March 8, 2013
602.4.15-04, 38, 39: Teaching Methods—Mathematics
Teaching students to count rationally beyond ten must incorporate many different levels of number sense on the part of the teacher. As the teacher I must be able to help the students understand the cardinality of numbers, order irrelevance, one-to-one correspondence, and stable order. All of these concepts play a major role in number sense. The cardinal rule is where the student is extracting a quantity. The student counts the number of objects to determine how many objects are present. Order irrelevance indicates that when counting the order in which objects are counted is not important. The quantity remains the same. One-to-one correspondence verifies that each object is counted and represented one and only one time. Stable order is when the student is able to correctly state the number order repeatedly. This is the established counting sequence being taught. All mathematical counting methods have repeating patterns no matter what language, culture, or heritage from which it originates.
When teaching first grade students to count beyond ten, a quick analysis is necessary to ensure the students have a solid foundation of the numbers one through ten. The students should be able to verbally count in sequence from one to ten, randomly recognize quantities presented to them the quantities one through ten, be able to show different ways to make the numbers one through ten, and show one-to-one correspondence when counting to ten.
The next step is to begin by introducing the lesson and what will be taught. This lesson will introduce the numbers eleven through fifteen. These numbers are eleven, twelve, thirteen, fourteen, and fifteen. It would be advisable to write the numbers in order from one to fifteen on the board, highlighting the numbers eleven through fifteen to show the new numbers. Proceed with asking the students what they know about the numbers eleven through fifteen. This...