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Trends, insights, and developments in research on the teaching and learning of algebra

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Abstract

This paper addresses the recent body of research in algebra and algebraic thinking from 2018 to 2022. We reviewed 74 journal articles and identified four clusters of content areas: (a) literal symbols and symbolizing, (b) equivalence and the equal sign, (c) equations and systems, and (d) functions and graphing. We present the research on each of these content clusters, and we discuss insights on effective teaching practices and the social processes supporting algebraic reasoning. The research base shows that incorporating algebraic thinking into the elementary grades, emphasizing analytic and structural thinking processes, and emphasizing covariational reasoning supports students’ meaningful learning of core algebraic ideas. We close with a discussion of the major theoretical contributions emerging from the past five years, offering suggestions for future research.

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Notes

  1. https://researchguides.library.vanderbilt.edu/mathed/journals.

  2. https://sites.google.com/site/ditmerg/journals.

  3. https://www.edb.gov.hk/attachment/en/curriculum-development/kla/ma/res/journal_e.pdf.

  4. https://guides.ucf.edu/education-mathematics/journals.

  5. https://ued.uniandes.edu.co/portfolio/ranking-of-mathematics-education-journals/.

References

*The papers included in the review have been marked with one asterisk, along with their number in brackets.

  • *Ayala-Altamirano, C., Molina, M. & Ambrose, R. (2022). Fourth graders’ expression of the general case. ZDM–Mathematics Education, 54, 1377–1392. https://doi.org/10.1007/s11858-022-01398-8

  • *Ayala-Altamirano, C., & Molina, M. (2020). Meanings attributed to letters in functional contexts by primary school students. International Journal of Science and Mathematics Education, 18, 1271–1291. https://doi.org/10.1007/s10763-019-10012-5

    Article  ADS  Google Scholar 

  • *Ayalon, M., & Wilkie, K.J. (2019). Exploring secondary students’ conceptualization of functions in three curriculum contexts. The Journal of Mathematical Behavior, 56. https://doi.org/10.1016/j.jmathb.2019.100718.

  • *Ayalon, M., & Wilkie, K. (2020). Students’ identification and expression of relations between variables in linear functions tasks in three curriculum contexts. Mathematical Thinking and Learning, 22(1), 1–22. https://doi.org/10.1080/10986065.2019.1619221

    Article  Google Scholar 

  • *Bajwa, N. P., & Perry, M. (2021). Features of a pan balance that may support students’ developing understandings of mathematical equivalence. Mathematical Thinking and Learning, 23(1), 1–27. https://doi.org/10.1080/10986065.2020.1700587

    Article  Google Scholar 

  • *Barbieri, C. A., Miller-Cotto, D., & Booth, J. L. (2019). Lessening the load of misconceptions: Design-based principles for algebra learning. JouRnal of the Learning Sciences, 28(3), 381–417. https://doi.org/10.1080/10508406.2019.1573428

    Article  Google Scholar 

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

    Article  Google Scholar 

  • *Blanton, M., Stroud, R., Stephens, A., Gardiner, A. M., Stylianou, D. A., Knuth, E., Isler-Baykal, I., & Strachota, S. (2019b). 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

    Article  Google Scholar 

  • *Bråting, K., & Kilhamn, C. (2021). Exploring the intersection of algebraic and computational thinking. Mathematical Thinking and Learning, 23(2), 170–185. https://doi.org/10.1080/10986065.2020.1779012

    Article  Google Scholar 

  • Britt, M. S., & Irwin, K. C. (2011). Algebraic thinking with and without algebraic representation: A pathway for learning. In Cai, J. & Knuth, E. (Eds.), Early Algebraization, 137–159.

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

  • Carraher, D., & Schliemann, A. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2, pp. 669–705). Information Age.

  • *Chimoni, M., Pitta-Pantazi, D., & Christou, C. (2018). Examining early algebraic thinking: Insights from empirical data. Educational Studies in Mathematics, 98, 57–76.

