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

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

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)

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

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

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

The Lesson

 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

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

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

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

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

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?

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

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