Poster #31 - Intuitive Division in Non-symbolic and Symbolic Format

• In Event: 2-110 - Poster Session 07
  In Poster Session: PS 07 Section - Cognitive Processes

Integrative Statement

Children have the ability to perform mathematical calculations non-symbolically and approximately before they are taught to solve the corresponding symbolic math problem (Barth et al., 2006; Honoré & Noël, 2016; Kibbe & Feigenson, 2017). For example, previous work has shown that children can perform a scaling operation that multiplies or divides dot arrays by a factor of 2 or 4 (McCrink, Shafto, & Barth, 2016). However, it is unclear whether children can perform a true division operation where both the initial set and the divisor vary from trial to trial. Here we tested 89 children aged 6 to 9 years old (mean age = 7.9, 50 female) on their ability to perform division using a non-symbolic divisor with both dot arrays and numerals. During the training phase subjects were presented with non-symbolic or symbolic dividends ranging from 32 to 185, and non-symbolic divisors of 2, 5, and 8. Children were given feedback on the correctness of their response. During the test phase, subjects were presented with the novel non-symbolic divisors 3 and 6 and were not provided feedback. Subjects successfully solved the division tasks with above chance accuracy in the test with both non-symbolic (t88 = 27.4, p <.001) and symbolic (t88 = 17.4, p <.001) operands, indicating successful generalization to novel divisors. These results indicate that not only can children intuitively divide with non-symbolic quantities, but they are able to integrate their intuitive sense of division within their growing knowledge of symbolic number.

Children were better at the non-symbolic compared to the symbolic version of the task (t88 = 5.52, p < .001). This format effect independently held for both the younger and older children in our sample (6 & 7 years old t44 = 5.13, p < .001; 8 & 9 years old t43 = 2.81, p = .007). To determine whether this format effect held into adulthood, we ran a companion sample of 87 university undergraduates on both division tasks (mean age = 20.7). We ran a mixed effects ANOVA predicting accuracy on the division tasks with a main effect of task format (symbolic or non-symbolic) and age (adult or child), an age by format interaction, and a random effect of subject. Unsurprisingly, adults performed with higher accuracy on the division tasks than children (F1,174 = 331.8, p < .001). But interestingly, there was also a significant age by format interaction (F1,174 = 104.0, p < .001). Adults performed with higher accuracy on the symbolic version of the division task (t86 = -10.5, p < .001), whereas children showed the opposite effect. These results indicate a developmental progression, where young children are better at performing a mathematical operation using non-symbolic quantities, and adults, who are adept at performing symbolic mathematical calculation, are better at using their symbolic math system to divide. The point at which symbolic calculation becomes more effective than non-symbolic calculation may mark an important conceptual milestone in mathematical education.

Authors

• Emily Szkudlarek, University of Pennsylvania
  Presenting Author

• Elizabeth M Brannon, University of Pennsylvania
  Non-Presenting Author