    Article  Google Scholar 

  • *Christou, K. P., Kyrvei, D. I., & Vamvakoussi, X. (2022). Interpreting literal symbols in algebra under the effects of the natural number bias. Mathematical Thinking and Learning, 1–14. https://doi.org/10.1080/10986065.2022.2128276

  • *Chval, M., Vondrova, N., & Novotna, J. (2021). Using large-scale data to determine pupils’ strategies and errors in missing value number equations. Educational Studies in Mathematics, 106, 5–24.

    Article  Google Scholar 

  • *Coles, A., & Ahn, A. (2022). Developing algebraic activity through conjecturing about relationships. ZDM–Mathematics Education, 54(6), 1229–1241.

  • Crea, F., Guzik, T., & Kavaney, A. F. (2023). The Journal Citation Indicator: What is the relevance of this new metric? European Heart Journal, 44(4), 243–244.

    Article  PubMed  Google Scholar 

  • De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler’s study. Journal for Research in Mathematics Education, 42(2), 109–126.

    Article  Google Scholar 

  • *Demattè, A., Furinghetti, F. (2022). Today's students engaging with Abbacus problems. ZDM–Mathematics Education, 54, 1521–1536. https://doi.org/10.1007/s11858-022-01397-9

  • *Díaz-Berrios, T., & Martínez-Planell, R. (2022). High school student understanding of exponential and logarithmic functions. The Journal of Mathematical Behavior, 66, 100953. https://doi.org/10.1016/j.jmathb.2022.100953

    Article  Google Scholar 

  • *Donovan, A. M., Stephens, A., Alapala, B., Monday, A., Szkudlarek, E., Alibali, M. W., & Matthews, P. G. (2022). Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign. ZDM–Mathematics Education, 54, 1199–1213. https://doi.org/10.1007/s11858-022-01405-y

  • Van Dooren, W., De Bock, D., & Verschaffel, L. (2012). How students understand aspects of linearity: Searching for obstacles in representational flexibility. In T. Y. Tso (Ed.), Proceedings of the 36th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 179–186). Taipei, Taiwan: PME.

  • *Duijzer, C., Van den Heuvel-Panhuizen, M., Veldhuis, M. et al. (2019). Supporting primary school students’ reasoning about motion graphs through physical experiences. ZDM–Mathematics Education 51, 899–913. https://doi.org/10.1007/s11858-019-01072-6

  • *Eames, C. L., Graf, E. A., van Rijn, P. W., Budzban, G., & Voepel, T. (2021). The finite-to-finite strand of a learning progression for the concept of function: A research synthesis and cognitive analysis. The Journal of Mathematical Behavior, 62, 100864. https://doi.org/10.1016/j.jmathb.2021.100864

    Article  Google Scholar 

  • *Ellis, A. B., Ely, R., Singleton, B., & Tasova, H. (2020). Scaling-continuous variation: Supporting students’ algebraic reasoning. Educational Studies in Mathematics, 104(1), 87–103. https://doi.org/10.1007/s10649-020-09951-6

    Article  Google Scholar 

  • Ellis, A.B. (2022). Decentering to build asset-based learning trajectories. In Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (Eds.), Proceedings of the Forty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 15 – 29). Middle Tennessee State University.

  • *Fonger, N. L. (2019). Meaningfulness in representational fluency: An analytic lens for students’ creations, interpretations, and connections. The Journal of Mathematical Behavior, 54, 100678. https://doi.org/10.1016/j.jmathb.2018.10.003

    Article  Google Scholar 

  • *Fonger, N., Ellis, A. B., & Dogan, M. F. (2020). A quadratic growth learning trajectory. Journal of Mathematical Behavior, 59, 1–22. https://doi.org/10.1016/j.jmathb.2020.100795

    Article  Google Scholar 

  • *Günster, S.M., Weigand, HG. (2020). Designing digital technology tasks for the development of functional thinking. ZDM–Mathematics Education 52, 1259–1274. https://doi.org/10.1007/s11858-020-01179-1

  • *Hackenberg, A. J., Aydeniz, F., & Jones, R. (2021). Middle school students’ construction of quantitative unknowns. The Journal of Mathematical Behavior, 61, 100832. https://doi.org/10.1016/j.jmathb.2020.100832

    Article  Google Scholar 

  • *Hemmi, K., Bråting, K., & Lepik, M. (2021). Curricular approaches to algebra in Estonia, Finland and Sweden – A comparative study. Mathematical Thinking and Learning, 23(1), 49–71.

