2.4 Early mathematics
Children’s growing abilities to connect mathematical ideas and vocabulary supports their early numeracy development. Children develop early mathematical understanding when they have experiences that support their understanding of number concepts. For example, during play and everyday experiences children can count, discuss and compare quantities and qualities (more, less, same, different), measure objects, order and classify and investigate patterns.
In the next video, as a mother and son play a simple game together, she incorporates some concepts and words related to mathematics. As you watch, consider all the ways she supports his development.
The goal of the Who’s Counting: When and how do we introduce number concepts in child care study was “….to gather information about the early numeracy and literacy knowledge, practices, and beliefs of early learning and child care (ELCC) practitioners” (Fast et al., n.d., p. 1). Listen to Dr. Joanne LeFevre, one of the researchers, speak about some of the findings. Read the research summary for more information.
How do the findings resonate with you?
What is your comfort level with mathematics?
How knowledgeable do you feel about children’s capabilities?
Dr. LeFevre, director of the Institute of Cognitive Science at Carleton University, describes the terms “early mathematics skills” and “numeracy”.
What is the progression of numeracy and mathematical understanding that children develop in the early years? See the following for a summary.
Infants can discriminate between two collections varying in numbers and locate objects in space. Often a quantity word, such as ‘more’, is a baby’s first word.
From age two or so, children often begin to learn the language and grammar of counting. They memorize the first ten or so counting words as nonsense words with no underlying meaning. They then begin to understand that ‘one’ means one apple while three means more than one and also more than two, gradually building a true understanding of number. Later, children pick up a set of rules to generate higher numbers.
Between ages two and five children become increasingly aware of their own thinking about numbers and begin to express it in words. Preschool children are capable of big ideas about numbers and operations, geometry (or shape and space), measurements and patterns (or algebra).
Understanding shape means analyzing and constructing shapes and defining their features. Children begin to be able to sort and also build shapes and gradually can verbally explain the differences between and square, a triangle and a circle for example.
Understanding numbers involves reasoning about them, making inferences and developing a mental number line, with smaller numbers on the left and spaced further apart than larger numbers on the right.This helps children hold numbers in their mind and manipulate numbers in arithmetic problems as they begin school.
The following resource sheet, from the Canadian Child Care Federation, provides an overview of the many numeracy abilities that children typically show from birth through age six.
In the next video, five year old Jordyne enlists a friend’s help to gather children for bubble blowing. While this goes on, the children demonstrate knowledge of some early math concepts. See how many you can spot.
It is fascinating to delve into children’s thinking as they gain numerical and mathematical knowledge. In the next video, LeFevre describes how children learn to count, explaining the difference between verbal or rote counting and the more complex cardinality knowledge (or counting objects). In the second video, LeFevre explains how children learn how those quantities map onto written symbols.
How would you explain the difference between verbal (or rote) counting and counting objects?
What knowledge do children need, and what strategies do they use, when learning to meaningfully count objects?
The concept of numeracy and mapping is fascinating – and quite complex when you consider all that is involved! What are the three kinds of representation that a number can have and why is this referred to as mapping?
As LeFevre has explained, children need to acquire a “number sense” before they can acquire skills necessary for the mathematical operations of addition, subtraction, multiplication and division. Number sense begins with the ability to see patterns and relationships between numbers. Computation and estimation abilities develop from a foundation of understanding of those patterns and relationships. As young children discover number patterns and relationships, they also memorize related number words and facts – they acquire the language of numbers.
Learning mathematics involves both thinking processes and rote memory. An exclusive focus on rote memory of number facts leaves children without the foundational understanding to use numbers effectively. A focus on processes without attention to memory can leave children without the skills to manipulate numbers quickly and easily.
Four categories of mathematical concepts preschool-aged children can understand are described in the next reading and activity, along with examples of each.
Can you think of other real life examples of child behaviours that illustrate these four types of mathematical knowledge?
Researchers have found many local games and songs support children’s informal understanding of numeracy and mathematics. The next reading describes two children’s games that involve mathematical understanding: Nhodo, a numbers game played in Zimbabwe; and Mancala, a game dating back thousands of years and played in different versions around the world. Note that both games are more likely to be played by children ages six or seven and up, an age when many children are very fond of games with rules.
How do you think these games support mathematical understanding?
What games did you play as a child that involved math?
What are the local games in your community that support children’s understanding of numeracy and mathematics?
As you contemplate the various playful ways that children explore numbers and mathematics – it is clear that the focus does not need to be on always mastering new skills. Math should be fun! Children also gain confidence when they are encouraged to celebrate and enjoy what they have learned, what they know. In the next video, Sir Kevan Collins discusses some interesting research related to the concept of mastery or “roaming in the known”.
How can you apply this to your interactions with children?
Can you think of examples of how you can encourage ‘mastery’ of mathematical concepts as opposed to promoting new skill development?
Daily environments and experiences with frequent references to quantity and quality relationships and the use of numbers nurture stronger mathematical understanding. Young children can explore ideas about spatial sense, structure and pattern, number, measurement and data comparisons.
Preschool and primary-school-aged children benefit from teaching that focuses on helping children discover patterns and relations (Baroody, 2010). Memorization or informal mathematical knowledge alone is insufficient for later mathematical understanding. For example, it is relatively easy for many children to learn to count by rote, but it doesn’t necessarily mean they understand the meaning of numbers.
The authors of the next Encyclopedia on Early Childhood Development article apply research findings to identify ways parents, teachers, and caregivers can promote children’s mathematical knowledge through “playful learning”. They explore the range of playful learning that includes child-directed free play, as well as more adult directed guided play and games.
Play experiences should be meaningful and incorporate children’s daily routines so that they are relevant and engaging. Consider these play areas. The one on the left was taken in a North American preschool and the one on the right is from Kenya.
In what ways are the materials in each photo similar and different?
What mathematical concepts can children explore while using these materials?
What might be some differences between how three year olds and five year olds might explore and understand these materials mathematically?
Researchers agree concrete materials are extremely useful in aiding children’s understanding of mathematical concepts. As David Elkind (2003) writes, “it is hard to overemphasize the importance of these hands-on experiences for young children. . . . It is certainly important for children to learn number words, but it is even more important that they learn to classify and seriate real objects” (p. 41).
The following policy brief from the Society for Research in Child Development (SRCD) provides an overview of research on how young children acquire numeracy skills and related policy implications.
For more information see the SRCD review of North American research on mathematics education for young children, which concludes that an organized curriculum and intentional teaching support young children’s acquisition of formal mathematical skills.
For more information about numeracy, explore the following two links to the Encyclopedia on Early Childhood Development. The first link is to a summary highlighting the importance of numeracy, key research findings, as well as how best to promote of children’s numeracy. The second link is to a number of research studies related to numeracy and mathematics. Choose one to review. Consider how the findings relate to your work with children.
