This essay will explore how I would teach a group of 10 first grade students to count rationally to 15 assuming that all of them are already able to count rationally to 10. I shall explain how I would ensure that students understand each of the four rational counting principles of one-to-one correspondence, the stable order rule, the order irrelevance rule, and the cardinality rule. I shall present an assessment I would use to evaluate student mastery of rational counting to 15. Finally, I shall discuss how I would adapt my instruction to accommodate English Language Learners (ELL) and students with learning exceptionalities.
Rational counting means students apply all four of the following counting principles: ·Cardinality Rule means the total number of objects counted is represented by the last number name reached. ·Stable Order Rule means numbers are assigned in the correct order every time a group of items are counted. ·One-to-One Correspondence is the assignment of one number name to each item in the group that is being counted. ·Order Irrelevance Rule means it does not matter in which order the group of items are counted. (Reys, 2012)
The Cardinality Rule will be addressed first because it is probably the easiest and most basic of the counting principles for these students to understand as they move from 10 to 15. 1)I shall ask the ten students how many items total they would have if they counted each individual item once and went to 10. For example, if they had crayons on their desk and counted each one only once and counted to 10 in doing so, how many crayons would they have? Students would reply 10 because they can already apply the four counting principles up to ten. 2)I shall explain to students that the purpose of the lesson will be for them to expand their ability to count items from 10 to 15. 3)I shall ask students if they count each crayon on their desk and counted up to 15, how many crayons would you have? Students would reply 15. 4)In order for students to actually learn what 15 represents I shall place a number line on the white board with 15 dots evenly spaced along its length. 5)I shall label each one with its corresponding number 1 to 15 with the 10th dot circled. 6)I shall explain to the students that they can already count to 10 while pointing to 10 on the number line. 7)I shall then point to the 15th dot and explain they are going to be able to count up to fifteen by learning the numbers between ten and fifteen. 8)I shall instruct the students what those numbers are by saying and pointing to them on the number line, “eleven, twelve, thirteen, fourteen, and fifteen”. 9)I shall ask them questions to stimulate critical thinking and help them develop number sense such as:
Q: How many items would you have if you counted to 15?
Q: How many more than 10 is15?
Q: So if you had 10 crayons and I gave you 5 more you would then have how
The Stable Order Rule will be addressed second. Students can already count rationally to ten so they understand the four basic counting principles. I anticipate learning and applying the new number names eleven, twelve, thirteen, fourteen, and fifteen in correct order will probably be their greatest learning challenge. To help students learn these new number names and apply them in correct order I shall:
1)Model just the new names and numbers in proper order that are on the white board preceded by the numbers 1 to 10 they already know. 2)I shall say the new number names slowly in their correct order pointing to each one as I say it. 3)I shall then have the students repeat after me chorally each new number name as I point to them and say them. This process will be repeated several times until I formatively assess all 10 students are confidently restating each new number name. 4)I shall then ask them to chorally say...