“Young children reinvent arithmetic. Spontaneously or by imitating their peers, they imagine new strategies for calculation. They also learn to select the best strategy for each problem. The majority of their strategies are based on counting, with or without words, with or without fingers. Children often discover them by themselves, even before they are taught to calculate.”
― Stanislas Dehaene, The Number Sense: How the Mind Creates Mathematics
How does counting support all areas of mathematical competence?
Counting Collections
Counting Collections Video
Counting Collections is a classroom routine enacted small groups of learners.​
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The teacher creates sets of collections (100-300 items in each collection) and a supply of sorting containers. The children may work independently or in partners.
Counting Collections supports learners’ counting competence, number sense, place value, computation, and mathematical reasoning and communication.
Reynaurora Resendez
During this counting collections activity, I selected 4 students from kindergarten. Each student got a different collection (Mini-erasers, connecting cubes, colored disks and wooden sticks). The collections vary between 60-130 items. The students counted independently their collection and sort them however they wanted.
In this video we can see how each mathematician works in a different way when counting their collections. A student was connecting the cubes, another one was putting them in a line, another one started to separate them by colors and the other one started to count by one and move the sticks to the side.
During this activity, as I was walking around and I could experience some significance concepts of number sense being explore and shown. For example: all kindergarten students showed the right counting sequence when counting; they also use one-to-one correspondence when counting their collections; and, when students finished counting their collections and I asked "how many items did you count?" all of them mentioned the last number that was counted for so they had cardinality.
When it was time for students to represent their counting strategies on paper, all of them did something different. This being another example of how students show their mathematical thinking on different and unique ways that make sense to them. Counting collections promotes deep understanding on number sense for young mathematicians as well as providing opportunities for teachers to guide students through this process.
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