Funded Projects

Since 1998, the majority of our funded projects 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 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.

My studies have been funded through the following grants:

1998-1999 – NSF Grant #9722732
Role: Researcher
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.

2000-2003 – NSF Grant #9909591 – “Bringing out the Algebraic Character of Arithmetic”
Role: Researcher
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).

General Electric Math Excellence Fund – “Integrating Algebra and Engineering in the Classroom”
Role: Co-Principal Investigator
Award: $360,870
For publications see Wong & Brizuela, 2007a, 2007b, 2007c, Winners of “Distinguished Achievement Award” from the Association of Educational Publishers, 2008.

2003-2007 – NSF-ROLE #0310171 – “Algebra in Early Mathematics”
Role: Senior Researcher
Award: $1,527,925

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).

2007-2011 – NSF-REESE #REC-0633915 – “The Impact of Early Algebra on Later Algebra Learning”
Role: Principal Investigator
Award:$936,229

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.

2008-2009 – Spencer Foundation Grant – “Young Children’s Numerical Representations Across Different Systems”
Role: Principal Investigator
Award: $40,000

For publications see Brizuela & Cayton, 2010.

2010-2018 – National Science Foundation, Math/Science Partnership (MSP) Program [NSF-MSP #DUE-0962863] – “The Poincaré Institute for Mathematics Education”
Role: Senior Researcher
Award: $9,550,799

For publications see Bautista, Brizuela, Glennie, & Caddle, 2014; Bautista, Brizuela, & Ko, 2013; Bautista, Cañadas, Brizuela, & Schliemann, 2015; Bautista, Wilkerson-Jerde, Tobin, & Brizuela, 2013, 2014; Caddle, Bautista, Brizuela, & Sharpe, 2016; Wilkerson-Jerde, Bautista, Tobin, Brizuela, & Cao, 2016.

2010-2019 – National Science Foundation, Robert Noyce Teacher Scholarship Program [NSF-DUE #1035342] – “Urban Mathematics and Science Teacher Collaborative”
Role: Co-Principal Investigator
Award: $2,130,768

2011-2014 – NSF DRK-12 #1154355 – “Children’s Understanding of Functions in Grades K-2”
Role: Co-Principal Investigator
Award: $418,086

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. For publications see Blanton, Brizuela, Gardiner, Sawrey, & Newman-Owens, 2015, 2017; Brizuela, & Blanton, 2014; Brizuela, Blanton, Gardiner, Newman-Owens, & Sawrey, 2015; Brizuela, Blanton, Sawrey, Newman-Owens, & Gardiner, 2015; Sawrey, Brizuela, & Blanton, 2015; Cañadas, Brizuela, & Blanton, 2016.

2014-2017 – NSF DRK-12 #1415509 (sub-contract with TERC) – “Learning Trajectories in Grades K-2 Children’s Understanding of Algebraic Relationships”
Role: Co-Principal Investigator
Award: $449,893

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. For publications see Blanton, Otalora Sevilla, Brizuela, Sawrey, Gardiner, Gibbins, & Kim, 2018; Ramirez Uclés, Brizuela, & Blanton, 2020; Ventura, Brizuela, Blanton, Sawrey, Gardiner, & Newman-Owens, 2021.

2014-2022 – National Science Foundation, Robert Noyce Teacher Scholarship Program [NSF-DUE #1439880] – “The 1-12 Urban Mathematics and Science Teacher Collaborative”
Role: Principal Investigator
Award: $1,799,092

2019-2023 – National Science Foundation, Innovations in Graduate Education program [NSF-IGE #1855886] – “STEM Graduate training in Data Science: solution-oriented, student-led, team-based, computationally-enriched (SOLSTICE) training”
Role: Co-Principal Investigator
Award: $499,733

2022 – Tufts Springboard – “Developing and piloting a measure for mathematical mindsets and identities”
Role: Principal Investigator
Award: $74,342.70

2022-2024 – National Science Foundation, DRK-12 Program [NSF DRK-12 # 2201095] – “Exploring K-2 Children Understandings of Visual Representations in Algebraic Reasoning”
Role: Principal Investigator
Award: $449,998