Five Counting Principles

 

Five Counting Principles

Students usually are introduced to the world of mathematics in early childhood. They observe objects around them and learn to sort them by colors, shapes and so on. Slowly, students start understanding that objects can be 1 or many and thus they start building number sense. They count objects and start associating the quantity with a number.

Though teaching the numbers 1 to 20 is useful, simply teaching this is not equivalent to learning to count. Children need a strong foundation in counting and quantity to be able to build number sense.

Here are 5 counting principles that can help parents and educators in helping children with counting and quantity.

Principle	Explanation	Potential Misconceptions	How to help students?
1.Stable Order	This involves understanding the verbal sequence of counting          It also means that a student should know a list of words that must be used in repeatable sequence          The list of number names must be atleast as long as the number of items that need to be counted. For example, if a student knows sequential counting only upto 5, then there cannot be 6 items.	Students might not say the numbers in the right sequence	Encourage students to count on           Provide students opportunities to practice this with different types of objects (household items like spoons, lego blocks etc)         Model the correct order when students say the incorrect sequence and encourage them to repeat after you.          Use number songs and rhymes to help students with the sequence
2.One to one correspondence principle	This involves understanding that every object in a group must be counted once and only once.          Rote learning of numbers (which is done through stable order principle) is a pre-requisite here.	Students count the same object more than once          Student miss counting of objects	This can be promoted by helping students count regularly during play          Students need to touch each object as they say aloud the number name. This ways they can keep a track of the objects counted.          Children need to be encouraged to line up the objects in a row or touch and move them from one end of table to another to avoid misses.         Students can also use fingers to show the numbers.          Once students are comfortable, they can also use tally marks for counting.
3. Cardinal principle	Pre-requisite (stable order and one to one principle)          This involves understanding that the last number used to count a group of objects indicates the total number of objects in the group. For example when a student counts 5 blocks, they would count 1,2, 3, 4,5. The last number 5 tells us that there are 5 blocks.          Students should understand that the last number not only names the last object but also indicates the total number of items.	Students who recount the number of objects when asked how many objects are there in the set usually have not grasped this principle	Students can count the items and then you can ask them to place the same number of items in the bag.          Show a number and ask students to count the number of items to match that number          Ask students to count the number of objects in a set and then ask them ‘How many objects have you counted?’
4. Abstraction Principle	Pre-requisites (the first 3 principles)         This involves helping a student understand that any collection of objects can be counted (not only tangible or objects that can be touched)          For example, when children sit on a swing in the park, they can count the number of times they moved from one position to the other.          Through this principle, they can also understand that dissimilar items or items of different size can also be counted. For example if earlier they counted only the number of spoons, now they can count spoons and plates and tell the total number of utensils.	Students not being able to move on from tangible objects.	Provide opportunities like rolling a ball and counting the number of times the ball moved from point A to B.          Number of times the traffic signal went green while walking on the road.          Drop a coin into a glass multiple times and ask the number of times the glass made a sound.          Have 2 large items and 3 small items and ask which group has more (this helps understand if students consider larger sized items as being larger in number. Through dialog and discussion this misconception can be addressed).
5. Order Irrelevance Principle	This involves understanding that the order in which items are counted is irrelevant.          Students may choose to count items from right to left or left to right and as long as they follow the one to one principle, the result remains the same.	If a student counts objects placed horizontally and then recounts when the same set is placed vertically then student may not have grasped the principle	Encourage students to count in different ways -  left to right, right to left, top to bottom, bottom to top

 

The above 5 principles help in establishing a foundation in building number sense and quantity.

 

Reference Articles and Websites

https://makemathmoments.com/counting-principles/

https://www.thrapston-primary.northants.sch.uk/attachments/download.asp?file=5966&type=pdf

https://sidebysideconsulting.com/2017/11/16/5-counting-principles-every-preschooler-needs-to-know/