    Article  Google Scholar 

  • Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: The effect of brackets. In Proceedings of the 28th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 49–56).

  • *Hohensee, C., Willoughby, L., & Gartland, S. (2022). Backward transfer, the relationship between new learning and prior ways of reasoning, and action versus process views of linear functions. Mathematical Thinking and Learning, 1–19. https://doi.org/10.1080/10986065.2022.2037043

  • *Hunter, R., Hunter, J., & Gibbs, B. (2022). Taking an asset-based approach in the use of a culturally located task to construct functional reasoning. Teachers College Record, 124(5), 69–88. https://doi.org/10.1177/01614681221103958

    Article  Google Scholar 

  • Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462–500.

    Article  Google Scholar 

  • *Jiang, R. H., Star, J. R., & Pejlare, J. (2022). Which one is the “best”: A cross-national comparative study of students’ strategy evaluation in equation solving. International Journal of Science and Mathematics Education, 21, 1127–1151. https://doi.org/10.1007/s10763-022-10282-6

    Article  ADS  Google Scholar 

  • *Johnson, H. L., & McClintock, E. (2018). A link between students’ discernment of variation in unidirectional change and their use of quantitative variational reasoning. Educational Studies in Mathematics, 97, 299–316. https://doi.org/10.1007/s10649-017-9799-7

    Article  Google Scholar 

  • *Kafetzopoulos, G. I., & Psycharis, G. (2022). Conceptualization of function as a covariational relationship between two quantities through modeling tasks. The Journal of Mathematical Behavior, 67, 100993. https://doi.org/10.1016/j.jmathb.2022.100993

    Article  Google Scholar 

  • *Kapon, S., Halloun, A., & Tabach, M. (2019). Incorporating a digital game into the formal instruction of algebra. Journal for Research in Mathematics Education, 50(5), 555–591.

    Article  Google Scholar 

  • Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? In J. J. Kaput, D. W. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 5–17). Mahwah, NJ: Lawrence Erlbaum/Taylor & Francis Group; Reston, VA: National Council of Teachers of Mathematics.

  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139–151.

    Google Scholar 

  • Kieran, C. (2018). Seeking, using, and expressing structure in numbers and numerical operations: A fundamental path to developing early algebraic thinking. 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. 79–105). Springer.

    Chapter  Google Scholar 

  • *Kieran, C. (2022). The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions. ZDM–Mathematics Education, 54, 1131–1150. https://doi.org/10.1007/s11858-022-01435-6

  • *Kieran, C., & Martinez-Hernandez, C. (2022). Coordinating invisible and visible sameness within equivalence transformations of numerical equalities by 10-to 12-year-olds in their movement from computational to structural approaches. ZDM–Mathematics Education, 54, 1215–1227. https://doi.org/10.1007/s11858-022-01355-5

  • *Kilhamn, C., Bråting, K., Helenius, O., & Mason, J. (2022). Variables in early algebra: Exploring didactic potentials in programming activities. ZDM–Mathematics Education, 54(6), 1273–1288.

  • *Kop, P. M., Janssen, F. J., Drijvers, P. H., & van Driel, J. H. (2020). The relation between graphing formulas by hand and students’ symbol sense. Educational Studies in Mathematics, 105, 137–161. https://doi.org/10.1007/s10649-020-09970-3

    Article  Google Scholar 

  • *Kop, P. M., Janssen, F. J., Drijvers, P. H., & van Driel, J. H. (2021). Promoting insight into algebraic formulas through graphing by hand. Mathematical Thinking and Learning, 23(2), 125–144.

