In the second in a series of papers discussing neuroscience, psychology and research Dr Kate Reid explores preschool children's early numeracy development and how to help foster it.
Children think mathematically long before they start school, and there is substantial growth in numeracy skills during preschool. Such informal knowledge about numbers is often referred to as ‘number sense'. Children show their number sense in many everyday problem-solving situations involving numbers and measurement. They may reason about who has more or less, devise strategies for creating equal shares of countable objects or amounts, or use counting in a range of situations to reason about a single group of objects or to compare two groups. Children informally build these skills in their everyday interactions with carers and with other children, and they can be encouraged to develop their understanding in play situations.
What does the research say?
Investigations in developmental and cognitive psychology have found that infants can detect changes in small numbers of up to about five (Wynn, 1995). They can also detect differences between large numbers. For example, six-month-old infants differentiated between displays of eight and 16 objects (Xu & Spelke, 2000). Other studies have shown that these abilities are not limited to visual displays, with infants discriminating differences between small (vanMarle & Wynn, 2009) and large numbers of sounds (Lipton & Spelke, 2003), and different numbers of actions (Wynn, 1996).
Research suggests that infants' number sense extends from simple number discrimination to more complex awareness of ordinal relationships (numbers ordered by size) and even the results of simple calculations. Infants seem to recognise when results of simple number transformations are correct (for example, 1 + 1 = 2 and 2 – 1 = 1) or incorrect (for example, 1 + 1 = 1 and 2 – 1 = 2).
Research from developmental and cognitive psychology has yielded significant evidence that infants have a basic capacity to respond to numerical information. Neuroscience has provided complementary evidence of structural location and changes in brain activity when infants detect changes in number. This evidence shows that infants have a basic capacity to process numbers, not as a fixed capacity for developing mathematical understanding, but as an early foundation that may provide some direction for children as they grow and develop their numerical skills.
How early learning affects later learning
Children enter school with a wide range of early numeracy skills but they vary greatly in how they acquire, and how quickly they acquire, different concepts (Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006; Kroesbergen, Van Luit, Van Lieshout, Van Loosbroek, & Van de Rijt, 2009). Children's informal number sense when they enter school provides a foundation for their school mathematics achievement and strongly predicts their maths competence later in school (Geary, 2015).
Several recent longitudinal studies have investigated mathematical development in the transition from preschool to the early years of primary school. For instance, in one study, counting skills and understanding of quantities and the relationships between them in the year before starting primary school predicted children's maths achievement and teacher ratings of competence in maths one year later (Aunio, & Niemivirta, 2010). Other studies have demonstrated that, on entry to school, number sense and numeracy knowledge predict maths achievement in later school years (Aubrey, Godfrey, & Dahl, 2006).
Research illustrating the link between maths skills in infancy and preschool does not suggest that maths development is fixed, as a range of additional factors can promote and enhance maths achievement. For example, self-regulatory behaviour has been shown to be a significant predictor of the acquisition of academic skills, including early numeracy. Other research has suggested that working memory may contribute to maths achievement.
How to support early numeracy development
Given that early numeracy skills predict achievement in maths as children progress through school, interest has developed in identifying predictors of variation in numeracy growth, particularly as preschoolers already show wide variation in numeracy skills. This implies that school teachers will encounter children with a wide range of early numeracy skills even at school entry.
Already in preschool learning environments, teachers can vary significantly in the amount of mathematical information they convey while interacting with children. Such variation is related to the growth in numeracy skills over a year, with greater growth in numeracy skills related to greater maths-specific talk by teachers (Klibanoff, et al., 2006).
Fostering understanding of early numeracy development among early childhood educators is an important step in helping children in the early years to develop their mathematical thinking. Early childhood educators could be trained in the explicit use of ‘maths talk' in their everyday interactions with children to enhance opportunities for children to develop their early numeracy skills.
Research strongly suggests that early numeracy development can be supported by interactions between young children, and family members and early childhood educators. Parents positively influence their preschool child's maths achievement when they engage with their child at home in direct numeracy practices like teaching their children the number words and counting, and indirect numeracy practices like integrating numeracy into everyday tasks such as cooking (LeFevre et al., 2009).
Understanding more about preschoolers' early numeracy development is important in informing educational practices, understanding the variation in early numeracy skills among preschoolers, fostering early numeracy among children whose skills are less developed, and understanding why some children with well-developed early numeracy have difficulties learning mathematics at school.
This is a summary of Counting on it: Early numeracy development and the preschool child by Dr Kate Reid, the second in a series of papers, Changing minds: Discussions in neuroscience, psychology and research, published by ACER. Read the full paper at www.research.acer.edu.au/learning_processes/19
References
Aubrey, C., Godfrey, R., & Dahl, S. (2006). Early mathematics development and later achievement: Further evidence. Mathematics Education Research Journal, 18(1), 27–46.
Aunio, P., & Niemivirta, M. (2010). Predicting children's mathematical performance in grade one by early numeracy. Learning and Individual Differences, 20(5), 427–435.
Geary, D. C. (2015). Development and Measurement of Preschoolers' Quantitative Knowledge. [doi: 10.1080/10986065.2015.1016823]. Mathematical Thinking and Learning, 17(2-3), 237–243.
Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children's mathematical knowledge: The effect of teacher" math talk.". Developmental Psychology, 42(1), 59.
Kroesbergen, E., Van Luit, J., Van Lieshout, E., Van Loosbroek, E., & Van de Rijt, B. (2009). Individual Differences in Early Numeracy The Role of Executive Functions and Subitizing. Journal of Psychoeducational Assessment, 27(3), 226-236.
LeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children's math performance in the early school years. Canadian Journal of Behavioural Science/Revue canadienne des sciences du comportement, 41(2), 55.
Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense large-number discrimination in human infants. Psychological Science, 14(5), 396–401.
vanMarle, K., & Wynn, K. (2009). Infants' auditory enumeration: Evidence for analog magnitudes in the small number range. Cognition, 111(3), 302–316.
Wynn, K. (1995). Origins of numerical knowledge. Mathematical Cognition, 1(1), 35–60.
Wynn, K. (1996). Infants' individuation and enumeration of actions. Psychological Science, 7(3), 164–169.
Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11.
Given that research illustrating the link between maths skills in infancy and preschool does not suggest that maths development is fixed, as a teacher, how can you promote and enhance maths achievement in your classroom?
In what ways could you convey more mathematical information or ‘maths talk’ while interacting with children?
As an early childhood educator, think about the way you interact with your students’ parents and family members. How could you support parents to engage with their child at home in direct numeracy practices?
