Project Activities
The researchers developed and tested a Grades K–2 early algebra intervention that included (1) a curricular framework that specified learning goals around core algebraic concepts and practices; (2) an intervention (instructional sequence) designed to achieve these goals; and (3) assessments that measured student learning in response to the intervention. They used a quasi-experimental design to conduct a preliminary study of the potential and feasibility of the intervention when taught by classroom teachers.
Structured Abstract
Setting
The study took place in elementary schools in Rhode Island.
Sample
The sample consisted of approximately 300 students and 6 elementary school teachers from a school district in Rhode Island. The district consisted of approximately 10% minority (non-white) student population, with about 16% of the district's school population categorized as low SES.
The early algebra intervention focuses on developing students’ core algebraic thinking practices (generalizing, representing, justifying, and reasoning with mathematical relationships) across key content domains (functional thinking; generalized arithmetic; and equivalence, expressions, equations, inequalities). The full intervention consists of 56 lessons (20 for Grade K; 18 for Grade 1; 18 for Grade 2).
Research design and methods
Researchers conducted a longitudinal classroom teaching experiment across Grades K–2 to develop and conduct preliminary tests on the early algebra intervention. To demonstrate the promise of the intervention, researchers then conducted a cross-sectional, quasi-experimental study with the intervention taught by classroom teachers. The sample included two classrooms at each grade level, with one classroom serving as the treatment classroom and one as the comparison classroom. Fidelity of implementation was examined through teacher logs, interviews, and surveys.
Control condition
The control condition was business-as-usual mathematics instruction.
Key measures
Measures of student learning outcomes included grade-level interview assessments and digital (online) assessments that were developed and validated as part of the project. Measures used to characterize teacher's fidelity of implementation included teacher logs, surveys, and interviews.
Data analytic strategy
In the initial design phase, researchers used qualitative methods of analysis of students' written work, interviews, and classroom teaching experiment lessons to identify themes and strategy use in students’ algebraic thinking. Researchers also used quantitative methods to measure growth in student performance across time, with differences in post-test scores collected at each grade level examined using analysis of covariance. For the quasi-experimental study, interviews and online assessments were analyzed quantitatively for pre-to-post gains. Teacher fidelity of implementation data were analyzed qualitatively for themes regarding teachers’ experience with implementing intervention lessons.
Key outcomes
The main findings of this project are as follows:
- The intervention supported the development of students’ algebraic thinking by helping students develop a correct understanding of the equal sign as showing two quantities are equivalent (Stephens, Veltri Torres et al., 2021; Sung et al., 2022), an understanding that is essential for making sense of equations and understanding how to solve them but which is typically problematic for young learners.
- Students also grew in their ability to represent mathematical quantities with variable notation (Veltri Torres et al., 2019), another core aspect of algebraic thinking.
- Results of the one-year quasi-experimental study where the intervention was taught by classroom teachers, showed that students in the Grades K-2 early algebra intervention group improved in their understanding of mathematical equivalence and equations, relationships with evens and odds, properties of arithmetic, the representation of varying unknown quantities, and functional thinking compared to students in the comparison condition (Stephens et al., 2023). Results also showed that the impact of the intervention was similar across Grades K to 2.
People and institutions involved
IES program contact(s)
Project contributors
Products and publications
The full early algebra curriculum for Grades K–5 curriculum is available at www.didax.com/LEAP.
Project website:
Publications:
Find available citations in ERIC for this award here.
Books
Blanton, M., Gardiner, A., Stephens, A., & Knuth, E., (2022). LEAP: Learning through an early algebra progression (Grade K). Didax: Rowley, MA.
Blanton, M., Gardiner, A., Stephens, A., & Knuth, E., (2022). LEAP: Learning through an early algebra progression (Grade 1). Didax: Rowley, MA.
Blanton, M., Gardiner, A., Stephens, A., & Knuth, E., (2022). LEAP: Learning through an early algebra progression (Grade 2). Didax: Rowley, MA.
Book chapters
Blanton, M., Gardiner, A., Stephens, A., Stroud, R., Knuth, E., & Stylianou, D. (2023). Lessons learned from designing an effective early algebra curriculum for Grades K–5. In D. Thompson, M. Huntley, & C. Suurtamm (Eds.), Lessons learned from research on mathematics curriculum. Information Age: Charlotte, NC.
Journal articles
Blanton, M. , & Gardiner, A. (2024). Developing an effective curriculum for early algebra. TERC Hands-On!
Blanton, M., Gardiner, A., Ristroph, I., Stephens, A., Stroud, R., & Knuth, E. (2024). Progressions in young learners’ understandings of parity arguments. Mathematical Thinking and Learning, 26(1), 90–121. https://doi.org/10.1080/10986065.2022.2053775
Rycroft-Smith, L. & Blanton, M. (2024). Espresso (Functional Thinking). Available at https://www.cambridgemaths.org/Images/espresso_48_early_development_of_functional_thinking.pdf
Stephens, A., Sung, Y., Strachota, S., Veltri Torres, R., Morton, K., Gardiner, A.M., Blanton, M., Knuth, E., & Stroud, R. (2022). The role of balance scales in supporting productive thinking about equations among diverse learners[CC1] . Mathematical Thinking and Learning, 24(1), 1–18.
Stephens, A., Veltri Torres, R., Sung, Y., Strachota, S., Murphy Gardiner, A., Blanton, M., Stroud, R., & Knuth, E. (2021). From "You have to have three numbers and plus sign" to "It's the exact same thing": K–1 students learn to think relationally about equations. Journal of Mathematical Behavior, 62.
Sung, Y., Stephens, A. C., Veltri Torres, R., Strachota, S., Blanton, M., Gardiner, A. M., Stroud, R., & Knuth, E. (2024). Teacher use of multimodal signs to support kindergarten students’ developing understanding of mathematical equivalence. Mathematics Education Research Journal.
Proceedings
Blanton, M. (2022). The role of learning progressions in “democratizing”students’ access to algebra. Invited plenary address at the North American Chapter of the Psychology of Mathematics Education, Nashville, TN. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. N. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the forty-fourth annual meeting of the North American chapter of the international group for the psychology of mathematics education. Middle Tennessee State University.
Ristroph, I., Blanton, M., Gardiner, A., Stephens, A., Stroud, R. Knuth, E. (2022). Progressions in Grade 1 Students’ Understanding of Parity Arguments. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. N. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the forty-fourth annual meeting of the North American chapter of the international group for the psychology of mathematics education, Nashville, TN: Middle Tennessee State University.
Sung, Y., Stephens, A., Veltri Torres, R., Strachota, S., Blanton, M., Gardiner, A., Stroud, R., & Knuth, E. (2022). Teacher language and gesture in an intervention focused on developing kindergarteners’ understandings of the equal sign. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. N. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the forty-fourth annual meeting of the North American chapter of the international group for the psychology of mathematics education (pp. 321–330). Middle Tennessee State University.
Stephens, A. C., Sung, Y., Blanton, M., Gardiner, A., Stroud, R., & Knuth, E. J. (2023). Kindergarten–Grade 2 students’ algebraic reasoning before and after a one-year early algebra intervention. Paper presented at the Annual Meeting of the American Education Research Association, Chicago, IL.
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