    Article  Google Scholar 

  • *Lee, J., & Pang, J. (2021). Students’ opposing conceptions of equations with two equal signs. Mathematical Thinking and Learning, 23(3), 209–224. https://doi.org/10.1080/10986065.2020.1777364

    Article  Google Scholar 

  • *Lenz, D. (2022). The role of variables in relational thinking: An interview study with kindergarten and primary school children. ZDM–Mathematics Education, 54(6), 1181–1197.

  • *Lepak, J. R., Wernet, J. L., & Ayieko, R. A. (2018). Capturing and characterizing students’ strategic algebraic reasoning through cognitively demanding tasks with focus on representations. The Journal of Mathematical Behavior, 50, 57–73.

    Article  Google Scholar 

  • *Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: A Knowledge in Pieces perspective on the development of algebraic thinking. ZDM–Mathematics Education 54, 1303–1314. https://doi.org/10.1007/s11858-022-01374-2

  • *Lingefjärd, T., & Farahani, D. (2018). The elusive slope. International Journal of Science and Mathematics Education, 16, 1187–1206. https://doi.org/10.1007/s10763-017-9811-9

    Article  ADS  Google Scholar 

  • *Litke, E. (2020a). Instructional practice in algebra: Building from existing practices to inform an incremental improvement approach. Teaching and Teacher Education, 91, 103030. https://doi.org/10.1016/j.tate.2020.103030

    Article  Google Scholar 

  • *Litke, E. (2020b). The nature and quality of algebra instruction: Using a content-focused observation tool as a lens of understanding and improving instructional practice. Cognition and Instruction, 38(1), 57–86. https://doi.org/10.1080/07370008.2019.1616740

    Article  Google Scholar 

  • *Madej, L. (2022). Primary school students’ knowledge of the equal sign – The Swedish case. International Journal of Science and Mathematics Education, 20, 321–343. https://doi.org/10.1007/s10763-020-10144-z

    Article  ADS  Google Scholar 

  • *Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the visual representation of a figural pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599

    Article  Google Scholar 

  • *Naftaliev, E., & Yerushalmy, M. (2022). Guiding students’ learning with an interactive diagram: The case of equations. Journal of Mathematical Behavior, 68, 101008. https://doi.org/10.1016/j.jmathb.2022.101008

    Article  Google Scholar 

  • *Nemirovsky, R., Ferrara, F., Ferrari, G., & Adamuz-Povedano, N. (2020). Body motion, early algebra, and the colours of abstraction. Educational Studies in Mathematics, 104, 261–283. https://doi.org/10.1007/s10649-020-09955-2

    Article  Google Scholar 

  • Norton, A. (2008). Josh’s operational conjectures: Abductions of a splitting operation and the construction of new fractional schemes. Journal for Research in Mathematics Education, 39(4), 401–430.

    Article  MathSciNet  Google Scholar 

  • *Olsson, J. (2018). The contribution of reasoning to the utilization of feedback from software when solving mathematical problems. International Journal of Science and Mathematics Education, 16(4), 715–735. https://doi.org/10.1007/s10763-016-9795-x

    Article  ADS  Google Scholar 

  • Orton, J., Orton, A., & Roper, T. (1999). Pictorial and practical contexts and the perception of pattern. In A. Orton (Ed.), Patterns in the teaching and learning of mathematics (pp. 121–136). Cassell.

    Google Scholar 

  • *Pang, J., & Sunwoo, J. (2022). Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook. ZDM–Mathematics Education, 54, 1315–1331. https://doi.org/10.1007/s11858-022-01411-0

  • *Papadopoulos, I. (2019). Using mobile puzzles to exhibit certain algebraic habits of mind and demonstrate symbol-sense in primary school students. The Journal of Mathematical Behavior, 53, 210–227. https://doi.org/10.1016/j.jmathb.2018.07.001

    Article  Google Scholar 

  • *Papadopoulos, I., & Patsiala, N. (2019). When the “tug-of-war” game facilitates the development of algebraic thinking. International Journal of Science and Mathematics Education, 17, 1401–1421. https://doi.org/10.1007/s10763-018-9928-5

