LITERATURE REVIEW
A Systematic Review on Algebraic Thinking in Education
 
More details
Hide details
1
Department of Pedagogy of Higher Education, Kazan (Volga Region) Federal University, Kazan, RUSSIA
 
2
Department of Medical and Biological Physics, I. M. Sechenov First Moscow State Medical University (Sechenov University), Moscow, RUSSIA
 
3
Faculty of Design and Software Engineering, Kazan National Research Technological University, Kazan, RUSSIA
 
4
Department of Informatics, Management and Technology, Moscow City University, Moscow, RUSSIA
 
5
Department of Natural Sciences and Information Technologies, Kazan National Research Technical University Named after A. N. Tupolev - KAI, Kazan, RUSSIA
 
6
Department of Foreign Languages, RUDN University, Moscow, RUSSIA
 
 
Publication date: 2022-01-03
 
 
EURASIA J. Math., Sci Tech. Ed 2022;18(1):em2065
 
KEYWORDS
ABSTRACT
Algebraic thinking is a method of solving math problems that stresses the significance of general connections. Excellent algebraic thinking necessitates strong symbolization and generalization ability. Students aged 7 to 15 are at the Piaget thinking stage’s formal operational stage. Teachers, especially those working with secondary school students, must be aware of how kids think and reason algebraically. A detailed literature review provides an overview of research on algebraic thinking. The goal of this study was to compile a list of full-text papers that presented empirical research on algebraic thinking. The “algebraic thinking” search phrase was used to search the ERIC and Scopus databases. A total of 36 studies were included in the review. The educational levels, participants, nations, research methodologies, study objectives, data collecting tools, and analytic approaches have all been considered in studies on algebraic thinking. The number of studies published has risen over time. 2019 was the year with the most studies. The majority of the research was carried out in the United States of America. The majority of the participants in the study were elementary and secondary school pupils. Teachers’ knowledge, elements impacting algebraic thinking, relations, and comprehension, as well as measuring categories, were determined when the study was grouped according to the study’s topic. The algebraic thinking exam was the most popular data gathering instrument. The qualitative technique was used in the study of algebraic thinking. The most common method was found to be qualitative analysis. While inferential statistics are preferred in quantitative techniques, latent class analysis, cluster analysis, and test development analysis are used depending on the study design. According to the results, it was stated that in-service or pre-service teacher training is needed for the development of algebraic thinking and non-routine activities such as games should be used in the classroom. In addition, it has been determined that teaching strategies such as geometry representation, multiple representation strategies, mental computational activity also improve algebraic thinking.
 
REFERENCES (73)
1.
Adamuz-Povedano, N., Fernández-Ahumada, E., Teresa García-Pérez, M., & Montejo-Gámez, J. (2021). Developing number sense: An approach to initiate algebraic thinking in primary education. Mathematics, 9(5), 1-25. https://doi.org/10.3390/math90....
 
2.
Afonso, D. G. (2019). The development of algebraic thinking in the foundation phase: A comparative study of two different curricula. Cape Peninsula University of Technology.
 
3.
Afonso, D., & Mc Auliffe, S. (2019). Children’s capacity for algebraic thinking in the early grades. African Journal of Research in Mathematics, Science and Technology Education, 23(2), 219-232. https://doi.org/10.1080/181172....
 
4.
Agoestanto, A., Sukestiyarno, Y. L., Isnarto, Rochmad, & Lestari, M. D. (2019). The position and causes of students errors in algebraic thinking based on cognitive style. International Journal of Instruction, 12(1), 1431-1444. https://doi.org/10.29333/iji.2....
 
5.
Apsari, R. A., Putri, R. I. I., Sariyasa, Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics Education, 11(1), 45-58. https://doi.org/10.22342/jme.1....
 
6.
Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272. https://doi.org/10.1080/109860....
 
7.
Ayber, G., & Tanisli, D. (2017). An analysis of middle school mathematics textbooks from the perspective of fostering algebraic thinking through generalization. Kuram ve Uygulamada Egitim Bilimleri [Educational Sciences in Theory and Practice], 17(6), 2001-2030. https://doi.org/10.12738/estp.....
 
8.
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....
 
9.
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J. S. (2015). The development of children’s algebrai 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/jresem....
 
