**Journal articles**

Stephens, A., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., & Gardiner, A. M. (In press). What early algebra knowledge persists one year after an elementary grades intervention? *Journal for Research in Mathematics Education*.

Blanton, M., Stroud, R., Stephens, A., Gardiner, A., Stylianou, D., Knuth, E., Isler, I., & Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3–5. *American Educational Research Journal*, 56(5), 1930-1972.

Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Murphy Gardiner, A. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. *Educational Studies in Mathematics*, 102, 193–219.

Stylianou, D., Stroud, R., Cassidy, M., Gardiner, A., Stephens, A., Knuth, E., Demers, L. (2019). Putting early algebra in the hands of elementary school teachers: Examining fidelity of implementation and its relation to student performance. *Journal for the study of education and development/**Infancia y Aprendizaje** *(Special Issue: Early Algebra).

Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., Gardiner, A. (2018). Developing a learning progression for curriculum, instruction, and student learning. *Cognition and Instruction, 36*(1), 30–55.

Stephens, A., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Gardiner, A. (2017). A learning progression for elementary students’ functional thinking.* Mathematical Thinking and Learning, 19*(3), 143–166.

Knuth, E., Stephens, A., Blanton, M., & Gardiner, A. (2016). Building an early foundation for algebra success. *Phi Delta Kappan, 97*(6), 65–68.

Blanton, M., Stephens, A., Knuth, E., Gardiner, A., Isler, I., & Kim, J. (2015). The development of children's algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. *Journal for Research in Mathematics Education, 46*(1), 39–87.

Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. (2015). Just say YES to early algebra! *Teaching Children Mathematics, 22*(2), 92–101.

Isler, I., Marum, T., Stephens, A., Blanton, M., Knuth, E., & Gardiner, A. (2014). The string task: Not just for high school. *Teaching Children Mathematics, 21*(5), 282–292.

Stephens, A., Knuth, E., Blanton, M., Isler, I., Gardiner, A., & Marum, T. (2013). Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings. *Journal of Mathematical Behavior 32*(2), 173–182.

**Book chapters**

Blanton, M., Brizuela, B., Stephens, A., Knuth, E., Isler, I., Gardiner, A., Stroud, R., Fonger, N., & Stylianou, D. (2018). Implementing a framework for early algebra. In C. Kieran (Ed.), *Teaching and Learning Algebraic Thinking with 5- to 12-year-olds. The Global Evolution of an Emerging Field of Research and Practic*e (pp. 27–49). Springer International Publishing.

Strachota, S., Knuth, E., & Blanton, M. (2018). Cycles of generalizing activities in the classroom. In C. Kieran (Ed.), *Teaching and Learning Algebraic Thinking with 5- to 12-year-olds. The Global Evolution of an Emerging Field of Research and Practice* (pp. 351–378). Springer International Publishing.

Blanton, M. (2017). Algebraic reasoning in Grades 3-5. In M. Battista (Ed.), *Reasoning and Sense Making in Grades 3-5* (pp. 67–102). Reston, VA: National Council of Teachers of Mathematics.

Stephens, A., Ellis, A., Blanton, M., & Brizuela, B. (2017). Algebraic thinking in the elementary and middle grades. In J. Cai (Ed.),* Compendium for Research in Mathematics Education* (pp. 386–420). Reston, VA: National Council of Teachers of Mathematics.

Stephens, A., & Knuth, E. (2017). Algebraic reasoning in grades 6–8. In M. Battista (Ed.),* Reasoning and Sense Making in Grades 6–8* (pp. 47–71). Reston, VA: National Council of Teachers of Mathematics.

Blanton, M. & Kaput, J. (2016). Classroom practices that promote algebraic reasoning. In E. Silver & P. Kenney (Eds.), *Lessons learned from research: Volume 2: Useful research on teaching important mathematics to all student *(pp. 123–134). Reston, VA: National Council of Teachers of Mathematics.

Bolt, D., Kim, J., Blanton, M., & Knuth, E. (2016). Applications of item response theory in mathematics education research. Invited chapter in *Psychometric methods in mathematics education: Opportunities, challenges, and interdisciplinary collaborations, Monograph #15 of the Journal for Research in Mathematics Education *(pp. 31–51)*.*

Knuth, E., & Stephens, A. (2016). The equal sign does matter. In E. Silver & P. Kenney (Eds.),* Lessons learned from research: Volume 2: Useful research on teaching important mathematics to all students *(pp. 135–140). Reston, VA: National Council of Teachers of Mathematics.