    Article  ADS  Google Scholar 

  • *Patterson, C. L., & McGraw, R. (2018). When time is an implicit variable: An investigation of students’ ways of understanding graphing tasks. Mathematical Thinking and Learning, 20(4), 295–323. https://doi.org/10.1080/10986065.2018.1509421

    Article  Google Scholar 

  • *Pearn, C., Stephens, M., & Pierce, R. (2022). Algebraic reasoning in years 5 and 6: Classifying its emergence and progression using reverse fraction tasks. ZDM–Mathematics Education, 54(6), 1257–1271.

  • *Peck, F. A. (2020). Beyond rise over run: A learning trajectory for slope. Journal for Research in Mathematics Education, 51(4), 433–467.

    Article  Google Scholar 

  • *Pinto, E., Canadas, M. C., & Moreno, A. (2022). Functional relationships evidenced and representations used by third graders within a functional approach to early algebra. International Journal of Science and Mathematics Education, 20, 1183–1202. https://doi.org/10.1007/s10763-021-10183-0

    Article  ADS  Google Scholar 

  • *Pittalis, M. (2022). Young students’ arithmetic-algebraic structure sense: An empirical model and profiles of students. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-022-10333-y

    Article  Google Scholar 

  • *Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2020). Different types of algebraic thinking: An empirical study focusing on middle school students. International Journal of Science and Mathematics Education, 18, 965–984. https://doi.org/10.1007/s10763-019-10003-6

    Article  ADS  Google Scholar 

  • Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26, 257–277.

    Article  ADS  Google Scholar 

  • Radford, L. (2018). The emergence of symbolic algebraic thinking in primary school. 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. 3–25). Springer.

    Chapter  Google Scholar 

  • *Radford, L. (2022). Introducing equations in early algebra. ZDM –Mathematics Education, 54, 1151–1167. https://doi.org/10.1007/s11858-022-01422-x

  • *Ramírez, R., Cañadas, M. C., & Damián, A. (2022). Structures and representations used by 6th graders when working with quadratic functions. ZDM–Mathematics Education, 54(6), 1393–1406. https://doi.org/10.1007/s11858-022-01423-w

  • *Schifter, D., & Russell, S. J. (2022). The centrality of student-generated representation in investigating generalizations about the operations. ZDM–Mathematics Education, 54(6), 1289–1302.

  • *Sharpe, S. T. (2019). An algebraic translation task solved by grade 7–9 students. Mathematical Thinking and Learning, 21(1), 78–84.

    Article  Google Scholar 

  • *Soneira, C. (2022). The use of representations when solving algebra word problems and the sources of solution errors. International Journal of Science and Mathematics Education, 20(5), 1037–1056. https://doi.org/10.1007/s10763-021-10181-2

    Article  ADS  Google Scholar 

  • *Soneira, C., González-Calero, J. A., & Arnau, D. (2018). Indexical expressions in word problems and their influence on multiple referents of the unknown. International Journal of Science and Mathematics Education, 16, 1147–1167.

    Article  ADS  Google Scholar 

  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20, 147–164. https://doi.org/10.1007/BF00579460

    Article  Google Scholar 

  • Steffe, L. P. (1991). The learning paradox: A plausible counterexample. In L. P. Steffe (Ed.), Epistemological foundations of mathematical experience (pp. 26–44). Springer.

    Chapter  Google Scholar 

  • Steffe, L. P. (1992). Schemes of action and operation involving composite units. Learning and Individual Differences, 4(3), 259–309.

    Article  Google Scholar 

  • Stephens, A., Ellis, A. B., 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). National Council of Teachers of Mathematics.

