# Unit 2 - Principles for Designing a Cognitive Apprenticeship Classroom We have the following math equation to solve:

### 2 x 2 + 10 =?

I will talk you through the process of solving this math equation. The first thing I do is to identify all the factors involved. I create a mental picture. I list the facts and the questions the problem is asking. I write them down or keep them in my mind. I do this Susan because it helps me to visually think through the process of what I am doing.

Next I think about the math rules of operation; I ask myself what operations I need to perform to solve this math problem. The answer, multiplication and addition; is that correct Susan? Yes Mrs. Miller, you need to multiply and add. Then I ask myself what is the rule for solving a math problem with 2 types of operators? Do I multiply first or add? I recall that the rule is to multiply first then add, I learned this rule in basic math just as we did earlier today.

Then I write the equation into a structure that I can read and interpret. I know that I am multiplying 2 x 2 so I put them together in a parenthesis. I use the parenthesis to group together the numbers that will be used by the same operators, for example 2 and 2 uses the multiplication operator. Also, I use the parenthesis to group the numbers that need to work out together. My new equation now becomes: (2 x 2) + 10=? Now it is time to work out the equation and come up with the solution. I multiply the first group and come up with the answer 4, because I know that 2 x 2 is equal to 4. I dropped the parenthesis because there is only one operator so it is not needed. Now my equation is: 4 + 10=? So I would add 4 + 10 to arrive at the solution 14. Okay Susan I have solved the problem, now I want you to solve the next equation: 8 x 10 + 1 + 2 =? and talk me through your thinking process as your come up with the solution.

The following scenario of instruction is an example of a Cognitive Apprenticeship instructional model where the teacher-expert teaches the student-apprentice problem-solving skills. The teacher has walked the student through solving a math equation by modeling, coaching, and explaining every step she does to arrive at the solution and why. This has helped the student internalize the process for solving math problem and so that she can work out similar math equations in the future.

In this unit you will learn how to apply the principles of Cognitive Apprenticeship in your classroom instruction. At the end of this unit you will be able to:

• Compare two Modeling Cognitive Apprenticeship modelsthat can be incorporated in the classroom and identify the best model to be used in your classroom.
• Demonstrate the ability to perform as Learning Activity - Unit 2 expert/master by using the teaching methods: modeling, coaching, and scaffolding in a in a reading problem solving task.
• Demonstrate the ability to instruct the [Learning Activity - Unit 2.html apprentice/learner] on how to articulate, reflect, and explore in a math problem solving task.
• Understand how to design a cognitive apprenticeship learning environment.

### Conclusions

As these models and examples illustrate there are a variety of learning applications which can use the Cognitive Apprenticeship instructional model. The essential elements of the Cognitive Apprenticeship model are modeling, coaching, scaffolding, and articulation, reflection, and exploration. Incorporating these elements into the learning environment: content, method, sequencing, and sociology will provide students grounded opportunity to become an expert Apprentice in the subject to be learned.