Poster #2 - Integrating Quantity Across Decimals and Fractions is Essential, But Not Necessarily Linear Representation

• In Event: Poster Session 16

Abstract

Children's comprehension of rational numbers such as fractions and decimals is pivotal to their mathematics achievement (Siegler et al., 2012). The integrated theory of numerical development states that children extend number knowledge from whole numbers to rational numbers and gradually develop a quantitative understanding of these numbers that is similar to a number line (Siegler & Lortie-Forgues, 2014). Consistent with the theory, Park and Esposito (2022) found that children in 5th grade were conceptualizing fractions and decimals by quantity in an integrative way (e.g., understanding 0.5 equals ½) more than children in younger grades. Further, this conceptualization predicted children’s math achievement. However, they did not find evidence of linear representation across fractions and decimals in children aged 8-14. This is inconsistent with the theory and previous findings with number comparison tasks (Hurst & Cordes, 2018). This may be because the Numerical Spatial Arrangement Methods (NSpAM) task used did not prompt a quantity comparison. Therefore, it is unclear whether individuals do not develop a spontaneous mental number line representation or if this is a later developing skill. Further, it is unknown if a linear representation, if it emerged, would be associated with higher mathematics achievement. We hypothesized that (1) college students would show evidence of a linear representation of rational numbers across distinct notations (i.e., fractions and decimals) and that (2) individuals who showed a linear representation of such numbers will have higher math performance than those who did not.
Fifty-nine college students (N = 54, 41 females; M = 19yrs 10mths, SD = 1yr 5mths) completed a NSpAM task (Park & Esposito, 2022), a standardized mathematics assessment, and a math anxiety scale. We examined whether their number organization (coded as notation vs quantity; non-linear quantity vs linear quantity) was related to math performance while controlling for math anxiety (Table 1). College students organized the numbers by quantity more than by notation (χ2 = 6, p = .01). However, among those who used a quantity organization, linear was not significantly more likely than non-linear (χ2 = 2.78, p = .095). Students organizing the numbers by quantity had higher math achievement than their peers organizing by notation (t = 6.43, p = .01). Interestingly, there were no differences in math scores between linear and non-linear quantity organizers (t = 1.23, p = .72). Importantly, the relation between number organization by notation versus quantity and math achievement was no longer significant after controlling for math anxiety (F = 2.81, p = .10; Table 2).
Our results suggest that an integrative number line-like representation of fractions and decimals is not consistent even in college students. Number line representation was also not associated with higher math achievement. Quantity organization did predict math achievement, congruent with studies with children. However, this relation was no longer significant when math anxiety was included in the model. The results will be discussed in relation to cognitive development, numerical development, mathematics performance, and the development and implications of math anxiety.

Authors

• Sangmi Park, Clark University
  Presenting Author

• Alena G Esposito, Clark University