Stephens, A., with Blanton, M. (2016). Algebraic reasoning in prekindergarten–grade 2. In M. Battista (Ed.),* Reasoning and Sense Making in Prekindergarten-Grade 2 *(pp. 71–104). Reston, VA: National Council of Teachers of Mathematics.

**Conference Proceedings**

Stephens, A., Stroud, R., Strachota, S., Blanton, M., Stylianou, D., Knuth, E., Veltri Torres, R., Murphy Gardiner, A., & Sung, Y. (2019). Sixth-grade students’ retention of early algebra understandings after an elementary grades intervention. In Otten, S., Candela, A. G., de Araujo, Z., Haines, C., & Munter, C. (Eds.), Proceedings of the forty-first annual meeting *of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 147–156). St. Louis, MO: University of Missouri.*

Cassidy, M., Stroud, R., Stylianou, D., Blanton, M., Gardiner, A., Knuth, E. & Stephens, A. (2017).* *Examining the fidelity of implementation of an early algebra intervention and student learning*. *In Galindo, E., & Newton, J., (Eds.),* Proceedings of the thirty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 299–302)*. Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Prough, S., Strachota, S., Veltri, R., Isler, I., Blanton, M., Gardiner, A., Knuth, E., & Stephens, A. (2017). Fostering generalizations: A classroom discourse analysis*. *In Galindo, E., & Newton, J., (Eds.),* Proceedings of the thirty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 287–298)*. Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Strachota, S., Stephens, A., Knuth, E., Blanton, M., Isler, I., & Gardiner, A. (2017). The interplay between students’ understandings of proportional and functional relationships. In Galindo, E., & Newton, J., (Eds.),* Proceedings of the thirty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 251–258)* Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.

Isler, I., Strachota, S., Stephens, A., Fonger, N., Blanton, M., Gardiner, A., & Knuth, E. (2017). Grade 6 students’ abilities to represent function rules.In T. Dooley, & G. Gueudet (Eds.). *Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education* (pp. 432–439). Dublin, Ireland: DCU Institute of Education and ERME.

Strachota, S., Fonger, N., Stephens, A., Blanton, M., Knuth, E., & Gardiner, A. M. (2016). Understanding variation in elementary students’ functional thinking. In C. Csíkos, A. Rausch, & J. Szitányi (Eds.), *Proceedings of the fortieth annual conference of the International Group for the Psychology of Mathematics Education, *(pp. 243–250). Szeged, Hungary.

Fonger, N., Stephens, A., Blanton, M., & Knuth, E. (2015). A learning progressions approach to early algebra research and practice. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), *Proceedings of the thirty-seventh annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 201–204). East Lansing, MI: Michigan State University.

Isler, I., Blanton, M., Murphy Gardiner, A., Knuth, E., Stephens, A., & Kang, H. (2014). A comparison of elementary and middle grade students’ algebraic reasoning.In Oesterle, S., Nicol, C., Liljedahl, P., & Allan, D. (Eds.), *Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol. 6: pp. 110). Vancouver, Canada: PME.*

Isler, I., Stephens, A., Gardiner, A., Knuth, E., & Blanton, M. (2013). Third-graders’ generalizations about even numbers and odd numbers: The impact of an early algebra intervention. In Martinez, M., & Castro Superfine, A. (Eds.), *Proceedings of the thirty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 140–143). Chicago, IL: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Stephens, A., Isler, I., Marum, T., Blanton, M., Knuth, E., & Gardiner, A. (2012). From recursive pattern to correspondence rule: Developing students’ abilities to engage in functional thinking. In Van Zoest, L. R., Lo, J.-J., & Kratky, J. L. (Eds.),* Proceedings of the thirty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 821–828)*. *Kalamazoo, MI: Western Michigan University.

Marum, T., Isler, I., Stephens, A., Gardiner, A., Blanton, M., Knuth, E. (2011). From specific value to variable: Developing students’ abilities to represent unknowns. In L. R. Wiest & T. Lamberg (Eds.), *Proceedings of the thirty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education *(pp. 106–113). Reno, NV: University of Nevada, Reno.

**Research Presentations**

Stephens, A., Sung, Y., Strachota, S., Veltri Torres, R., Morton, K., Murphy Gardiner, A., Blanton, M., Knuth, E., & Stroud, R. (2020). How do balance scales shape K–2 students’ understandings of equations? Poster presented at the Annual Conference of the Society for Research on Educational Effectiveness, Washington, D.C.

