Developmental Cognitivism Lesson Plan

 Objective: Students will be given 6 different colors of paper and will make fraction strips of paper representing whole, 1/2, 1/3, 1/4, 1/6, and 1/8 in 15 minutes.

Hook:

The students will walk into the room and find a tray of brownies at the front of the classroom. They will wonder what they are for and be very curious. Once everyone has taken their seats explain to them that you are going to break them into different pieces to represent fractions of the whole. Have someone come up and cut the brownies in half. Repeat this step until the brownies are cut into enough pieces for the whole class. Once the brownies have been cut, let each student have a fraction of the brownie. 

Instruction:

At the end of this activity, students will have explored their fraction strips and will understand what a numerator and denomenator of a fraction represents. They will also see the relationship between whole, 1/2, 1/3, 1/4, 1/6, and 1/8. They will also understand that the larger the denominator, the more parts the whole has been broken into.

1. First students will be given 6 sheets of different colored paper. Be sure that everyone knows that these pieces are whole pieces of paper. Have them write whole on one of the papers.
2. Next,have the students cut one of the pieces in half and write 1/2 on both pieces of paper.
3. Do these same steps with each piece of paper.
4. As they cut the pieces of paper, be sure that they are exploring writing the fractions on the paper.
5. After all of the pieces of paper are cut, have them explore the different sizes and the numbers that are written on the paper. Which piece is larger?
6. Explain what numerator and denominator are.
7. Why are the pieces of paper with the largest number on the bottom, smaller than the rest? Have them explore and answer this question.
8. After students have explored their strips of paper by them selves, have them write down why they think the largest number on the bottom is the smallest piece of paper. Then discuss as a class. 
9. At the end of the discussion all of the students will understand that the bigger the number on the bottom, the more parts the whole has been broken into.

This lesson is stage-based learning because it is part of the preoperational and concrete-operational stage. Some of the student will be able to solve hands-on problems while others will not be able to think them through yet. Each child is unique in the way they learn. The teacher will model a little to help those that may not be able to think them through yet. There is also more than one activity so that students can identify with at least one. Piaget believes that to know an object or to gain knowledge, you have to act on the object. In this lesson plan, the students are able to manipulate their own pieces of paper. The lesson involved action and not much teacher intervention. Social interaction isn't necessary for students to gain knowledge, but it is sometimes necessary to guide students away from egocentricism. In this lesson, the students didn't work in groups very much, but at the end they had a discussion about what their discoveries. 

Accommodation and assimilation are both apparent in this lesson. When students are cutting up the papers and realizing that the bigger the number on the bottom, the smaller the piece of paper, they are most likely experiencing disequilibrium. They have always thought that a bigger number will mean a bigger piece of paper. After experiencing this disequilibrium they will have to accommodate their existing schemes and make sense of the new situation. Assimilation is also happening has they are exploring their pieces of paper. They are using what they already know about numbers and trying to make sense of the fractions. Piaget believed that children gained knowledge on their own and with little teacher interference. This lesson was more of a discovery learning lesson because it didn't have much teacher intervention. The reason there is a little is because some of the children are still in the preoperational stage and need assistance working through tasks. Other than the little intervention, the students are working on their own and making their own hypothesis. The students will also be mastering the operation of classification while they are performing this task. They are learning how to focus on the characteristic of how big the strips are and comparing them to each other.