Trends of abstraction research in mathematics education: A bibliometric analysis

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Hodiyanto
Mega Teguh Budiarto
Rooselyna Ekawati
Gemi Susanti
Jeonghyeon Kim
Daisy Mae R. Bongtiwon

Abstract

Abstraction is fundamental in mathematics learning because students can discover the studied concepts through abstraction. Bibliometric analyses of abstraction research in mathematics education have yet to be published. A bibliometric analysis is conducted to explore trends in abstraction research. The mathematics education researchers will gain insights from studying the development of abstraction research over the last fifteen years. The primary objective of this study is to evaluate the primary journals published, the most productive authors, universities, and countries and to identify current trends in abstraction research. Data were collected from the Scopus database and analysed using VOSviewer and R software. A thorough review was conducted on 271 articles published between 2008 and 2022. The collected data was analysed and presented using R studio and VOSviewer software. The publication of abstraction research has increased every year. Abstraction studies related to geometry, computational thinking, and preschool are trend and abstraction studies related to gesture, preschool child, arithmetic, physiology, mathematical concepts, geometry, language, and cognition. Abstraction research is exciting because it will still trend until 2022. This study offers valuable insights to researchers interested in mathematics education for exploring alternative research directions to the primary research trends. Based on these results, recommendations for further research are given so that they can explore various options for research trends.

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References

Aktoprak, A., & Hursen, C. (2022). A bibliometric and content analysis of critical thinking in primary education. Thinking Skills and Creativity, 44, 101029. https://doi.org/10.1016/j.tsc.2022.101029

Benis-Sinaceur, H. (2014). Facets and levels of mathematical abstraction. Philosophia Scientae, 18(1), 81-112. https://doi.org/10.4000/philosophiascientiae.914

Boonstra, K., Kool, M., Shvarts, A., & Drijvers, P. (2023). Theories and practical perspectives on fostering embodied abstraction in primary school geometry education. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1162681

Börner, K., Chen, C., & Boyack, K. W. (2003). Visualizing knowledge domains. Annual Review of Information Science and Technology, 37(1), 179-255. https://doi.org/10.1002/aris.1440370106

Borriello, G. A., Flynn, M. E., & Fyfe, E. R. (2022). Developmental differences in children's and adults’ strategies on a repeating pattern task. Early Childhood Research Quarterly, 59, 300-310. https://doi.org/10.1016/j.ecresq.2021.12.012

Breive, S. (2022). Abstraction and embodiment: Exploring the process of grasping a general. Educational Studies in Mathematics, 110(2), 313-329. https://doi.org/10.1007/s10649-021-10137-x

Dreyfus, T. (2007). Processes of abstraction in context the nested epistemic actions model. Journal for Research in Mathematics Education, 32(2). http://medicina.iztacala.unam.mx/medicina/dreyfus.pdf

Dreyfus, T. (2015). Constructing abstract mathematical knowledge in context. In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 115-133). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_7

Dreyfus, T., Hershkowitz, R., & Schwarz, B. (2015). The nested epistemic actions model for abstraction in context: Theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to Qualitative Research in Mathematics Education: Examples of Methodology and Methods (pp. 185-217). Springer Netherlands. https://doi.org/10.1007/978-94-017-9181-6_8

Drijvers, P., Grauwin, S., & Trouche, L. (2020). When bibliometrics met mathematics education research: the case of instrumental orchestration. Zdm, 52(7), 1455-1469. https://doi.org/10.1007/s11858-020-01169-3

Dvir, A., & Tabach, M. (2017). Learning extrema problems using a non-differential approach in a digital dynamic environment: the case of high-track yet low-achievers. Zdm, 49(5), 785-798. https://doi.org/10.1007/s11858-017-0862-8

Elias, D., & Dreyfus, T. (2022). High school students constructing knowledge about convergence and limits. Teaching Mathematics and its Applications, 41(2), 167-181. https://doi.org/10.1093/teamat/hrab035

Ellegaard, O., & Wallin, J. A. (2015). The bibliometric analysis of scholarly production: How great is the impact? Scientometrics, 105(3), 1809-1831. https://doi.org/10.1007/s11192-015-1645-z

Ferrari, P. L. (2003). Abstraction in mathematics. Philosophical Transactions of the Royal Society B: Biological Sciences, 358(1435), 1225-1230. https://doi.org/10.1098/rstb.2003.1316

Gilboa, N., Kidron, I., & Dreyfus, T. (2019). Constructing a mathematical definition: the case of the tangent. International Journal of Mathematical Education in Science and Technology, 50(3), 421-446. https://doi.org/10.1080/0020739X.2018.1516824