Stephens, A., Knuth, E., Blanton, M., Gardiner, A., Stylianou, D., & Stroud, R. (2019). A comprehensive approach to early algebra. Paper presented at the Annual Meeting of the American Education Research Association as part of the symposium *Exploring Diversity and Synergy Across Research Programs within Early Algebra*, Toronto, CA.

Stroud, R., Blanton, M., Gardiner, A., Knuth, E., Stephens, A., & Stylianou, D. (2019). Project LEAP: Results of a grades 3–5 early algebra intervention with at-risk populations. Paper presented at the Annual Meeting of the American Education Research Association, Toronto, CA.

Veltri Torres, R., Prough, S., Strachota, S., Stephens, A., Sung, Y., Gardiner, A., Blanton, M., & Knuth, E., (2019). Describing the unknown: Moving toward variable notation and algebraic thinking in kindergarten. Paper presented at the Annual Meeting of the American Educational Research Association, Toronto, Canada.

Strachota, S., Blanton, M., Stephens, A., Gardiner, A.M., & Ristroph, I. (2019). Supporting instruction that fosters algebraic thinking*. *Paper presented at the Association of Mathematics Teacher Educators Conference, Orlando, FL.

Strachota, S., & Gardiner, A.M. (2019). Building students’ algebraic thinking: Explorations with evens and odds. Presentation at the National Council of Teachers of Mathematics Practitioner Conference, San Diego, CA.

Blanton, M. (2018). Can young children think algebraically? Invited presentation, The Kaput Center for Research and Innovation in STEM Education, University of Massachusetts Dartmouth, Dartmouth, MA.

Blanton, M. (2018). Early algebraic thinking: The case of variable notation. Invited presentation, MESA, University of Georgia, Athens, GA.

Prough, S., Veltri, R., Strachota, S., Stephens, A., Knuth, E., & Blanton, M. (2017). Supporting students’ algebraic reasoning in the early grades. Presentation at Wisconsin Mathematics Council Annual Conference (National Council of Teachers of Mathematics-Affiliate), Green Lake, WI.

Blanton, M., Isler, I., Stephens, A., Gardiner, A., Knuth, E., Demers, L., & Strachota, S. (2017). Longitudinal growth in children’s algebraic thinking: Results of an Early Algebra Intervention across Grades 3–5. Paper presented at the National Council of Teachers of Mathematics Research Conference, San Antonio, TX.

Stephens, A., Stroud, R., Knuth, E., Blanton, M., Stylianou, D., Strachota, S., Isler, I., & Gardiner, A. (2017). The impact of a large-scale early algebra intervention. Paper presented at the National Council of Teachers of Mathematics Research Conference, San Antonio, TX.

Strachota, S., Knuth, E., Stephens, A., & Blanton, M. (2017). The co-development of functional thinking and equivalence.* *Paper presented at the National Council of Teachers of Mathematics Research Conference, San Antonio, TX.

Veltri, R., Prough, S., & Strachota, S. (2017). Supporting student generalizing: An analysis of classroom discourse*. *Poster presented at the 27th Society of Text and Discourse Conference, Philadelphia, PA.

Veltri, R., Prough, S., Strachota, S., Knuth, E., Stephens, A., Stylianou, D., Blanton, M., Stroud, R., & Gardiner, A. (2017). The impact of a teacher-led early algebra intervention. Poster presented at thirty-ninth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics, Indianapolis, IN: Purdue University.

Blanton, M., (2016). How do we prepare students for algebra? Invited keynote address at the 2016 North Carolina Council of Teachers of Mathematics, Greensboro, NC.

Blanton, M., Brizuela, B., & Stephens, A. (2016). Children’s understanding and use of variable notation. Paper presented at the 13th International Congress on Mathematics Education. Hamburg, Germany.

Blanton, M., Brizuela, B., & Stephens, A. (2016).* *Elementary children’s algebraic thinking. Paper presented at the 13th Annual Conference of the International Congress on Mathematical Education, Hamburg, Germany.

Blanton, M., Isler, I., Stephens, A., Knuth, E., Gardiner, A., Strachota, S. (2016). A longitudinal study of elementary students’ use of variable notation to represent mathematical generalizations. Paper presented at the Annual Meeting of the American Educational Research Association, Washington, DC.

