AlgebraByExample: Example-Based Problem Sets

The AlgebraByExample site analyzes mathematical mistakes.

The SERP-MSAN Partnership
Author(s) Organizational Affiliation
The Serp Institute
Publication Year
Resource Type
Instructional Material
Product Type
Target Audience

The SERP-MSAN partnership was supported to conduct this work by The Goldman Sachs Foundation and by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A100150 to Strategic Education Research Partnership Institute. The AlgebraByExample site analyzesmathematical mistakes, which are made over and over again. Research suggests these kinds of repeated errors are often due to students' underlying misconceptions.

To address these underlying misconceptions, teachers and researchers worked in partnership to create AlgebraByExample assignments that:

  1.   Target students’ misconceptions
  2.   Effectively remediate repeated errors
  3.   Fit flexibly with many different textbooks and teaching styles 
  4.   Support the Common Core State Standards (CCSS) for Mathematical Practice
  5.   Promote students’ spontaneous mathematical discussions

According to the site, this helps students identify, discuss, and reduce misconceptions, deepen their correct conceptual understanding, and strengthen their procedural skills. It provides teachers with insights into students' thinking, a launch point for mathematically rich discussion, and shared language for analyzing mistakes.

Benefits and Uses

The activities in this resource are designed to address misconceptions that lead to common mistakes. These common conceptual misunderstandings often result in procedural and conceptual errors that transfer over to other topics in the sequence. The activities provide student-generated examples of correct and incorrect answers to an algebra problem and questions, which lead to an analysis of these answers. Instructors without a background in mathematics education will find the materials a good source of information on common student misconceptions.

These activities are not specifically aligned to the CCSS or College and Career Readiness (CCR) standards. However, the focus of this resource is algebra which makes it is easy for a teacher to match activities to some of the most critical concepts (Major Work of the Level) in the mathematical standards for Levels C and D. The resource also supports MP3 (critique reasoning of others) and MP6 (attend to precision).

The primary audience for this resource is teachers who provide instruction aligned to CCR standards. Teachers could print out these activities and use them as part of a larger lesson focused on one of the algebra standards. Students would have to have previous knowledge of the content before working on these activities since they are evaluating misconceptions.  Although the tasks are self-explanatory, teachers would also need to be familiar with the mathematical content.

The resource suggests that the materials could be used as a warm-up, exit ticket, formative assessment, homework, pre-test, review, summer packet, prompts for discussion, independently, and in pairs/groups.

The common misconceptions outlined in the student worksheets can become good discussion prompts for mathematics discussions in which students are asked to critique the reasoning of others.

The download center ( provides a series of activities that correspond to a set of algebra topics. Teachers can print out these activities and use them immediately with students.  An introduction for teachers and students that explains the purpose of the materials and an answer key are also provided. The materials are already appropriate for adult students; the content would just have to be matched up to the appropriate CCR standards.

Resource Notice

This site includes links to information created by other public and private organizations. These links are provided for the user’s convenience. The U.S. Department of Education does not control or guarantee the accuracy, relevance, timeliness, or completeness of this non-ED information. The inclusion of these links is not intended to reflect their importance, nor is it intended to endorse views expressed, or products or services offered, on these non-ED sites.

Please note that privacy policies on non-ED sites may differ from ED’s privacy policy. When you visit, no personal information is collected unless you choose to provide that information to us. We do not give, share, sell, or transfer any personal information to a third party. We recommend that you read the privacy policy of non-ED websites that you visit. We invite you to read our privacy policy.