Rationale of Rational Numbers: Semantic Organization of Rational Numbers Relates to Mathematics Achievement

• In Event: Poster Session 12
  In Poster Session: PS 12 Topic - Cognitive Processes

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 their number knowledge from whole numbers to rational numbers and gradually develop quantitative understandings of these numbers (Siegler & Lortie-Forgues, 2014). However, it is unknown how children understand different rational numbers. Fractions and decimals can represent an equal numerical value, but they are shown in different ways (e.g., ½ and 0.5). The difference in notation may interfere with children’s quantitative understanding of rational numbers. In Park et al. (2019), we found that children less than 10 years old are more likely to organize numbers by notation (½ and ¼; 0.5 and 0.25) and that children older than 12 organize by quantity (½ and 0.5; ¼ and 0.25). This suggests that 1) young children use notation rather than quantity to guide their rational number organization, despite fractions being in the curriculum from age 8, and 2) the transition from organization by notation to quantity happens between the ages of 10-12. However, it is unknown whether children’s number organization by quantity versus notation contributes to their mathematics achievement. Suppressing the interference of the salience of notation and understanding these numbers indicate specific numerical value may be critical for their mathematics achievement. We hypothesized that children who organize the numbers by quantity, independent of age, would have higher mathematical achievement than those who organize the numbers by notation since quantitative organization is an indication of comprehension of rational numbers as values.
Thirty-six children aged 10-12 (Mmonths = 132.31, SDmonths = 10.80) completed a Spatial Arrangement Method (SpAM) task (Goldstone, 1994) specifically designed to measure children’s rational number organization and a standardized mathematics assessment. We analyzed both the Euclidean distances (EDs) between two numbers and the category in the Rational Number Organization (RNO) coding scheme (Park et al., 2019) in relation to the math assessment, controlling for age. The results showed that EDs for quantity pairs significantly predicted math achievement (Table 1), indicating that the closer children put numbers of the same quantity together, the higher their math score. The results of the analyses with the RNO also supported that organization by quantity is related to significantly higher math scores compared to organization by notation (Figure 1).
Our results suggest that quantitative understanding of rational numbers while suppressing the surface feature of notation is pivotal for children’s math achievement. This is, to our knowledge, the first investigation of how notation may interfere with children’s quantitative numerical understanding. Given the importance of understanding fractions by age 10 years for later mathematical success (Siegler et al., 2012), knowing that the visual features of fractions are a barrier to comprehension even for children aged 10-12 years has significant implications for mathematics education. Future research should focus on developing educational practices that help children overcome this barrier, possibly by encouraging children’s bidirectional translation between fractions and decimals.

Authors

• Sangmi Park, Clark University
  Presenting Author

• Alena G Esposito, Clark University
  Non-Presenting Author