Research

The TERC-Tufts Early Algebra Project

Since 1998, we have been implementing and documenting children's learning of algebra in the early grades. 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.

Over the past ten years, we have carried out three longitudinal interventions with children in the elementary school grades. Currently, we are following up the students from our last intervention. 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. 2006-ongoing – NSF-REESE #REC-0633915 – "The Impact of Early Algebra on Later Algebra Learning":
   We are currently following up a subset of our experimental group of students 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 June-July 2008.