Parents’ and Children’s use of Magnitude and Ordinal Relational Vocabulary

• In Event: Navigating Number Concepts Across Development

Abstract

Children’s understanding of the magnitude and ordinal relations between numbers is a strong predictor of mathematical achievement (e.g. Fazio et al., 2014; Lyons et al., 2014). While much research has been devoted to understanding how the concepts of magnitude and ordinality develop, little attention has been paid to the vocabulary used to represent such relations.

Relational language has been shown to help children think about relational concepts in spatial reasoning contexts (Lowenstein & Gentner, 2005). Moreover, mathematical language in general has been shown to be an important predictor of math knowledge (Purpura & Reid, 2016). In the current project, we are interested in where these two domains intersect: how do children reason about language for mathematical relations?

In a recent study children ages 4-7 showed a better understanding of size-based magnitude terms (‘bigger’ and ‘smaller’) and quantity-based magnitude terms (‘more’ and ‘less’) than of the ordinal terms (‘before’ and ‘after’) (Hurst et al., in prep), even in the context of symbolic number. Why could this be? One possibility is that children’s early experience with these different relational terms. Much like how children who hear more number words as toddlers have a better understanding of those words later on (Levine et al., 2010), it may be that hearing relational language in numerical contexts can support children’s mathematical learning. In this study we sought to explore how frequently and in which contexts, numeric or otherwise, parents and children use these relational terms in order to better understand children’s early experience with relational mathematical language.

Parents and children were recorded interacting in their homes for 90 minutes every 4 months from when the child was 14-months to 58-months old. All instances of the terms ‘bigger’, ‘smaller’, ‘more’, ‘less’, ‘before’, and ‘after’ from parents or children were analyzed and further coded for the context in which they were used. Bigger/smaller were coded as: numerical (“2 is smaller than 3”), spatial (“make a bigger tower”), or an abstract concept (“we have bigger things to do”). Before/after were coded as: numerical order (“what comes after 3?”), temporal order (“wash your hands before dinner”), alphabetical order (“P comes after O”), spatial order (“the engine goes before the caboose”), or other (“I’m looking after the dog”). More/less coding is still on-going.

We find that both parents and children use the terms more/less most frequently and bigger/smaller least frequently. Across the board, however, these terms were used in non-numeric contexts much more frequently than in numeric contexts. Moreover, the proportion of before/after uses that reference numerical order is greater than the proportion of bigger/smaller uses that reference numeric magnitude, suggesting that children’s difficulty with before/after relative to bigger/smaller likely does not stem from limited experience with these terms in numerical contexts.

This study raises many questions for future work about how children connect the meaning of these terms across contexts, whether the variation in children’s experience with these terms relate to math learning, and how cross-domain use of these terms can be leveraged to facilitate numerical learning.

Authors

• Madeleine Oswald, University of Chicago
  Presenting Author

• Michelle A Hurst, University of Chicago
  Non-Presenting Author

• Kierra D. Thompson, The University of Chicago
  Non-Presenting Author

• Susan Cohen Levine, University of Chicago
  Non-Presenting Author