# Functional Gardens

Mathematical problem solving in the real-world continues to be a concern for mathematics educators. Algebra, Geometry, Calculus, and other math content subjects have long been taught in the same way. Teachers usually rely on the ‘stand-and-deliver’ lecture and heavily on the unimaginative textbook. Though some textbooks have changed in recent years, the central focus is still on paper and pencil, memorization of rules, and recurring use of postulates. The Curriculum and Evaluation Standards for the School District of Philadelphia Mathematics Instructional Model (NCTM 1989) articulates a vision for mathematics instruction to “meet students’ needs to understand and be able to use mathematics in an increasingly challenging world” and “represent and analyze relationships using tables, verbal rules, equations, and graphs”. The standards also urge teachers to give students the opportunity to be ‘actively involved’ in math through data analysis and statistics that are integrated into the curriculum. My hope is to show that these types of activities can be incorporated into an Algebra I course using perpetually basic concepts. Several of these are: look for a pattern, guest and check, make a list, make a table, draw a picture, diagram, work backwards, and try to simplify the problem. Along with addition, subtraction, multiplication, division, the order of operations, and several other rudimentary concepts, those just mentioned need to be incorporated into the art and crafts of problems solving.

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