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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