What Early Algebra Knowledge Persists 1 Year After an Elementary Grades Intervention?

Author:
Ana Stephens University of Wisconsin–Madison

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Rena Stroud Merrimack College, MA

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Susanne Strachota Ohio University

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Despina Stylianou City University of New York

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Maria Blanton TERC

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Eric Knuth University of Texas at Austin

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Angela Gardiner TERC

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Volume/Issue:
Volume 52: Issue 3
Page(s):
332–348
DOI:
https://doi.org/10.5951/jresematheduc-2020-0304
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Keywords:
Algebraic thinking; Early algebra; Elementary grades; Retention study

This research focuses on the retention of students’ algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3–5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance.

Footnotes

The research reported here was supported in part by the U.S. Department of Education under IES Award R305A140092. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the U.S. Department of Education. This article was accepted under the editorship of Jinfa Cai.

Contributor Notes

Ana Stephens, Wisconsin Center for Education Research, University of Wisconsin–Madison, 683 Educational Sciences Building, 1025 W. Johnson Street, Madison, WI 53706; acstephens@wisc.edu

Rena Stroud, School of Education and Social Policy, Merrimack College, 315 Turnpike Street, North Andover, MA 01887; stroudr@merrimack.edu

Susanne Strachota, The Patton College of Education, Ohio University, 100 East Union Street, McCracken Hall 309J, Athens, OH 45701; strachot@ohio.edu

Despina Stylianou, School of Education, City University of New York, Covent Avenue at 138th Street, New York, NY 10031; dstylianou@ccny.cuny.edu

Maria Blanton, TERC, 2067 Massachusetts Avenue, Cambridge, MA 02140; Maria_Blanton@terc.edu

Eric Knuth, College of Education, University of Texas at Austin, 1912 Speedway STOP D5700, Austin, TX 78712; eric.knuth@austin.utexas.edu

Angela Gardiner, TERC, 2067 Massachusetts Avenue, Cambridge, MA 02140; Angela_Gardiner@terc.edu

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  • 1.

    Bailey, D., Duncan, G. J., Odgers, C. L., & Yu, W. (2017). Persistence and fadeout in the impacts of child and adolescent interventions. Journal of Research on Educational Effectiveness, 10(1), 7–39. https://doi.org/10.1080/19345747.2016.1232459

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 2.

    Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., & Newman-Owens, A. (2015). A learning trajectory in 6-year-olds’ thinking about generalizing functional relationships. Journal for Research in Mathematics Education, 46(5), 511–558. https://doi.org/10.5951/jresematheduc.46.5.0511

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 3.

    Blanton, M., Brizuela, B. M., Stephens, A., Knuth, E., Isler, I., Gardiner, A. M., Stroud, R., Fonger, N. L., & 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 practice (pp. 27–49). Springer. https://doi.org/10.1007/978-3-319-68351-5_2

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 4.

    Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children’s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102(2), 193–219. https://doi.org/10.1007/s10649-019-09894-7

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 5.

    Blanton, M., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3–5. National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • 6.

    Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (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. https://doi.org/10.5951/jresematheduc.46.1.0039

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 7.

    Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., Isler-Baykal, I., & Strachota, S. (2019). Does early algebra matter? The effectiveness of an early algebra intervention in grades 3 to 5. American Educational Research Journal, 56(5), 1930–1972. https://doi.org/10.3102/0002831219832301

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 8.

    Brizuela, B. M., Blanton, M., Sawrey, K., Newman-Owens, A., & Gardiner, A. M. (2015). Children’s use of variables and variable notation to represent their algebraic ideas. Mathematical Thinking and Learning, 17(1), 34–63. https://doi.org/10.1080/10986065.2015.981939

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 9.

    Brizuela, B. M., & Earnest, D. (2008). Multiple notational systems and algebraic understandings: The case of the “best deal" problem. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 273–301). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781315097435-13

    • Search Google Scholar
    • Export Citation
  • 10.

    Carpenter, T. P., Franke, M. L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Heinemann.

    • Search Google Scholar
    • Export Citation
  • 11.

    Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades (Report No. NCISLA-RR-00-2). University of Wisconsin–Madison, National Center for Improving Student Learning and Achievement in Mathematics and Science.

    • Search Google Scholar
    • Export Citation
  • 12.

    Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, 40(1), 3–22. https://doi.org/10.1007/s11858-007-0067-7

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 13.