    Google Scholar 

  • *Stephens, M., Day, L., & Horne, M. (2021). An empirically based practical learning progression for generalisation: An essential element of algebraic reasoning. Australian Journal of Education, 65(3), 313–328. https://doi.org/10.1177/00049441211044798

    Article  Google Scholar 

  • *Sumpter, L., & Lowenhielm, A. (2022). Differences in grade 7 students’ understanding of the equal sign. Mathematical Thinking and Learning. https://doi.org/10.1080/10986065.2022.2058160

    Article  Google Scholar 

  • Tall, D., Gray, E., Bin Ali, M., Crowley, L., DeMarois, P., McGowen, M., Pitta, D., Pinot, M., Thomas, M., & Yusof, Y. (2001). Symbols and the bifurcation between procedural and conceptual thinking. Canadian Journal of Science, Mathematics & Technology Education, 1(1), 81–104. https://doi.org/10.1080/14926150109556452

    Article  ADS  Google Scholar 

  • Thompson, P. W. (2011). Quantitative reasoning and mathematical modeling. In L. L. Hatfield, S. Chamberlain, & S. Belbase (Eds.), New perspectives and directions for collaborative research in mathematics education WISDOMe Monographs (Vol. 1, pp. 33–57). University of Wyoming Press.

  • *Tondorf, A., & Prediger, S. (2022). Connecting characterizations of equivalence of expressions: Design research in grade 5 by bridging graphical and symbolic representations. Educational Studies in Mathematics, 111(3), 399–422. https://doi.org/10.1007/s10649-022-10158-0

    Article  Google Scholar 

  • *Vlassis, J., & Demonty, I. (2022). The role of algebraic thinking in dealing with negative numbers. ZDM–Mathematics Education, 54(6), 1243–1255.

  • Wagner, S., & Parker, S. (1993). Advancing algebra. In P. Wilson (Ed.), Research ideas for the classroom: High school mathematics (pp. 119–139). National Council of Teachers of Mathematics.

    Google Scholar 

  • *Walkoe, J., & Levin, M. (2020). Seeds of algebraic thinking: Towards a research agenda. For the Learning of Mathematics, 40(2), 27–31.

    Google Scholar 

  • *Watson, A., Ayalon, M., & Lerman, S. (2018). Comparison of students’ understanding of functions in classes following English and Israeli national curricula. Educational Studies in Mathematics, 97, 255–272.

    Article  Google Scholar 

  • *Wilkie, K. J. (2019). Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions. The Journal of Mathematical Behavior, 54, 100689. https://doi.org/10.1016/j.jmathb.2019.01.005

    Article  Google Scholar 

  • *Wilkie, K. J. (2020). Investigating students’ attention to covariation features of their constructed graphs in a figural pattern generalisation context. International Journal of Science and Mathematics Education, 18, 315–336. https://doi.org/10.1007/s10763-019-09955-6

    Article  ADS  Google Scholar 

  • *Wilkie, K. J. (2022). Generalization of quadratic figural patterns: Shifts in student noticing. The Journal of Mathematical Behavior, 65, 100917. https://doi.org/10.1016/j.jmathb.2021.100917

    Article  Google Scholar 

  • *Xie, S., & Cai, J. (2022). Fifth graders’ learning to solve equations: The impact of early arithmetic strategies. ZDM –Mathematics Education, 54, 1169–1179. https://doi.org/10.1007/s11858-022-01417-8

  • *Xolocotzin, U., Medrano-Moya, A.M., & Rojano, T. (2022). Starting points: Understanding children's pre-instructional intuitions about function tables. ZDM–Mathematics Education, 54, 1363–1376. https://doi.org/10.1007/s11858-022-01424-9

  • *Zwanch, K. (2022). Examining middle grades students' solutions to word problems that can be modeled by systems of equations using the number sequences lens. Journal of Mathematical Behavior, 66, https://doi.org/10.1016/j.jmathb.2022.100960

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  1. University of Georgia, Athens, GA, USA

    Amy B. Ellis

  2. Dokuz Eylül University, Konak, Turkey

    Zekiye Özgür

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Ellis, A.B., Özgür, Z. Trends, insights, and developments in research on the teaching and learning of algebra. ZDM Mathematics Education (2024). https://doi.org/10.1007/s11858-023-01545-9

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