Higher Order Cognition and Linear Systems of Equations by hcj

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									Higher Order Cognition and Linear Systems of Equations
An algebraic lesson plan for 9-12 grades

Time needed: Approximately 2-3 class periods (hours)

Teacher Preparation and Materials:

              Four to five seven card sets with the explanation of one of the seven higher order
              cognition functions listed on each card. As listed below:

              Concept formation: Integrating a set of features that go together to form a class
              Critical thinking:                  Evaluation of ideas
              Creativity and Brainstorming:       Thinking independently
              Reasoning and Logical Thinking:     Thoughtful answers to complex problems
              Problem Solving:                    A systematic stepwise approach to questions
              Rule Use:             Learning, developing, and applying rules and principles
              Mental Representation:              Portraying new ideas into one’s mind so that
                                                  they are meaningful and lasting.
Lesson:
        The purpose of this lesson is two-fold: First, to introduce the concept of higher order
cognition, understand the seven major functions of higher order cognition and how they applying
to learning; second, to introduce the concept of a system of linear equations.

       Write on the blackboard, a simple system of linear equations:
       For example,         2x + 3y = 6
                            4x – 3y = 12

       1)     As a group, ask students what they observe about the items written on the
              board. Be overly vague about their meaning or significance. Allow students to
              brainstorm answers for several minutes. Write all comments down on the board or
              on an overhead projector. Encourage participation if needed.

       2)     After the brainstorming session, break the class into four or five equally sized
              groups. Give each group the task of going through the brainstormed ideas and
              developing an explanation of what the meaning or significance of the items
              written on the blackboard. Each group should be allowed five to eight minutes to
              complete this task. Then, each group should be given a minute or so to explain
              their findings to the class as a whole.

       3)     At this point, one of the key concepts about the problem that in all likelihood will
              be brought out is that each of these is a linear equation. If that concept isn’t
              introduced by this point, redirect and have the students establish that these are two
              linear equations. A concept that the students should be very familiar with at the
              point this lesson is used.
       4)   In their groups, ask students the following question. If we were to draw two
            straight lines on the same coordinate axes, what are the possible outcomes? Allow
            students several minutes to discuss and refine their answers.

       5)   Once it is established that two lines either intersect at a point or are parallel, give
            students a small worksheet in which they are to graph two lines on a single
            coordinate plane and determine the point of intersection. This is one way to solve
            a system of linear equations.

       6)   In their groups, have students attempt to find other ways to solve a simple linear
            system.

       7)   Explain and demonstrate the substitution method for solving linear equations.
            Have students discuss what method they will use to solve linear systems and what
            will help them remember how to solve a linear system.

       8)   Remind students of the previous seven steps used to introduce and reinforce the
            concept of solving linear systems. Provide students with a written outline of each
            of these seven steps. Give each group of students a set of higher order cognition
            function cards as described above. Have students assign one or more of each
            higher order cognition functions to each step of the process listed above.

            For example:

            Step One:       Write on the blackboard, a simple system of linear equations:
                            For example,          2x + 3y = 6
                                                  4x – 3y = 12
                            1)     As a group, ask students what they observe about the items
                                   written on the board. Be overly vague about their meaning
                                   or significance. Allow students to brainstorm answers for
                                   several minutes. Write all comments down on the board or
                                   on an overhead projector.

            Higher Order Cognitive Function(s) used in this step:
                                                        Creativity and Brainstorming

       9)   Have each group share their answers and their justification.

Debrief:    Have students give an example of when they have used each type of higher order
            cognitive function in a different class or situation.

								
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