Research

The TERC-Tufts Early Algebra Project

Since 1998, we have been investigating and documenting children's learning of algebra from Kindergarten through 8th grade. Through our research, we have shown that introducing algebra as part of the early mathematics curriculum is highly feasible and we have also clarified how specific representational tools — tables, graphs, numerical and algebraic notation, and certain natural language structures — can be employed to help students express functional relations among numbers and quantities and solve algebra problems.

A general characteristic of our work, which is also basic for other proponents of Early Algebra (EA), is the belief that early mathematics (especially arithmetic) and algebra are not fully distinct: a deep understanding of arithmetic requires mathematical generalizations and understanding of basic algebraic principles.

Since 1998, we have carried out longitudinal interventions with children in the elementary school grades and followed them up into middle school. Our studies have been funded by the National Science Foundation through the following grants:

1. 1998-1999 - NSF Grant #9722732:
   Intervention I was developed over the course of a school year with a group of 18 3rd grade students (see Carraher, Schliemann, & Brizuela, 2000, 2005; Schliemann, Carraher, & Brizuela, 2006) and involved the design, implementation, and evaluation of 16 EA lessons.
2. 2000-2003 - NSF Grant #9909591 – "Bringing out the Algebraic Character of Arithmetic":
   Intervention II was implemented in four classrooms (69 students total) with whom we worked from the second semester in 2nd grade to the end of 4th grade, implementing one weekly 90-minute EA lesson (see Brizuela & Earnest, 2007; Carraher, Schliemann, Brizuela, & Earnest, 2006; Carraher, Schliemann, & Schwartz, 2008; Schliemann, Carraher, Brizuela, Earnest, Goodrow, Lara-Roth, & Peled, 2003).
3. 2003-2006 - NSF-ROLE #0310171 – "Algebra in Early Mathematics":
   In Intervention III we worked with 26 students from 3rd to 5th grade. In 3rd and 4th grades we implemented two weekly 60-minute lessons followed each with a homework assignment and 30-minute homework review sessions (50 lessons in third grade and 36 lessons in fourth grade). In 5th grade, we implemented 18 lessons throughout the year; each weekly lesson was 90 minutes long and was followed by a homework assignment and a 45-minute homework review session (see Carraher & Schliemann, 2007; Carraher, Schliemann, & Brizuela, 2008; Carraher, Martinez, & Schliemann, 2008; Martinez & Brizuela, 2006).
4. 2007-2011 – NSF-REESE #REC-0633915 – "The Impact of Early Algebra on Later Algebra Learning":
   In this project, we followed up a subset of our experimental group of students from study #3 into middle school, exploring the impacts of our 3rd to 5th grade intervention over time. For this purpose, we implemented an Algebra Summer Camp in Summer 2008 and Summer 2009. For publications, see Brizuela, Martinez, & Cayton, 2013; Schliemann, Carraher, & Brizuela, 2012).
5. 2011-2014 – NSF DRK-12 #1154355 (sub-contract with TERC) – "Children's Understanding of Functions in Grades K-2":
   This research project addresses how children in grades K-2 understand concepts associated with functions—particularly as these concepts relate to different representational tools (e.g. natural language, algebraic notation, tables, and Cartesian coordinate tools). We studied how students are able to coordinate co-varying data and identify and express relationships with such data—particularly examining the connections between their thinking about recursive patterning and co-varying relationships and correspondence relationships.
6. 2014-2017 – NSF DRK-12 #1415509 (sub-contract with TERC) - "Learning Trajectories in Grades K-2 Children's Understanding of Algebraic Relationships":
   This research project's goal was to identify levels of sophistication in children's thinking as it develops through instruction. Understanding how children's thinking develops can provide a critical foundation for designing curricula, developing content standards, and informing educational policies, all in ways that can help children become successful in algebra and have wide access to STEM-related careers.