Developing Numerical Magnitude Understanding in Young Children

By Dawn Woods, RME Elementary Mathematics Coordinator

Research shows general math achievement is closely related to children’s understanding of numerical magnitudes, or the amount of a quantity (Gersten, Jordan, & Flojo, 2005; Siegler & Booth, 2004). Children develop the ability to quantify and order numbers through subitizing and counting (Clements and Sarama, 2009) and many children can answer the question “which is more, 5 or 3?” by five years of age. However, some children may be unable to tell which of two numbers is bigger or which number is closer to another number and may not have developed the “mental number line” representation of numbers (Gersten, Jordan, & Flojo, 2005; Griffin, Case, & Sigler, 1994; Clements and Sarama, 2009).

This concept of numerical magnitude is a core component of number sense, which is widely viewed as crucial to success in mathematics (National Council of Teachers of Mathematics, 2006). Furthermore, existing data on the relationship between mathematical proficiency and understanding of magnitudes are consistent with the view that helping young children develop a better understanding of numerical magnitudes may lead to improved performance on mathematics tasks (Laski & Siegler, 2007).

So with this research in mind, how can teachers and parents help young children develop a better understanding of numerical magnitudes? One way is to use a clothesline as number line in order to build understanding of numerical relationships (Suh, 2014). The list of activities below can help young children develop flexible thinking with numbers.

• Encourage young children to equally space and hang number cards on the number line, using benchmark numbers such as 0, 5, and 10 as a guide. As the child masters this range of numbers, expand or change the range. Encourage the child, as he/she hangs the number cards, to reason and talk about mathematical ideas such as: 
•  Is your number card closer to 0 or 5? How do you know? 
•  Is your number card closer to 5 or 10? How do you know? 
•  How far is 4 from 10? How do you know? 
•  Support children’s reasoning about comparing and ordering numbers by having them justify solutions. For example, 
•  Which number is bigger, 4 or 5? Why? 
•  Why is 225 smaller than 250? 
• Discussing placement of fractions and decimals highlights equivalency concepts. As children work with these number cards ask questions such as, 
•  Which fraction is equivalent to 1/2? 
•  Are 0.09 and 0.90 the same or different number? How do you know?

References
Clements, D. & Sarama, J. (2009). Learning and teaching early math: the learning trajectories approach. New York: Routlege. 

Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293 – 304. 

Griffin, S., Case, R., & Siegler, R. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 24–49). Cambridge, MA: MIT Press. 

Laski, E., & Siegler, R. (2007). Is 27 a big number? Correlational and casual connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development 78(6), 1723-1743. 

National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Washington, DC: National Council of Teachers of Mathematics. 

Siegler, R. S., & Booth, J. (2004). Development of numerical estimation in young children. Child Development, 75, 428 – 444. Suh, J. (2014). 

Line ‘em up! Teaching Children Mathematics, 20(5), 336.