Algebraic Thinking and Misconceptions

Algebra is considered the "gateway" to higher education. Failure rates in Algebra courses are staggering in school districts across the country. This lack of success disproportionately affects high needs students and impacts high school graduation rates, success in higher mathematics, and college enrollment. A new, innovative approach that prepares new teachers to stem the tide of failure is needed that takes into account why students struggle in algebra. Over 800 studies examine students’ struggles in algebra and potential strategies to help students overcome conceptual obstacles. Yet, the size of this resource makes it essentially inaccessible to preservice teachers. 

The mission of the Center is to help open the algebra gateway for students. We aim to help restructure preservice math teacher education and professional development of veteran teachers by utilizing research on students’ algebraic thinking. After initial funding by the Fund for the Improvement of Post-Secondary Education (FIPSE), we are now a non-profit organization. The innovative Center includes

  1. an online encyclopedia of algebraic thinking,
  2. catalog of formative assessment problems,
  3. database of technological tools,
  4. a collection of videos of students explaining their thinking as they work on problems, 
  5.  iPad apps,
  6. modules for math methods courses that incorporate research, and
  7. collaborative social network for teachers of algebra.

We also have two new books published to help teachers use our iOS apps. You can get the iBook, Teaching Algebra through iPad Apps, through the iTunes store (try searching by the title or one of the authors: Doug Neill or Steve Rhine) or through Gumroad. The Kindle version and student PDF pages are also available at Gumroad ( 

The objective of the Center is to increase preservice and veteran teachers’ knowledge, skills, and dispositions towards students’ algebraic thinking. Ultimately, through better preparation of teachers, students will have increased understanding of algebra, higher test scores, graduation rates, and college enrollment.  The Center was developed by a consortium of four public and private universities: Willamette UniversityPacific UniversityGeorge Fox University, and Western Oregon University and evaluated by the International Society for Technology in Education. Also participating are Portland State UniversityLewis & Clark College, and University of Northern Colorado.

In order to contribute to the Encyclopedia and Discussion forum, please create an account.

CONTACT: algebrathinking[at]

The Center for Algebraic Thinking

Supported by a grant from the United States Department of Education

Fund for the Improvement of Post-Secondary Education

Creative Commons License
The suite of resources including the Encyclopedia of Algebraic Thinking, Formative Assessment Database, Technology Database, and iOS Apps by Center for Algebraic Thinking are licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
Based on a work at