Overview

This course provides teachers of grades 3 through 5 with an opportunity to explore how activities that foster algebraic thinking can be integrated into the elementary classroom. Algebraic thinking consists of more than just learning how to solve for the variables x and y; it helps students think about mathematics at an abstract level, and provides them with a way to reason about real-life problems. In this course, participants will explore three components of algebraic thinking: making generalizations, thinking about the equals sign, and being able to reason about unknown quantities. As participants stretch their own algebraic reasoning skills, they will also spend considerable time thinking about how to integrate algebraic tasks into their own classroom instruction. This course uses readings, video, online discussion boards, a final project, and engaging mathematics problems to promote the idea that the incorporation of algebraic thinking tasks in elementary school mathematics is critical to students’ future success.

Goals and Products

This course will enable participants to

• learn how children in grades 3-5 can think about basic algebraic concepts;
• appreciate the importance of algebraic thinking in the upper elementary curriculum;
• read and discuss relevant research on the importance of algebraic thinking in elementary school instruction;
• explore a variety of problems that can be used with students to develop their algebraic thinking;
• understand student misconceptions about the sign “=” and why this is such a pivotal concept in elementary mathematics;
• identify generalization as a strategy for solving some, but not all, algebraic problems;
• appreciate the role of “unknown quantity” problems in the development of algebraic reasoning;
• learn how to design and “algebrafy”** activities that encourage algebraic thinking;
• create a collection of activities which promote algebraic thinking that can be integrated into classroom practice;
• promote a “learning-by-doing” methodology, which is applicable to students at all ages.

Format and Requirements

This course is divided into six one-week sessions that include readings, an activity, and an online discussion among course participants. Each session is designed to take approximately two to four hours to complete. The outline for the course is as follows:

• Session One: What is Algebraic Reasoning?
• Session Two: Understanding Algebraic Representations and Patterns
• Session Three: The Meaning of Equality
• Session Four: Using Algebra to Think About Unknown Quantities
• Session Five: ‘Algebrafying’ Elementary Math Instruction
• Session Six: What is the Value of Algebra in Elementary School?

Course participants are expected to complete weekly assignments along with actively participating in the online discussion board. In addition, participants will develop and share their ideas to incorporate tools and strategies presented in the course into their own curricula.

Prerequisites

This course is for teachers, technology specialists, curriculum specialists, professional development specialists, or other school personnel. Participants are expected to have regular access to computers. In addition, participants should be proficient with using email, browsing the Internet, and navigating to computer files.

Content and Technology Standards

This course, Algebraic Thinking in Elementary School, will help teachers to enable their students to meet the following Content Standards as identified by the National Council for Teachers of Mathematics (NCTM):

• describe, extend, and make generalizations about geometric and numeric patterns;
• represent and analyze patterns and functions, using words, tables, and graphs;
• represent the idea of a variable as an unknown quantity using a letter or a symbol;
• express mathematical relationships using equations;
• model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. investigate how a change in one variable relates to a change in a second variable.