Blanton, M., Knuth, E., Stephens, A., Stylianou, D., Stroud, R., Gardiner, A., Isler, I., & Strachota, S. (2016). The impact of a teacher-led early algebra intervention on children's algebra-readiness for middle school: Grade 3 results. Presentation at the Institute of Education Sciences Principal Investigators’ Meeting, Washington, DC.

Brizuela, B., Blanton, M., & Stephens, A. (2016). Children’s use and understanding of variable notation. Paper presented at the 13th Annual Conference of the International Congress on Mathematical Education, Hamburg, Germany.

Eiland, M.D. (2016). Impact of early algebra instruction across populations of diverse learners. Paper presented at the National Council of Teachers of Mathematics Research Pre-Session, San Francisco, CA.

Fonger, N. L., Stephens, A., Isler, I., Strachota, S. Blanton, M., Knuth, E. (2016).* An early algebra learning *progression for characterizing and supporting students’ generalization and representation of functions: A longitudinal approach to integrating curriculum, instruction, assessment, and student learning. Presentation at the Institute of Education Sciences Principal Investigators’ Meeting. Washington, D.C.

Gardiner, A., (2016). A journey through early algebra*.* Invited keynote address at the 2016 North Carolina Council of Teachers of Mathematics, Greensboro, NC.

Stephens, A., Fonger, N., Blanton, M, Knuth, E., Strachota, S., & Isler, I. (2016). Elementary students’ generalization and representation of functional relationships: A learning progressions approach. Poster presented at the Annual Meeting of the American Education Research Association, Washington, DC.

Strachota, S. (2016). Cycles of generalizing activities in the classroom. Paper presented at the 13th Annual Conference of the International Congress on Mathematical Education, Hamburg, Germany.

Strachota, S., Isler, I., Fonger, N., Blanton, M., & Gardiner, A. M. (2016). Analyzing generalizations through discourse. Poster presented at thirty-eighth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics, Tuscon, AZ: The University of Arizona.

Strachota, S., Kang, H., & Isler, I. (2016). Engaging in algebraic reasoning through properties of number and operation. Presentation at Wisconsin Mathematics Council Annual Conference (National Council of Teachers of Mathematics-Affiliate), Green Lake, WI.

Blanton, M. (2015). Early algebra problems worth solving and why*. *Invited presentation for “Problems Worth Solving” Strand, Annual Conference of the National Council of Teachers of Mathematics, Boston, MA.

Kang, H., Stephens, A., Blanton, M., Gardiner, A., Isler, I., & Knuth, E. (2015). Examining students’ algebraic thinking through interview assessments. Paper presented at the National Council of Teachers of Mathematics Research Conference, Boston, MA.

Strachota, S., Isler, I., Kang, H., Stephens, A., Blanton, M., Knuth, E., & Gardiner, A. (2015). Arithmetic properties as a route into algebraic reasoning.* *Poster presented at thrity-seventh annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI.

Blanton, M. (2014). Learning progressions in algebraic practices: Developing the ideas of equality and variables. Invited Online Keynote Address for NCTM: Algebra Readiness for All Students.

Blanton, M. (2013). Early algebra: Functional thinking as a context for proof and reasoning. Invited presentation for the Learn-Reflect Strand for Wisconsin Mathematics Council Annual Conference (National Council of Teachers of Mathematics-Affiliate), Green Lake, WI.

Stephens, A.C. (2013). Extending arithmetic tasks to engage students in proof. Invited presentation for the Learn-Reflect Strand for Wisconsin Mathematics Council Annual Conference (National Council of Teachers of Mathematics-Affiliate), Green Lake, WI.

Blanton, M. (2013). Early algebra in the era of Common Core.* *Invited Keynote Address, North Carolina Math Summit, SAS, Cary, NC.

Blanton, M., & Gardiner, A. (2013).* *Creating mathematical tasks to support children’s early algebraic reasoning. Gallery workshop presented at the National Council of Teachers of Mathematics Annual Meeting, Denver, CO.

Isler, I., Stephens, A., Gardiner, A., Blanton, M., & Knuth, E. (2013). Fourth-grade students’ abilities to write algebraic expressions and equations. Poster presented at the National Council of Teachers of Mathematics Research Pre-Session, Denver, CO.

Blanton, M. (2012). Can children reason algebraically? Invited presentation at the National Council of Teachers of Mathematics Regional Conference, Chicago, Illinois.

