Counting Counts
- By Christine Hopkinson
- Sep 17, 2024
Mathematical Foundation
Counting is at the core of such math knowledge as it forms the foundation for many higher-level mathematical concepts. Here are some reasons why counting concepts and skills are so crucial:
- Counting helps children and students develop basic numeracy skills, such as understanding number sequences, order, and quantity.
- Counting lays the groundwork for developing number sense, which is the understanding of what numbers represent and how they relate to each other.
- Counting is essential for problem-solving in math as it forms the basis for solving mathematical equations and word problems.
- Counting helps students understand mathematical operations and their relationships. For example, addition involves counting up, while subtraction involves counting down (or up!).
- Counting is essential for grasping more advanced mathematical concepts like place value, fractions, percentages, integers, algebra, etc.
Counting to Mathematize
Young children also use counting skills they develop to “mathematize,” or make sense of their world in a variety of ways:
Quantifying Objects: They learn to assign a number to a set of objects, which allows them to compare and understand the relative sizes of distinct groups.
Order and Sequence: They learn that numbers follow a specific sequence (1, 2, 3, 4, etc.) and this order is crucial for organizing events and objects in their world.
Problem-Solving: Children use counting to solve everyday problems, such as figuring out how many toys they have, how many friends are playing, or how many cookies are on the plate. They learn that adding more objects increases the count, while taking objects away decreases the count.
Sorting & Patterning: They discern attributes of objects to sort and count. Young children also begin to recognize, continue, and create patterns (numerical and visual).
Developing Counting
Teaching and learning to count proficiently is quite rigorous and includes several distinct, yet related, concepts and skills such as:
- Number List & Stable Order - rote oral counting, numbers are always in the same order (also includes counting backwards and starting from a # other than 1).
- Activity- Chorally count daily using fingers, a rekenrek, or simply orally.
- Subitizing- look at a small set of objects (1-6) and know how many there are without counting them, or later, counting on from a known group in the set.
- Activity- Flash a Subitizing (dot) Card for about ten seconds and ask, “How many dots are there? How do you know?”
- One-to-One Correspondence - uses one number to count each item once using tracking strategies (either to count a given set or count out a set for a given number).
- Activity- Ask students to count a set of stackable counters by picking each one in the set up and placing it in a stack; or ask students to count out a given number of counters from a pile.
- Cardinality - when counting a set, the last number stated tells how many or how much.
- Activity- Guide students to count and place the correct Unifix Cubes Number Hat on a Unifix Cube tower.
- Order Irrelevance & Conservation of Number - objects can be counted in any order; no matter the order a set is counted in or the arrangement the set is in, the total is the same.
- Activity- Place some Buddy Bear Counters in a line and ask students to count them. Invite students to count the line again, in a different way (order). Confirm the total did not change. Then arrange them in a more spaced-out line, circle, array, square, or scattered arrangement. Ask students “How many now?”
- Abstraction - counting things that cannot be touched/seen; items, even if dissimilar, can be counted as a set, or a collection of objects.
- Activity- Invite students to count the number of family members and/or pets. Consider having them track the count by representing each with a Jumbo Unifix Cube or finger.
- Numeral Recognition and Writing - connecting the concrete representation (or abstract verbal numeral) to a written physical representation.
- Activity- Model for students how to form numerals and then allow them to practice with Sandpaper Numerals.
- Activity- Count chorally each day as a class routine, pointing to each numeral on the Number Path Pocket Chart.
- Teen Numbers - understanding 11-19 as ten and some more.
- Activity- Guide students to build each teen number using 2 Magnetic Rainbow Ten Frames. Help them to count each out and recognize that the teen number is made up of ten and some more.
Looking for a ready-to-go kit that engages students in all these skills and MORE? Check out our new Pre-K and TK Math Activity kits:
Overall, counting is a fundamental skill that allows young children to make sense of quantity, order, and relationships in their world. It forms the basis for their mathematical understanding and prepares them for more advanced math concepts in the future.
Happy counting!