preview

Pattern Based Problem Solving Essay

Better Essays

Introduction In this paper, I will discuss the importance of pattern based problem solving as a prerequisite to algebra teaching. I will present a real-world task that students will encounter in a secondary, introductory algebra class. Solving problems involving patterns is essential to students’ ability to make generalizations. Such generalizations open the door to algebraic thinking and student understanding of algebraic variables, expressions, and equations. Literary Review Herbert and Brown (1997) describe a three-phase process that students undergo when solving problems: (1) pattern seeking, (2) pattern recognition, and (3) generalization. The generalization phase is where students develop a “rule” that could be applied to other problems. Stacey(1989) took a deeper look at the different types of generalizations formed by students during the problem-solving process. Student responses were categorized into four methods used to solve the problems. The methods were: (1) counting method where students counted from a drawing; (2) the difference method where students used some sort of constant multiple; (3) the whole-object method where students used a multiple of a smaller known quantity; (4)the linear method where students created a linear model of “an + b”. Student work that did not fit into any of the four methods was labeled as unclassified. Stacey (1989, p. 150) also defined near and far generalizations as a question that can be solved by step-by-step

Get Access