both visuo-spatial working memory and mental rotation. Therefore, these data highlight the important relationship between visuo-spatial processing, visuo-motor integration skills and number line estimation and replicate previous research by both LeFevre et al (2013) and Crollen and Noël (2015).…”

“…However, hierarchical regressions indicated that PAE, but not R 2 LIN , was a significant predictor of mathematical achievement over and above visuo-spatial and visuo-motor integration scores. LeFevre et al (2013) observed that number line estimation performance (albeit as measured by linear slope values between to-be-estimated and actual estimates) was not an independent predictor of mathematical achievement after accounting for visuo-spatial skills, and the current study has replicated this finding using R 2 LIN values.…”

“…However, a more complex interpretation of these studies may be necessary; for example, some researchers have suggested that performance on number line estimation task measures may be highly confounded by an individual's general cognitive skills (e.g. LeFevre et al, 2013).…”

“…This may have reduced the individual differences in performance on this task and therefore the strength of the relationship between visuo-spatial skills and task performance. LeFevre et al (2013) assessed the relationship between visuo-spatial skills, number line estimation and mathematical achievement in a longitudinal study of 5-9-year-olds.…”

Numerical Development - From cognitive functions to neural underpinnings

“…With respect to cross-domain influences LeFevre et al (2013) showed a reliable impact of children's spatial abilities on numerical skills. Additionally, Durkin et al (2013) observed that language ability is a unique predictor of actual and future numerical achievement.…”