Counting Rationally to Fifteen, Research Paper Example

Many children go into the first grade with deficient counting skills and difficulty in learning how to count.  Counting skills and understanding numbers are important for future learning.  In fact, understanding how numbers work or number sense leads to the ability to manipulate mathematical concepts in order to solve more complex problems.  It is therefore imperative to have a structured method or methods for teaching counting as children enter elementary school.  This essay describes methods in which I would practice in order to teach a group of ten first graders how to count rationally to 15.

First grade students can develop skills to rationally count to 15 through a variety of different methods, such as one-to-one correspondence, stable order rule, order irrelevance rule and cardinality rule.  The first method of teaching counting is instructing the children to perform one-to-one correspondence. In one-to-one correspondence the children verbalize the numbers in order and connect it to a memory game.  For instance, I would have the children sit quietly while I clap my hands a certain amount of times.  I would then have the children repeat the claps the same number of times, while counting aloud. (Pica, 2012).

The next method would be applying the stable order rule, which states that the words used to count must be the same string from one count to the next. For instance, I would have the students count to fifteen repeatedly.  The students whom are saying the numbers in an incorrect order, but consistently missing the same numbers will be instructed to listen to others count to fifteen in order to establish the correct sequence.

The third method is applying the order irrelevance rule, in which an object is assigned a number in order to count.  In order to apply this rule to teaching students to count to fifteen, I will instruct the students to pick fifteen objects in the classroom to count.  For instance, the student can choose posters, maps or books.  I will instruct the students to start at one position in the room and move their way around the room counting the object they chose until they reach fifteen.  The purpose of the exercise is for the students to realize that each object represents a number.  The fourth method to incorporate for counting is the cardinality rule.  The cardinality rule states that the number that is last in the group represents the group.  For instance, if the students are counting objects in the room, such as pencils, fifteen would represent the group of pencils.  (Mounts, 2007)

In order to properly evaluate the students rationally counting to fifteen, an assessment is required.  Each individual method should be evaluated individually.  For instance, for the one-to-one correspondence, I will conduct the clapping game and note if the child is able to complete the clapping to fifteen.  For the stable order rule, I will have each student count to fifteen individually three times and indicate if they are repeating the sequence consistently.  For the order of relevance rule, I will place animal pictures on a piece of paper and instruct each student individually to look and count the fifteen animals on the paper, noting if the child was able to count to fifteen.  Finally, to assess the cardinality rule, I will place fifteen crayons in a basket and instruct each student to pull each crayon out, while counting to fifteen.  The result will be noted.

After evaluating each individual student, the necessary methods will be practiced as needed.

It is also proper to understand that there are different needs for some students, such as English Language Learners and students with learning exceptions.  In order to allow the student this type of student to feel comfortable, I would allow the student to count at a slower pace.  In addition, I would help the student by pointing to the objects and helping them with the numbers as they are counting. (Mounts, 2007)   Furthermore, positive encouragement can also help and make the assessment less stressful for the all types of students, as well as help them learn to count to fifteen rationally.


Pica, R. (2012). Help Your Child Understand One-to-One Correspondence. Retrieved on

February 7, 2012 from:

Mounts, P. (2011). Rationally Counting to Fifteen. Easy Ways to Help First Graders Count.

Retrieved on February 7, 2012 from: