Algebra is an essential area of mathematics and a content strand of mathematics education (NCTM, 2000). It is a fundamental area because "Algebra is a way of thinking and a set of concepts and skills that enable students to generalize, model, and analyze mathematical situations. Algebra provides a systematic way to investigate relationships; help to describe, organize, and understand the world" (NCTM, 2000, p. 1). Algebra education provides students with many skills, including generalization, representation, and problem-solving (Kaput, 1999).  

Several concepts examined in the literature on algebra education, such as algebraic thinking (Kieran, 2004), algebraic reasoning (Kaput, 1999), functional thinking (Blanton et al., 2011), relational thinking (Jacobs et al., 2007), covarational reasoning (Confrey & Smith, 1995), and pattern recognition (Wang, 2008).  Algebraic thinking is working on problems relationally by using various representations, modeling, working with numbers and letters, and understanding the meaning of equal signs (Kieran, 2004). Algebraic reasoning includes making generalizations about arithmetic relationships, generalizing patterns, using modeling, and representing various relationships (Kaput, 1999). Functional thinking, one of the main components of algebraic thinking, is associated with concepts such as covariance, correspondence, and change. It requires identifying patterns, describing relationships using variables and "understanding how quantities vary in relation to each other or covary" (Blanton et al., 2011, p. 52). Therefore, it is closely associated with covariational reasoning, which means understanding the variation between two quantities with respect to each other (Confrey & Smith, 1995). All of the mentioned concepts are related to relational thinking, which was defined as "looking at expressions and equations in their entirety, noticing the number relations among and within these expressions and equations." (Jacobs et al., 2007, p. 260) and also related to pattern recognition which can be defined as a higher cognitive process that helps to identify objects or the composition of various objects and denotes them (Wang, 2008).

Algebra education is considered the "gateway to higher mathematics" (Stein et al., 2011, p. 454), and many studies have been conducted in this area, examining topics such as classroom practices in algebra and the impact of instructional methods (Hegedus & Kaput, 2003), teachers' perspectives (Glassmeyer & Edwards, 2016) and specific algebra content such as linear equations (Brizuela & Schliemann, 2004), the equal sign (Lee & Pang, 2021). Thus, over the past three decades, this field has grown significantly. On the other hand, there is a limited bibliometric review that allows for examining wide-range data on algebra education; there are, for example, a study on algebra education covering the last 20 years with the Scopus database (Veith et al., 2023) a study examining algebraic trends (Jamil et al., 2025); a study examining algebraic materials (Hayu & Angraini, 2024). To better understand the field,  there is a need for more extensive bibliometric studies on algebra education. Therefore, this study aims to examine research on algebra education in the past three decades using bibliometric analysis.

In light of this, the research questions of this study are:

1. What are the annual publication trends and the predominant keywords and core topics in algebra education research?
2. Which authors, countries, and institutions are the most productive in algebra education research?
3. How are co-authorship and international collaboration networks in algebra education research?

This study employs the bibliometric method, which enables the analysis of all aspects of documents. This type of analysis can extract information from large amounts of comprehensive data and provide objective metrics, such as the number of documents, citations, topics, keywords, and collaborations (Passas, 2024). This method reflects the current state of the topic and future trends. Therefore, it was expected to highlight the field of algebra education in a comprehensive and detailed way. The main steps of bibliometric analysis, as defined by Passas (2024), were followed: defining the research objective, collecting data, data cleaning and preprocessing, selecting bibliometric techniques, data analysis, visualization, interpretation, and reporting. Accordingly, the Web of Science (WoS) database was used to collect data because it includes qualified studies. Data were extracted on 23 May 2025. As mentioned in the literature, articles on algebra education include some concepts such as functional thinking, relational thinking, pattern recognition, covariational thinking, and covariational reasoning. Therefore, these terms were combined with terms about mathematics education with following search strings: TS= (((algebra* OR "functional thinking" OR "relational thinking" OR "pattern recognition" OR "covariational thinking" OR "covariational reasoning") AND (math* AND (edu* OR teach* OR learn* OR student* OR teacher OR curricul* OR classroom OR instruction))). Thus, the aim was to ensure that all relevant studies were captured. According to the inclusion criteria, studies published between January 1996 and May 2025, written in English, classified as articles, and indexed under the education/educational research category were included in the analysis. 1769 articles were obtained in total. These articles were exported in Plain Text File formats. Plain Text File formats were later imported to the VOSviewer program for analysis. During data cleaning and preprocessing, data were exported from VOSviewer to Excel, and repeated author names, incorrect country names, and keywords with the same meaning were corrected to ensure accurate results. In selecting bibliometric techniques, the data analysis techniques were determined to be citation analysis, co-occurrence analysis, and co-authorship. The minimum values requested when running the analysis, such as the minimum number of publications and citations, were set to best represent the data. Then, performance analysis was used to examine quantitative variables, such as the number of articles by year, and science mapping was used to identify the most dominant keywords and core topics in algebra education and to describe co-authorships among authors, countries, and institutions. Thus, visualization, interpretation, and reporting were conducted.

