Problem Solving and the Common Core

Introduction

Creating a culture of critical thinkers is a unit concerned with building confidence in the elementary student’s ability to approach written math problems in an analytic, organized, and reasoned manner. Although this unit is intended for the use of third through fifth grade educators, the principle uses are applicable to a wide range of mathematics classrooms.  It is the intention of this unit to prepare students to parse and discuss and solve many types of one and two-step, addition and subtraction problems. Through this process of exploring problem scenarios, it is my hope that students will begin to view themselves as expert problem solvers.

As used in my title, “Key Words” is a reference to a method of approaching a written problem wherein students memorize words associated with: addition, subtraction, multiplication, and division. Students are then asked to use those words to assign a computation, or multiple computations to a word problem. Although I have observed that this method occasionally satisfies the problem posed, it is my assessment that students should not become too dependent on it because it can often be misleading. As Roger Howe expresses in Three Pillars of First Grade Mathematics, and Beyond, “Addition is often described as combining, and subtraction as taking away, but the types of situations in which these operations are used are more varied than these brief descriptions would suggest. Mathematics educators have articulated a taxonomy of one-step addition and subtraction word problems.”¹ A close study of the taxonomy of word problems as they progress sequentially through Kindergarten and on, advises that relying on key words after Second grade becomes very unhelpful. A popular educational blogger at The Math Spot² discusses this contentious issue in an entry entitled “Key Words Are Not the Key to Word Problems.” She relies on Common Core progression charts in Kindergarten through Third grade to demonstrate her point. After studying the taxonomy of word problems in Kindergarten, she finds that key words within problems are somewhat helpful. She then examines key words used in the types of problems that First graders encounter. The blogger notes that beginning in First grade, the unknowns in a problem may appear in any given part of the expression and that the types of problems students are exposed to vary much more than in Kindergarten. She concludes that again, ‘key words’ are somewhat helpful but cannot be relied on consistently. The blogger then examines the usefulness of keywords in Second grade. She notes that students begin to encounter word problems with key words that are misleading enough for students to write the wrong expression for a given problem. Her sentiments are echoed by the authors of Teaching Student-Centered Mathematics when they express, “Instead of making meaningless rules, create opportunities for discussing adding and subtracting, using contextual situations.”³

“Creating a culture of critical thinkers” refers to the style in which I will be approaching word problems in my classroom. The lessons will be anchored in classroom discussions and creating a structured and safe environment in which to explore mathematic possibilities as a whole class, in groups, and individually. Suggestions and tips for modeling the expectations and implementation of a student centered discussion will be a major component of my unit and will be elaborated on and referred to in the ‘Strategies’ portion of the unit.