10.
Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. Research Report. In Research Report: National Center for Improving Student Learning and Achievement in Mathematics and Science. https://eric.ed.gov/?id=ED4704....
 
11.
Carraher, D. W., Schliemann, A., & Brizuela, B. M. (2000). Early algebra, early arithmetic: Treating operations as functions. Pme-Na, XXII, 1-26.
 
12.
Chimoni, M., & Pitta-Pantazi, D. (2017). Parsing the notion of algebraic thinking within a cognitive perspective. Educational Psychology, 37(10), 1186-1205. https://doi.org/10.1080/014434....
 
13.
Chimoni, M., Pitta-Pantazi, D., & Christou, C. (2018). Examining early algebraic thinking: Insights from empirical data. Educational Studies in Mathematics, 98(1), 57–76. https://doi.org/10.1007/s10649....
 
14.
Demonty, I., Vlassis, J., & Fagnant, A. (2018). Algebraic thinking, pattern activities and knowledge for teaching at the transition between primary and secondary school. Educational Studies in Mathematics, 99(1). https://doi.org/10.1007/s10649....
 
15.
Di Paola, B., Battaglia, O. R., & Fazio, C. (2016). Non-hierarchical clustering as a method to analyse an open-ended questionnaire on algebraic thinking. South African Journal of Education, 36(1), 1-13. https://doi.org/10.15700/saje.....
 
16.
Eriksson, H., & Eriksson, I. (2021). Learning actions indicating algebraic thinking in multilingual classrooms. Educational Studies in Mathematics, 106(3), 363-378. https://doi.org/10.1007/s10649....
 
17.
Eriksson, H., & Sumpter, L. (2021). Algebraic and fractional thinking in collective mathematical reasoning. Educational Studies in Mathematics. https://doi.org/10.1007/s10649....
 
18.
Gambari, A. I., Shittu, A. T., & Taiwo, O. A. (2016). Enhancing students’ understanding of algebra concepts through cooperative computer instruction. Pedagogical Research, 1(2), 55. https://doi.org/10.20897/lecti....
 
19.
Goulding, M., & Kyriacou, C. (2008). A systematic review of the use of ICTs in developing pupils’ understanding of algebraic ideas. EPPI-Centre Report, 1606.
 
20.
Guler, M., & Celik, D. (2021). The effect of an elective algebra teaching course on prospective mathematics teachers’ pedagogical content knowledge. International Electronic Journal of Mathematics Education, 16(2), em0636. https://doi.org/10.29333/iejme....
 
21.
Herbert, K., & Brown, R. H. (1997). Patterns as tools. Teaching Children Mathematics, 3(1997), 340-345. https://doi.org/10.5951/TCM.3.....
 
22.
Herscovics, N., & Linchevscki, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies, 27(1), 59-78. https://doi.org/10.1007/BF0128....
 
23.
Hitt, F., Saboya, M., & Cortés Zavala, C. (2016). An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: Triangular numbers. ZDM, 48(6), 775-791. https://doi.org/10.1007/s11858....
 
24.
Hitt, F., Saboya, M., & Zavala, C. C. (2017). Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment. Educational Studies in Mathematics, 94(1), 97-116. https://doi.org/10.1007/s10649....
 
25.
Hodgen, J., Oldenburg, R., & Strømskag, H. (2018). Algebraic thinking. Developing Research in Mathematics Education, 32-45. https://doi.org/10.4324/978131....
 
26.
Hunter, J., & Miller, J. (2020). Using a culturally responsive approach to develop early algebraic reasoning with young diverse learners. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763....
 
27.
Inan, C. (2015). Elementary school preservice teachers’ competencies in the field of patterns under the process of scientific skills development. Universal Journal of Educational Research, 3(10), 663-670. https://doi.org/10.13189/ujer.....
 
28.
Kamol, N. (2005). A framework for characterizing lower secondary school students’ algebraic thinking [Unpublished doctoral dissertation]. Srinakharinwirot University.
 
29.
Kamol, N., & Har, Y. B. (2010). Upper primary school students’ algebraic thinking. In L. Sparrow, B. Kissane, & C. Kurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 289-296). MERGA.
 
30.
Kaput, J. J. (1999). Teaching and learning a new algebra. Mathematics Classrooms That Promote Understanding, Ccm, 133-155.
 
31.
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. Taylor & Francis Group.
 
32.
Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139-151.
 