Blanton, M. (2012). Children’s algebra understanding: Perspectives from upper and lower elementary grades. Presentation at CSTL Project SHARE, TERC, Cambridge, MA.

Blanton, M. (2012). Designing, refining, and validating learning trajectories/progressions in early algebra. Presented as part of the Research Symposium “Learning progressions and trajectories in research: Methodological and theoretical challenges” at the National Science Foundation DRK–12 Principal Investigators’ Meeting, Washington, DC.

Blanton, M. (2012). Does early algebra matter: Results of a Grades 3-5 early algebra intervention.* *Invited presentation at the North Carolina State University Friday Institute, November, 2012.

Blanton, M., Gardiner, A., & Marum, T. (2012). Building Common Core mathematical practices through early algebra. Presentation at the National Council of Teachers of Mathematics Annual Meeting, Philadelphia, PA.

Blanton, M., & Knuth, E. (2012).* *Developing algebra-ready students for middle school: Exploring the impact of early algebra.* *Poster presented at the National Science Foundation DRK-12 Principal Investigator Meeting, Washington, DC.

Blanton, M., Knuth, E., Stephens, A., Gardiner, A., Isil, I., Marum, T. (2012). Shifts in children’s algebra understanding using a learning progressions approach to early algebra. Paper presented as part of the Research Symposium *Measuring early algebra impact: Quantitative studies of children’s algebra learning* at the National Council of Teachers of Mathematics Research Pre-Session, Philadelphia, PA.

Blanton, M., Knuth, E., Stephens, A., Gardiner, A., Isler, I., & Marum, T. (2012). Within-grade impacts of an early algebra classroom intervention. Paper presented at the National Council of Teachers of Mathematics Research Pre-Session, Philadelphia, PA.

Blanton, M., Stephens, A., Gardiner, A., Marum, T., Knuth, E., Isler, I. (2012). Aligning early algebra learning progressions and assessments in Grades 6–7. Working symposium presented at the National Council of Teachers of Mathematics Research Pre-Session, Philadelphia, PA.

Isler, I., Stephens, A., Knuth, E., Blanton, M., Marum, T., Gardiner, A. (2012). Elementary students’ recognition of algebraic structure: Not all tasks are created equal. Paper presented at the Annual Meeting of the American Educational Research Association, Vancouver, BC.

Stephens, A. C., Blanton, M. L., Knuth, E. J., Gardiner, A. M., Marum, T., & Isler, I. (2012).* *Aligning early algebra learning progressions and assessments in grades 3–8.* *Working session presented at the National Council of Teachers of Mathematics Research Presession, Philadelphia, PA.

Blanton, M., Gardiner, A., & Marum, T. (2011). Integrating early algebra into the Common Core. Presentation at the Kaput Center STEM Regional Network Meeting Roundtable Series, University of Massachusetts Dartmouth.

Blanton, M., Knuth, E., Gardiner, A., Isler, I., Marum, T. & Stephens, A. (2011). Investigating early algebra learning progressions for Grades 3-8. Working symposium presented at the National Council of Teachers of Mathematics Research Pre-Session, Indianapolis, Indiana.

Blanton, M., Stephens, A., Marum, T., Gardiner, A. M., & Knuth, E. (2011). Investigating early algebra learning progressions for grades 3–8. Working session presented at the National Council of Teachers of Mathematics Research Presession, Indianapolis, IN.

Blanton, M. (2010). Children’s understanding of functions. Invited panel presentation at the CADRE/National Science Foundation PI Meeting, Washington, DC.

Blanton, M. (2010). Early algebra: What children can do and why it matters for mathematics education. Invited lecture, STEM Interdisciplinary Colloquium Series, Tufts University.

Blanton, M. (2010). What do we know about early algebra? Presented as part of the Invited Symposium *What Do We Know About Early Algebra?: Reflecting on a Decade of Research* at the National Council of Teachers of Mathematics Research Pre-Session, San Diego, CA

Blanton, M., & Knuth, E. (2010). Analyzing early algebra learning progressions for Grades 3–8. Symposium presentation at the CADRE/National Science Foundation PI Meeting, Washington, DC.

**Blog**

Isler, I., Stephens, A., & Kang, H. (2016). Even and odd numbers: A journey into the algebraic thinking practice of justification. *Teaching Children Mathematics*. [Web log]. Retrieved from http://www.nctm.org/tcm-blog/li