"Pure mathematics is, in its way, the poetry of logical ideas."
I devoured the most recent issue of Young Children (Volume 77, Number 3), especially the article Promoting Algebraic Reasoning in the Early Years by Lindsey Perry.
In her work Perry advocates for algebra in early math programs that explore two main ideas: composition and decomposition of numbers and properties of operations. According to Perry (2022) algebraic reasoning "involves seeing and describing patterns and relationships between quantities that may be unknown...which builds upon students' understanding of patterns and relationships with known quantities and values" (pg. 17). Perry posits that if children can observe and describe number relationships they can begin to symbolically represent relationships between numbers.
Composition and Decomposition of Numbers
children compose they understand that a number can be put together
using its parts (e.g., 5 plus 5 equals 10). Decomposition is the
opposite where a number can be broken apart in different ways (e.g., 10
can be broken into 8 and 2 or 7 and 3). When children compose and decompose numbers
they understand how to manipulate numbers in different ways, which
helps them become flexible when solving calculations. For example
mentally adding 68 + 22 can become easier when children realize that the
ones values total 10 and then add this to the tens value (10 + 60 +
20). Adding 68 plus 22 is the same as adding 10 plus 60 plus 20 but the second strategy may be easier to mentally calculate for many people.
Properties of Operations
Properties of operations encourage children to work flexibly with numbers in order to recognize and manipulate their relationships. This helps them simply calculations in order to more efficiently and accurately solve them. For example the order of addends (numbers added together) does not matter in order to arrive at a sum.
a + b = b + a
6 + 4 = 4 + a therefore a must be 6.
The commutative property applies to addition and multiplication. The order of numbers can be switched and it does not change the answer of the operation.
2 + 7 = 9 and 7 + 2 = 9
4 x 5 = 20 and 5 x 4 = 20
The inversion property states that all integers have an inverse number that when added equal zero.
3 + (-3) = 0
Although complicated young children can play with inversion when they become interested in, and work flexibly with equations.
3 + 2 - 2 = 3
So how can early childhood educators encourage children to participate in activities that promote early algebra? Here are some simple activities that can be used regularly to build children's confidence, ability and interest in number sense.
Provide children with a variety of subitizing cards and math symbols (addition sign, subtraction sign, equal sign). Encourage children to arrange the cards in different ways in order to create equivalencies.
Make 5 (or 10)
Show children a total number of cubes (starting with 5 and then 10 is helpful). Hide the cubes behind your back and remove some. Show children the remaining number of cubes and encourage them to calculate how many are hiding.
Singing Songs with a Five/Ten Frame
When singing popular songs and finger plays with children (e.g., 5 Little Monkeys, 10 in the Bed) add a five or ten frame as a visual and manipulate the number of counters in the frame to match the number being sang.
Roll a Ring
Calendar-based Number Talks
Which One Is Wrong?
Another favourite number talk is 'Which One is Wrong'. Different equations are displayed and children are challenged to explore each one using manipulatives (e.g., cubes, bead strings) to find the incorrect one.
What other activities do you use to help children with early algebra? Let's connect on social media @McLennan1977!