Analysis showed that the number of articles has increased over the years. After 2005, there have been at least 25 articles each year. The number of articles is the highest in 2022 (7.6%), followed by 2024 (7.3%) and 2021 (7.0%), while 1996, 2001, and 2002 had the fewest articles (0.2%). The most used ten keywords are algebra, mathematics education, mathematics, problem-solving, linear algebra, early algebra, algebraic thinking, curriculum, computer algebra system, and function. The core topics are algebra, problem-solving, functions, and linear algebra. Curriculum, computer algebra systems, early algebra, and covariational reasoning are potential core topics. Moreover, the most productive author is Timothy Fukawa-Connelly, with 21 articles, followed by Eric J. Knuth and Ana Stephens, each with 14 articles. Besides, Eric J. Knuth and Ana Stephens are the most cited authors, with 754 and 648 citations, respectively, and are also the most collaborative, frequently working with each other and with other scholars on early algebra, equality, and algebraic and functional thinking. The most productive country is the USA, with 881 (50.1%) articles. Turkiye (6%) and England (4%) follow the USA in terms of productivity, with 122 and 76 articles, respectively. According to the links, the USA is the most collaborative country. It collaborates with many countries in both Europe and the East. The second-most collaborative country is England, followed by Spain. The USA has the strongest link with Turkiye, indicating the highest level of collaboration between the two countries. The People's Republic of China has the second-highest link strength with the USA. While most productive institutions are Temple University, followed by the University of Delaware and the University of Wisconsin, most collaborative ones are the University of Texas at Austin, followed by Temple University, the University of Delaware, and Arizona State University.

Blanton, M., Levi, L., Crites, T., Dougherty, B., & Zbiek, R. M. (2011). Developing essential understandings of algebraic thinking for teaching mathematics in grades 3–5 (Series in Essential Understandings). National Council of Teachers of Mathematics. Brizuela, B., & Schliemann, A. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33-40. Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for research in mathematics education, 26(1), 66-86. https://doi.org/10.5951/jresematheduc.26.1.0066 Glassmeyer, D., & Edwards, B. (2016). How middle grade teachers think about algebraic reasoning. Mathematics Teacher Education and Development, 18(2), 92-106. Hayu, S. R., & Angraini, L. M. (2024). Research trends of students’ mathematical ability on algebra materials based on gender: Bibliometric analysis. International Journal of Applied Learning and Research in Algebra, 1(2), 120-128. https://doi.org/10.56855/algebra.v1i2.1268 Hegedus, S. J., & Kaput, J. (2003). The effect of a simcalc connected classroom on students' algebraic thinking. International Group for the Psychology of Mathematics Education, 3, 47-54. Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., and Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. J. Res. Math. Educ. 38(3), 258–288. https://doi.org/10.2307/30034868 Jamil, N., Rosli, R., & Mahmud, M. S. (2025). Algebraic trends impact school mathematics education: A bibliometric review. Multidisciplinary Reviews, 8(9), 2025261. https://doi.org/10.31893/multirev.2025261 Kaput, J. J. (1999). Teaching and learning a new algebra. In Mathematics classrooms that promote understanding (pp. 133-155). Routledge. Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151. 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 National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston. Passas, I. (2024). Bibliometric analysis: the main steps. Encyclopedia, 4(2). https://doi.org/10.3390/encyclopedia4020065 Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra: A challenge at the crossroads of policy and practice. Review of Educational Research, 81(4), 453-492. https://doi.org/10.3102/00346543114230 Veith, J. M., Beste, M. L., Kindervater, M., Krause, M., Straulino, M., Greinert, F., & Bitzenbauer, P. (2023). Mathematics education research on algebra over the last two decades: Quo vadis? Frontiers in Education, 8, https://doi.org/10.3389/feduc.2023.1211920 Wang, Y. (2008). On visual semantic algebra (VSA) and the cognitive process of pattern recognition. In Proceedings of the 7th IEEE International Conference on Cognitive Informatics (pp. 384–393). IEEE.