Teaching and learning algebra has undergone a critical transformation in the US over the last two decades. Recognizing that historical paths to algebra have been largely unsuccessful in terms of students’ achievement in algebra, mathematics educators have increasingly advocated that algebra be re-conceptualized in school mathematics as a longitudinal, grades K-12 strand of thinking. In particular, mathematics educators advocate that students have long-term, sustained algebra experiences in school mathematics, beginning in the elementary grades, that build their natural, informal intuitions about structure and relationships into formalized ways of mathematical thinking. Yet research has not systematically addressed how the development of children’s algebraic thinking effects their understanding of core algebraic concepts and practices in comparison to students who receive more traditional arithmetic-based instruction. Indeed, a fundamental assumption of early algebra education is that it will increase children’s understanding of algebraic concepts and practices and, ultimately, improve their success in the study of more advanced mathematics—particularly algebra—in secondary grades. To date, however, this premise is largely untested. The projects that comprise the Project LEAP portfolio (described below) seek to address this premise.



Eric Knuth – eric.knuth@austin.utexas.edu


Online Presence


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Current Projects


Building a Grades K-2 Early Algebra Learning Progression Prototype for Diverse Populations

Research indicates that students need sustained algebra instruction throughout Grades K-12 mathematics education, if their informal intuitions about mathematical structure and relationships are to be transformed into the more formal ways of mathematical thinking. Currently, however, no research-based models are available to guide the development, characterization, and assessment of young children’s algebraic thinking, particularly at the start of formal schooling. This study will design a curricular framework for developing children’s algebraic thinking across Grades K-2, with a particular focus on understanding how to support the teaching and learning of algebra with students in at-risk settings.

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Extending a Grades 3-5 Early Algebra Learning Progression into Grades K-2

The purpose of this project is to develop and test the promise of a Grades K–2 Early Algebra Learning Progression (EALP) to build young children’s algebraic thinking.

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Identifying Effective Instructional Practices that Foster the Development of Algebraic Thinking in Elementary School

This project seeks to identify teaching practices that can be linked to students’ early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices.

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The Impact of a Teacher-Led Early Algebra Intervention on Children’s Algebra-Readiness for Middle School (LEAP 3)

We scaled up our work in LEAP 2 to a much larger number of schools (approximately 46 schools) and students (approximately 3200 students), and are studying the effectiveness of our EALP’s instructional intervention when implemented by regular classroom teachers. We are comparing the performance of students who received the early algebra intervention in Grades 3-5 to students who received more traditional elementary grades instruction, and are following both sets of students (intervention and control) into Grade 6.

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Past Projects


Developing Algebra-Ready Students for Middle School: Exploring the Impact of Early Algebra (LEAP 1)

In our first project (NSF, 2009-2013), we constructed an Early Algebra Learning Progression [EALP] consisting of a curricular framework and progression developed by coordinating research, curricular, and mathematical perspectives; a Grades 3-5 instructional sequence based on the framework and progression; associated assessments; and levels of sophistication describing strategies observed in children’s mathematical work. We also conducted a preliminary study to examine the impact of our EALP’s instructional intervention as measured by our assessments.


The Impact of Early Algebra on Students’ Algebra-Readiness (LEAP 2)

In our second project (NSF, 2012-2016), we utilized the tools developed in LEAP 1 to conduct a small scale, quasi-experimental, longitudinal study of our EALP’s instructional intervention in Grades 3-5. In particular, we compared the performance of students who received the early algebra intervention to students who received more traditional elementary grades instruction.