CGI - Counting Collections
CGI - Counting Collections
Why is counting important?
Learning Mathematical Ideas through Counting Collections
The important skills and understandings that make up counting are developed through many opportunities to count. As adults who count with ease, it is hard to recall all of the component skills involved in learning to count and making sense of quantity. Some of the important concepts of number that children develop include:
- Number names: What do I say?
- Sequence of numbers: What order do the number names go in?
- Name-symbol relation: How do I write that number?
- One-to-one correspondence: Saying one number name for each object counted.
- Cardinality: The last number said is the total amount of objects.
- Relative size: Which is bigger?
- Base-ten structure: How do these numbers (written and verbal) go together?
- Efficiency and accuracy in counting: How can I group objects to count and record more efficiently?
- Representations: How do I communicate my ideas in words, numbers, and drawings?
Young students are working to coordinate three aspects of a number during Counting Collections. To really understand what 12 means, students need to connect the verbal name (“Twelve”), the quantity (12 items), and the written number (12). This activity asks students to work on all three aspects during Counting Collections by counting the items, assigning a unique number name to each item, determining the total amount, and then representing that quantity in words and written notation. Students often utilize number charts in order to find out how to write new numbers.
Later on, students develop a richer understanding of how our base-ten number system is structured and begin to make use of place value to count more efficiently. This is often done using tools like a ten-frame or cups to hold groups of ten.
In the past, students weren’t given enough practice counting and writing numbers far beyond 100. This can become a barrier for students as they are developing strategies for operating on larger numbers. Counting Collections provides a space for students to learn about and generalize the structure of the base-ten number system well into the hundreds and beyond, supported by tools such as 1,000 charts.
Developing Recording Strategies Over Time
After students count their collections, they will show how they counted. In the beginning, this might mean students leave out the items to show how they lined the items up, how they grouped their items, what it sounds like to count them, etc. Students will also record their count on paper. This is an important part of the activity; recording the counted collection is a chance for students to practice representing quantity and writing numbers.
When young students first record their collection on paper they might draw the collection by ones, draw how they organized the count, or write the total amount. Eventually students may use number sentences to show how items were grouped and combined when counting. Eventually students will use formal mathematical notation to record how they counted.