Children’s Gesture use Provides Insight into Proportional Reasoning Strategies

• In Event: From Proportions to Symbolic Rational Numbers

Abstract

Although infants are able to track proportional information (Denison et al., 2013; Duffy et al., 2005; McCrink & Wynn, 2007), by around 6-years-old, children show systematic whole number biases when reasoning about discrete proportions (e.g., Boyer et al., 2008; Hurst & Cordes, 2018; Jeong et al., 2007). For example, children make errors such as deciding 2/3 is less than 4/9 because 2 < 4, even though 2/3 > 4/9 (Hurst & Cordes, 2018). This numerical interference can be seen prior to formal fraction instruction (Boyer et al., 2008; Hurst & Cordes, 2018; Jeong et al., 2007) and with symbolic fractions (Ni & Zhou, 2005). Given these pervasive difficulties, recent work has focused on how to help children overcome their whole number bias. In the current study, we investigated whether gesture, a readily available communication and learning tool (Goldin-Meadow, 2015; Novack & Goldin-Meadow, 2017), may support proportional reasoning by drawing attention away from discrete whole number information and towards proportion magnitude.

Six-year-old children (N = 145) were introduced to visual equivalent proportions using area models (e.g., pie charts) in one of three conditions: (1) Discrete Gesture Condition that highlighted whole number parts, (2) Continuous Gesture Condition that highlighted continuous amounts, or (3) No Gesture Condition. After the training, children completed a match-to-sample task in which they chose which of two options matched a sample shape. On interference trials, one option matched the sample on absolute numerical information and the other matched on proportion (e.g., a sample proportion of 3/5, with 3/7 (number match) and 6/10 (proportion match) as options) to measure children’s tendency to rely on these separate features. Lastly, we asked children to indicate proportional amounts using gestures to investigate the role of children’s own gestures in proportional reasoning.

Overall, we did not find significant condition differences in proportional reasoning (ps > 0.05), suggesting that watching an experimenter gesture during the training was not sufficient to influence their performance on the task. However, as shown in Table 1, children in the Continuous Gesture condition produced more continuous gestures in the final task than children in the Discrete Gesture condition (p < 0.001, d = .71), and children in the Discrete condition produced more discrete gestures than children in the Continuous condition (p < 0.001, d = 0.73). Furthermore, children who showed lower numerical interference on the proportional reasoning task (i.e., were more likely to match on proportion) tended to use fewer discrete gestures (r = -0.24, p = 0.005) and more continuous gestures (r = 0.28, p = 0.001; see Figure 1).

Taken together, the current study highlights that children’s own gestures may be a powerful tool for revealing children’s proportional reasoning strategies, and in particular whether they are likely to be distracted by numerical information at the expense of proportional magnitude. Although we did not find a causal effect of watching someone else gesture, these findings suggest new future directions to investigate whether children’s own gestures can be leveraged to support proportional reasoning and inhibit numerical interference.

Authors

• Michelle A Hurst, University of Chicago
  Presenting Author

• Alyson Wong, Boston College
  Non-Presenting Author

• Raychel Barkin, University of Maryland - College Park
  Non-Presenting Author

• Aziza Alam, Boston College
  Non-Presenting Author

• Sara Cordes, Boston College
  Non-Presenting Author