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DISCOVERING ALGEBRA GRAPHING LINEAR EQUATIONS by David A. Thomas and Rex A. Thomas

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Brief Overview Use technology (a computer graphing program) to provide for student directed exploratory learning and the development of mathematical thinking and reasoning Students experimented with various linear equations and their graphs and the effect of changing variables on the graphs Attempted to help students learn how to learn math

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NCTM Standards Addressed Build new mathematical knowledge through problem solving (problem solving) Make and investigate mathematical conjectures (reasoning and proof) Communicate their mathematical thinking coherently and clearly to peers, teachers, and others (communication) Recognize and use connections among mathematical ideas (connections)

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NCTM Standards Addressed (Algebra) Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations

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NCTM Standards Addressed (Algebra) Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency - using technology in all cases

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The Lesson A three day lesson split between a computer lab and classroom each day Students worked in pairs to determine where a line would appear on a graph depending on the coefficients of AX + BY = C Students were encouraged to experiment and make conjectures with few instructions or directions given Students then shared their findings

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The Lesson

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Day 2 required critical thinking about a few given conjectures and a need to communicate their thoughts to the class Conjecture – Changing only the coefficient of x causes all lines to cross the y-axis in the same place The final part of the lesson was making predictions based on what they had learned

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Strengths Addresses higher order thinking and learning Allows for an emphasis on strategies of learning and thinking and not just on the correctness of an answer Encourages participation by all students as there is no “right” answer only the students’ thoughts and observations

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Strengths Provides for an in depth learning of a particular topic which if used at the beginning of a unit can give a good foundation for topics to come A great opportunity to introduce students to student directed learning

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Issues or problems If this is the first time students have done a student directed learning experience there will be confusion and resistance The time it takes to fully implement the lesson is prohibitive to material coverage Lesson didn’t provide any real life connections

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Implementation in the Classroom Could be done with students in the regular classroom with graphing calculators New TI technology allows students to share information with the teacher electronically in the classroom from graphing calculators Student ideas could be shared by showing graphs on overheads, smartboard, etc. Could be scaled back in scope or expanded depending on time to be devoted to the lesson

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Discussion Questions In what ways could you build on this lesson to make connections for the students to real life applications? How could this lesson be shortened or simplified and still accomplish some of the same objectives and outcomes?

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Field experience – A simpler lesson Students worked in pairs on a calculator activity Students used graphing calculators to determine the effect of changing m and b in an equation in slope- intercept form Students required to answer higher level questions including making predictions and explaining their thinking to the class

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CITATIONS Thomas, David A. and Thomas, Rex A. Discovering Algebra – Graphing Linear Equations. The Mathematics Teacher, Vol. 92, No. 7, October 1999

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