33.
Kieran, C. (2006). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick, & M. Kendal (Eds.), The Future of the Teaching and Learning of Algebra The 12th ICMI Study (pp. 21-33). Springer. https://doi.org/10.1007/1-4020....
 
34.
Kieran, C. (2011). Overall commentary on early algebraization: Perspectives for research and teaching. In J. Cai, & E. Knuth (Eds.), Early algebraization (pp. 579-593). https://doi.org/10.1007/978-3-....
 
35.
Kriegler, S. (2007). Just what is algebraic thinking? Introduction to Algebra :TeacherHandbook, 1-11.
 
36.
Kusumaningsih, W., Darhim, Herman, T., & Turmudi. (2018). Gender differences in algebraic thinking ability to solve mathematics problems. Journal of Physics: Conference Series, 1013(1). https://doi.org/10.1088/1742-6....
 
37.
Kyriacou, C. (2009). Effective teaching in schools theory and practice. Stanley Thornes. https://doi.org/10.1016/j.vetp....
 
38.
Lentz, U. (2018). Algebraic thinking of sixth graders through the lens of multimodality [PhD thesis, The University of North Carolina at Charlotte].
 
39.
Liberati, A., Altman, D. G., Tetzlaff, J., Mulrow, C., Gøtzsche, P. C., Ioannidis, J. P. A., Clarke, M., Devereaux, P. J., Kleijnen, J., & Moher, D. (2009). The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: Explanation and elaboration. Journal of Clinical Epidemiology, 62(10), e1-e34. https://doi.org/10.1016/j.jcli....
 
40.
Lins, R. C. (1992). A framework for understanding what algebraic thinking is [Unpublsihed Ph.D. thesis. University of Nottingham]. http://eprints.nottingham.ac.u....
 
41.
MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11-15. Educational Studies in Mathematics, 33(1), 1-19. https://doi.org/10.1017/CBO978....
 
42.
Magiera, M. T., van den Kieboom, L. A., & Moyer, J. C. (2013). An exploratory study of pre-service middle school teachers’ knowledge of algebraic thinking. Educational Studies in Mathematics, 84(1), 93-113. https://doi.org/10.1007/s10649....
 
43.
Magiera, M., van den Kieboom, L., & Moyer, J. (2017). K-8 pre-service teachers’ algebraic thinking: Exploring the habit of mind “Building rules to represent functions”. Mathematics Teacher Education and Development, 19(2), 25-50.
 
44.
Mason, J. (2008). Making use of children’s powers to produce algebraic thinking. Algebra In The Early Grades, 2008, 57-94. https://doi.org/10.4324/978131....
 
45.
Mulligan, J., Oslington, G., & English, L. (2020). Supporting early mathematical development through a ‘pattern and structure’ intervention program. ZDM - Mathematics Education, 52(4), 663-676. https://doi.org/10.1007/s11858....
 
46.
NCTM. (2000). Principles and standarts for school mathematics. The National Council of Teachers of Mathematics.
 
47.
Ntsohi, M. M. E. (2013). Investigating teaching and learning of grade 9 algebra through excel spreadsheets: A mixed-methods case study for Lesotho (Issue December). https://scholar.sun.ac.za/hand....
 
48.
Obara, S. (2019). Pre-service teachers exploring the role of pattern-based reasoning in the context of algebraic thinking. Eurasia Journal of Mathematics, Science and Technology Education, 15(11). https://doi.org/10.29333/ejmst....
 
49.
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(7), 1401-1421. https://doi.org/10.1007/s10763....
 
50.
Pincheira, N., & Alsina, Á. (2021). Teachers’ mathematics knowledge for teaching early algebra: A systematic review from the mkt perspective. Mathematics, 9(20), 2590. https://doi.org/10.3390/math92....
 
51.
Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2019). 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....
 
52.
Pourdavood, B. R., McCarthy, K., & McCafferty, T. (2020). The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 7(3), 241-254. https://doi.org/10.30958/aje.7....
 
53.
Radford, L. (2000). Signs and meanings in students’ emergent algebraic. Educational Studies in Mathematics, 42(3), 237-268. https://doi.org/10.1023/A:1017....
 
54.
Radford, L., & Sabena, C. (2015). The question of method in a Vygotskian semiotic approach. In Approaches to qualitative research in mathematics education (Issue January 2014, (pp. 157-182). https://doi.org/10.1007/978-94....
 
