Social Constructivism 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.

This lesson is an example of a Cognitive Apprenticeship

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. Show the students how you would break them in half. As you are showing them, be sure to speak out loud and explain what you are doing and why. Once the brownies have been cut, let each student have a fraction of the brownie. (Modeling: the first step in cognitive apprenticeship)

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. Tell them that these pieces are whole pieces of paper. Model for them how to write whole on their piece of paper. Have them write whole on one of the papers.
2. Next, show the students how to cut one of the pieces in half and write 1/2 on both pieces of paper. As you are doing each step, be sure to model for the children. After you have showed them, talk them through doing their own. Be sure to remind those that may be struggling. 
3. Do these same steps with each piece of paper. (make strips that are 1/3, 1/4, 1/6, and 1/8)
4. As they cut the pieces of paper, tell them to talk themselves through each step. Also, remind them to write the fractions on the paper. After watching the teacher model, and coach them through the steps, they should be able to use self talk and talk their way through the steps. Eventually they will be able to do it with inner speech. (Scaffolding: step 3)
5. After all of the pieces of paper are cut, guide them by asking them questions about each piece of paper? Why are the pieces of paper with the largest number on the bottom, smaller than the rest? As you are asking each question have them articulate their knowledge and put it into their own words. (Articulate: Step 4)
6. 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. (Reflect: step 5) 
7. 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. Ask them to explore new ways to apply what they are learning. Give them an assignment to go home and find different ways that fractions are used. ex: cooking measurements. (Explore: step 6)

This lesson plan is an example of Cognitive Apprenticeship. In this lesson, the students are learning skills and gaining knowledge from a more knowledgeable other, who is the teacher. The cultural tools used in this lesson are the symbols used for fractions (number system), and the language that the teacher is speaking. Cultural tools play a very important role in cognitive development. As they are learning fractions they are developing their "cultural tool kit". The teacher is within the Zone of Proximal Development as she teaches the children about fractions. Most of the children have most likely never dealt with them very much. The children are doing a task that they are able to do because the teacher is there helping them. If the teacher wasn't scaffolding and working through the steps with them, then they would wouldn't be able to accomplish the task. The steps the teacher takes to scaffold in this lesson are: first they model and work through the task with the brownies. Second, the teacher coaches them through cutting their own strips of paper. As they are cutting the strips she is encouraging private speech. Last, eventually the students will be able to accomplish the task using inner speech. They will be able to apply what they have learned and find other examples of fractions. The dialectical relationship between the learner and the teacher (more knowledgeable other - MKO) is constantly happening. As the teacher is modeling she is the one speaking. Later in the lesson she models and talks them through the task. After that, they walk themselves through the steps by themselves. At the end they have a discussion. The teacher is asking the questions and directing the discussion while the students participate in a conversation with the MKO.