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 12yearolds. The Global Evolution of an Emerging Field of Research and Practice (pp. 2750). Cham, Switzerland: Springer.
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 12yearolds. The Global Evolution of an Emerging Field of Research and Practice (pp. 351378). Cham, Switzerland: Springer.
Blanton, M. (2017). Algebraic reasoning in Grades 35. In M. Battista (Ed.), Reasoning and Sense Making in Grades 35 (pp. 67102). 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. 386420). Reston, VA: National Council of Teachers of Mathematics.
Stephens, A. & Knuth, E. (2017). Algebraic reasoning in Grades 68. In M. Battista (Ed.), Reasoning and Sense Making in Grades 68 (pp. 4772). 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 students (pp. 123134). 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 to appear in Psychometrics and assessment in mathematics education: Opportunities, challenges, and interdisciplinary collaborations, a monograph of the Journal for Research in Mathematics Education.
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. 135140). Reston, VA: National Council of Teachers of Mathematics.
Stephens, A. & Blanton, M. (2016). Algebraic reasoning in prekindergartengrade 2. In M. Battista (Ed.). Reasoning and Sense Making in PrekindergartenGrade 2 (pp. 71104). Reston, VA: National Council of Teachers of Mathematics.
Journal articles

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), 3055.
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), 143166.
Knuth, E., Stephens, A., Blanton, M., & Gardiner, A. (2016). Building an early foundation for algebra success. Phi Delta Kappan, 97(6), 6568.
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), 3987.
Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. (2015). Just say YES to early algebra! Teaching Children Mathematics, 22(2), 92101.
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), 282292.
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), 173182.
Conference Presentations

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.
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 American Educational Research Association Annual Meeting, Toronto, Canada.
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.
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.
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. Paper presented at 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics, Indianapolis, IN: Purdue University.
Isler, I., Strachota, S., Stephens, A., Fonger, N., Blanton, M., Gardiner, A., & Knuth, E. (2017). Grade 6 students’ abilities to represent function rules. Paper presented at the Tenth Congress of European Research in Mathematics Education, Dublin, Ireland.
Prough, S., Strachota, S., Veltri, R., Isler, I., Blanton, M., Gardiner, A., Knuth, E., & Stephens, A. (2017). Fostering Generalizations: a classroom discourse analysis. Paper presented at 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics, Indianapolis, IN: Purdue University.
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 MathematicsAffiliate), Green Lake, WI.
Stephens, A., Stroud, R., Knuth, E., Blanton, M., Stylinaou, D., Strachota, S., Isler, I., & Gardiner, A. (2017). The impact of a largescale 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 codevelopment of Functional Thinking and Equivalence. Paper presented at the National Council of Teachers of Mathematics Research Conference, San Antonio, TX.
Strachota, S., Stephens, A., Knuth, E., Blanton, M., Isler, I., & Gardiner, A. (2017). The interplay between students’ understandings of proportional and functional relationships. Paper presented at 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics, Indianapolis, IN: Purdue University.
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 Teacherled Early Algebra Intervention. Poster presented at 39th 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 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 TeacherLed Early Algebra Intervention on Children's AlgebraReadiness for Middle School: Grade 3 Results. Presentation at the Annual IES PI 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 PreSession, 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. Institute of Education Sciences Principal Investigators Meeting. Washington, D.C. December 2016.
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., 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 40th Annual Conference of the International Group for the Psychology of Mathematics Education, (pp. 243250). Szeged, Hungary.
Strachota, S., Isler, I., Fonger, N., Blanton, M., & Gardiner, A. M. (2016). Analyzing Generalizations Through Discourse. Poster presented at 38th 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 MathematicsAffiliate), 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.
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 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 201204). East Lansing, MI: Michigan State University.
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 37th 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.
Isler, I., Blanton, M., Murphy Gardiner, A., Knuth, E., Stephens, A., & Kang, H. (2014). A comparison of elementary and middle grade students’ algebraic reasoning. Proceedings of the Joint Meetings of the 38th Conference of the International Group for the Psychology of Mathematics Education and the 36th Annual Meeting of International Group for the Psychology of Mathematics Education, North American Chapter. Vancouver, BC.
Blanton, M. (2013). Early algebra: Functional thinking as a context for proof and reasoning. Invited presentation for the LearnReflect Strand for Wisconsin Mathematics Council Annual Conference (National Council of Teachers of MathematicsAffiliate), 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. (2013). 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., & 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). Fourthgrade students’ abilities to write algebraic expressions and equations. Poster presented at the National Council of Teachers of Mathematics Research PreSession, Denver, CO.
Isler, I., Stephens, A., Gardiner, A., Knuth, E., & Blanton, M. (2013). Thirdgraders’ generalizations about even numbers and odd numbers: The impact of an early algebra intervention. Proceedings of the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 140143). Chicago, IL: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.
Stephens, A.C. (2013). Extending arithmetic tasks to engage students in proof. Invited presentation for the LearnReflect Strand for Wisconsin Mathematics Council Annual Conference (National Council of Teachers of MathematicsAffiliate), Green Lake, WI.
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 DRK12 PI Meeting, Washington, DC.
Blanton, M. (2012). Does early algebra matter: Results of a Grades 35 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 algebraready students for middle school: Exploring the impact of early algebra. Poster presented at the National Science Foundation DRK12 PI 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 PreSession, Philadelphia, PA.
Blanton, M., Knuth, E., Stephens, A., Gardiner, A., Isler, I., & Marum, T. (2012). Withingrade impacts of an early algebra classroom intervention. Paper presented at the National Council of Teachers of Mathematics Research PreSession, Philadelphia, PA.
Blanton, M., Stephens, A., Gardiner, A., Marum, T., Knuth, E., Isler, I. (2012). Aligning early algebra learning progressions and assessments in Grades 67. Working symposium presented at the National Council of Teachers of Mathematics Research PreSession, 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 2012 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 38. Working session presented at the National Council of Teachers of Mathematics Research Presession, Philadelphia, PA.
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. Proceedings of the 34th Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.
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 38. Working symposium presented at the National Council of Teachers of Mathematics Research PreSession, Indianapolis, Indiana.
Blanton, M., Stephens, A., Marum, T., Gardiner, A. M., & Knuth, E. (2011). Investigating early algebra learning progressions for grades 38. Working session presented at the National Council of Teachers of Mathematics Research Presession, Indianapolis, IN.
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 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 106113). Reno, NV: University of Nevada, Reno.
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 PreSession, San Diego, CA
Blanton, M., & Knuth, E. (2010). Analyzing early algebra learning progressions for Grades 38. 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/tcmblog/li>