55.
Ralston, N. C. (2013). The development and validation of a diagnostic assessment of algebraic thinking skills for students in the elementary grades [PhD Dissertation, University of Washington].
 
56.
Ralston, N. C., Li, M., & Taylor, C. (2018). The development and initial validation of an assessment of algebraic thinking for students in the elementary grades. Educational Assessment, 23(3), 211-227. https://doi.org/10.1080/106271....
 
57.
Rittle-Johnson, B., Fyfe, E. R., McLean, L. E., & McEldoon, K. L. (2013). Emerging understanding of patterning in 4-year-olds. Journal of Cognition and Development, 14(3), 376-396. https://doi.org/10.1080/152483....
 
58.
Rudyanto, H. E., Marsigit, Wangid, M. N., & Gembong, S. (2019). The use of bring your own device-based learning to measure student algebraic thinking ability. International Journal of Emerging Technologies in Learning, 14(23), 233-241. https://doi.org/10.3991/ijet.v....
 
59.
Schliemann, A. D., Carraher, D. W., & Brizuela, B. M. (2013). Bringing out the algebraic character of arithmetic: From children’s ideas to classroom practice. Taylor & Francis Group. https://doi.org/10.4324/978020....
 
60.
Schunk, D. H. (2012). Learning theories an educational perspective. Pearson.
 
61.
Smith, J. P., & Thompson, P. W. (2007). Quantitative reasoning and the development of algebraic reasoning. Algebra In The Early Grades, 95-132. https://doi.org/10.4324/978131....
 
62.
Somasundram, P. (2021). The role of cognitive factors in year five pupils’ algebraic thinking: A structural equation modelling analysis. Eurasia Journal of Mathematics, Science and Technology Education, 17(1), 1-12. https://doi.org/10.29333/ejmst....
 
63.
Specht, B. J. (2005). Early algebra - Processes and concepts of fourth graders solving algebraic problems. CERME 4 - European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 4, 706-7016. http://www.mathematik.uni-dort....
 
64.
Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. M. (2015). Just say yes to early algebra! Teaching Children Mathematics, 22(2), 92. https://doi.org/10.5951/teacch....
 
65.
Syarifuddin, H., & Atweh, B. (2022). The use of activity, classroom discussion, and exercise (ACE) teaching cycle for improving students’ engagement in learning elementary linear algebra. European Journal of Science and Mathematics Education, 10(1), 104-138. https://doi.org/10.30935/scima....
 
66.
Usiskin, Z. (1999). Conceptions of school algebra and uses of variables. In B. Moses (Ed.), The ideas of algebra, K-12 (Issue 5, pp. 8-19). NCTM.
 
67.
van Amerom, B. (2002). Reinvention of early algebra. In K. Gravemeijer (Ed.), Developmental research on the transition from arithmetic to algebra (p. 352).
 
68.
van den Kieboom, L. A., Magiera, M. T., & Moyer, J. C. (2014). Exploring the relationship between K-8 prospective teachers’ algebraic thinking proficiency and the questions they pose during diagnostic algebraic thinking interviews. Journal of Mathematics Teacher Education, 17(5), 429-461. https://doi.org/10.1007/s10857....
 
69.
Venenciano, L. C. H., Yagi, S. L., Zenigami, F. K., & Dougherty, B. J. (2020). Supporting the development of early algebraic thinking, an alternative approach to number. Investigations in Mathematics Learning, 12(1), 38-52. https://doi.org/10.1080/194775....
 
70.
Walkoe, J. (2014). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18(6), 523-550. https://doi.org/10.1007/s10857....
 
71.
Walkowiak, T. A. (2014). Elementary and middle school students’ analyses of pictorial growth patterns. Journal of Mathematical Behavior, 33(1), 56-71. https://doi.org/10.1016/j.jmat....
 
72.
Wilkie, K. J. (2016). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333-361. https://doi.org/10.1007/s10649....
 
73.
Wu, Z. (2017). Effects of using problem of the week in teaching on teacher learning and change in algebraic thinking and algebra. ZDM - Mathematics Education, 49(2), 203-221. https://doi.org/10.1007/s11858....
 
eISSN:1305-8223
ISSN:1305-8215
Journals System - logo
Scroll to top