
Research
The TERCTufts 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:
 19981999  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.
 20002003  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 90minute EA lesson
(see Brizuela & Earnest, 2007; Carraher, Schliemann,
Brizuela, & Earnest, 2006; Carraher, Schliemann, &
Schwartz, 2008; Schliemann, Carraher, Brizuela,
Earnest, Goodrow, LaraRoth, & Peled, 2003).
 20032006  NSFROLE #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 60minute lessons followed
each with a homework assignment and 30minute
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 45minute homework
review session (see Carraher & Schliemann, 2007;
Carraher, Schliemann, & Brizuela, 2008; Carraher,
Martinez, & Schliemann, 2008; Martinez & Brizuela,
2006).
 20072011 – NSFREESE #REC0633915 – "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).
 2011ongoing – NSF DRK12
#1154355 (subcontract with TERC) –
"Children's Understanding of Functions in Grades
K2":
This research project addresses how children in
grades K2 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). Researchers will study how
students are able to coordinate covarying data and
identify and express relationships with such
data—particularly examining the connections between
their thinking about recursive patterning and
covarying relationships and correspondence
relationships.