    Carraher, D. W., Schliemann, A. D., & Schwartz, J. L. (2008). Early algebra is not the same as algebra early. In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 235–272). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781315097435-12

    • Search Google Scholar
    • Export Citation
  • 14.

    Clements, D. H., Sarama, J., Wolfe, C. B., & Spitler, M. E. (2013). Longitudinal evaluation of a scale-up model for teaching mathematics with trajectories and technologies: Persistence of effects in the third year. American Educational Research Journal, 50(4), 812–850. https://doi.org/10.3102/0002831212469270

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 15.

    Ellis, A. B. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229.

    • Search Google Scholar
    • Export Citation
  • 16.

    Fonger, N. L., Stephens, A., Blanton, M., Isler, I., Knuth, E., & Gardiner, A. M. (2018). Developing a learning progression for curriculum, instruction, and student learning: An example from mathematics education. Cognition and Instruction, 36(1), 30–55. https://doi.org/10.1080/07370008.2017.1392965

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 17.

    Kaput, J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying" the K–12 curriculum. In S. Fennel (Ed.), The nature and role of algebra in the K–14 curriculum: Proceedings of a national symposium (pp. 25–26). National Academies Press.

    • Search Google Scholar
    • Export Citation
  • 18.

    Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781315097435-2

    • Search Google Scholar
    • Export Citation
  • 19.

    Knuth, E. J., Alibali, M. W., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2008). The importance of equal sign understanding in the middle grades. Mathematics Teaching in the Middle School, 13(9), 514–519.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 20.

    Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C. (2005). Middle school students’ understanding of core algebraic concepts: Equivalence and variable. Zentralblatt Für Didaktik Der Mathematik, 37(1),68–76. https://doi.org/10.1007/BF02655899

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 21.

    Knuth, E. J., Stephens, A. C., McNeil, N. M., & Alibali, M. W. (2006). Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education, 37(4), 297–312.

    • Search Google Scholar
    • Export Citation
  • 22.

    Kwon, O. N., Rasmussen, C., & Allen, K. (2005). Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105(5), 227–239. https://doi.org/10.1111/j.1949-8594.2005.tb18163.x

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 23.

    MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33(1), 1–19.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 24.

    Molina, M., & Ambrose, R. (2008). From an operational to a relational conception of the equal sign: Third graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61–80.

    • Search Google Scholar
    • Export Citation
  • 25.

    National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. http://www.corestandards.org/

    • Search Google Scholar
    • Export Citation
  • 26.

    Rivera, F. D., & Becker, J. R. (2011). Formation of pattern generalization involving linear figural patterns among middle school students: Results of a three-year study. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 323–366). Springer. https://doi.org/10.1007/978-3-642-17735-4_18

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 27.

    Russell, S. J., Schifter, D., & Bastable, V. (2011a). Connecting arithmetic to algebra: Strategies for building algebraic thinking in the elementary grades. Heinemann.

    • Search Google Scholar
    • Export Citation
  • 28.

    Russell, S. J., Schifter, D., & Bastable, V. (2011b). Developing algebraic thinking in the context of arithmetic. In J. Cai & E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 43–69). Springer. https://doi.org/10.1007/978-3-642-17735-4_4

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 29.

    Schifter, D. (2009). Representation-based proof in the elementary grades. In D. A. Stylianou, M. L. Blanton, & E. J. Knuth (Eds.), Teaching and learning proof across the grades: A K–16 perspective (pp. 71–86). Routledge. https://doi.org/10.4324/9780203882009-4

    • Search Google Scholar
    • Export Citation
  • 30.

    Semb, G. B., & Ellis, J. A. (1994). Knowledge taught in school: What is remembered? Review of Educational Research, 64(2), 253–286. https://doi.org/10.3102/00346543064002253

    • Crossref
    • Search Google Scholar
    • Export Citation
  • 31.

    Shin, N., Stevens, S. Y., Short, H., & Krajcik, J. (2009, June 24–26). Learning progressions to support coherence curricula in instructional material, instruction, and assessment design [Paper presentation]. Learning Progressions in Science (LeaPS) Conference, Iowa City, IA, United States.

    • Search Google Scholar
    • Export Citation
Copyright:
The National Council of Teachers of Mathematics, Inc. All rights reserved. 2021
Page Count:
18
Article Category:
Research Article
Received:
17 Jun 2019
Accepted:
23 Dec 2019
Print Publication Date:
01 May 2021
Online Publication Date:
May 2021
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