Encyclopedia of Algebraic Thinking

A searchable database of students' algebraic thinking and misconceptions

Click here to view an alphabetized index of the encyclopedia content.

Over 800 studies research and discuss students’ struggles in algebra and potential strategies to help students overcome conceptual obstacles. Here we distill those articles into encyclopedia entries for teachers to use. This Encyclopedia is part of the Center for Algebraic Thinking. Here you will find 64 entries based on five domains and linked to the Common Core State Standards (CCSS). Each entry in the encyclopedia contains answers to the below questions when available from the research. You can search by the five domains below, Common Core State Standard, Learning Progression, or by keyword. An advanced search allows you to search the entire Center site, including the Encyclopedia, Formative Assessments, and Technologies. At the end of each entry is an opportunity for you to include your experience with students' thinking on that topic. Please add your experience!


1) Variables and Expressions

2) Algebraic Relations (Equations and Inequalities)

3) Analysis of Change (Graphing)

4) Patterns and Functions

5) Modeling (Word Problems)


1. What Common Core State Standard(s) does this research address?

2. What is the symbolic representation of thinking with the idea? (What does it look like?)

3. How do students think about the algebraic idea? (What does it sound like?)

4. What are the underlying mathematical issues involved?

5. What research-based strategies/tools could a teacher use to help students understand?