Gökçe, S., & Güner, P. (2021). Forty years of mathematics education: 1980-2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514-539. https://doi.org/10.46328/IJEMST.1361

Gray, E., & Tall, D. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23-40. https://doi.org/10.1007/BF03217454

Ha, C. T., Thao, T. T. P., Trung, N. T., Huong, L. T. T., Dinh, N. V., & Trung, T. (2020). A bibliometric review of research on STEM education in ASEAN: Science mapping the literature in Scopus database, 2000 to 2019. Eurasia Journal of Mathematics, Science and Technology Education, 16(10), em1889. https://doi.org/10.29333/ejmste/8500

Hallinger, P., & Kovačević, J. (2019). A bibliometric review of research on educational administration: Science mapping the literature, 1960 to 2018. Review of Educational Research, 89(3), 335-369. https://doi.org/10.3102/0034654319830380

Hazzan, O., & Zazkis, R. (2005). Reducing abstraction: The case of school mathematics. Educational Studies in Mathematics, 58(1), 101-119. https://doi.org/10.1007/s10649-005-3335-x

Hershkowitz, R., Dreyfus, T., & Tabach, M. (2023). Constructing the self-similarity concept. International Journal of Research in Undergraduate Mathematics Education, 9(2), 322-349. https://doi.org/10.1007/s40753-022-00173-0

Hershkowitz, R., Schwarz, B. B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 195-222. https://doi.org/10.2307/749673

Hodiyanto, H., Budiarto, M. T., Ekawati, R., Susanti, G., Kim, J., & Bonyah, E. (2024). How abstraction of a pre-service teacher in constructing relationships among quadrilaterals. Journal on Mathematics Education, 15(2), 339-362. https://doi.org/10.22342/jme.v15i2.pp339-362

Huan, C., Meng, C. C., & Suseelan, M. (2022). Mathematics learning from concrete to abstract (1968-2021): A bibliometric analysis. Participatory Educational Research, 9(4), 445-468. https://doi.org/10.17275/per.22.99.9.4

Julius, R., Halim, M. S. A., Hadi, N. A., Alias, A. N., Khalid, M. H. M., Mahfodz, Z., & Ramli, F. F. (2021). Bibliometric analysis of research in mathematics education using Scopus database. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), em2040. https://doi.org/10.29333/EJMSTE/11329

Kadarisma, G., Juandi, D., & Darhim, D. (2024). Global trends in flipped classroom research within mathematics education over past two decade: A bibliometric analysis. Infinity Journal, 13(2), 531-552. https://doi.org/10.22460/infinity.v13i2.p531-552

Kariadinata, R. (2021). Students' reflective abstraction ability on linear algebra problem solving and relationship with prerequisite knowledge. Infinity Journal, 10(1), 1-16. https://doi.org/10.22460/infinity.v10i1.p1-16

Kartika, H., Budiarto, M. T., Fuad, Y., & Bonyah, E. (2023). Bibliometrics analysis of research on argumentation in mathematics education. International Journal of Education in Mathematics, Science and Technology, 11(5), 1346-1365. https://doi.org/10.46328/ijemst.2904

Kiliçoğlu, E., & Kaplan, A. (2019). An examination of middle school 7th grade students’ mathematical abstraction processes. Journal of Computer and Education Research, 7(13), 233-256. https://doi.org/10.18009/jcer.547975

Liu, X., Zhan, F. B., Hong, S., Niu, B., & Liu, Y. (2013). Replies to comments on “a bibliometric study of earthquake research: 1900–2010”. Scientometrics, 96(3), 933-936. https://doi.org/10.1007/s11192-012-0914-3

Mathankar, A. R. (2018). Bibliometrics: an overview. International Journal of Library & Information Science (IJLIS), 7(3), 9-15.

Memnun, D. S., Altun, M., & Kesner, J. (2011). The abstraction process of the coordinate system concept. Management and Education, VII(4), 65-70.

Memnun, D. S., Aydın, B., Özbilen, Ö., & Erdoğan, G. (2017). The abstraction process of limit knowledge. Kuram ve Uygulamada Egitim Bilimleri, 17(2), 345-371.

Mitchelmore, M., & White, P. (2007). Abstraction in mathematics learning. Mathematics Education Research Journal, 19(2), 1-9. https://doi.org/10.1007/BF03217452

Nurjannah, S., & Kusnandi, K. (2021). Literature study: The role of abstraction ability to strengthen students early knowledge in mathematics learning. Journal of Physics: Conference Series, 1806(1), 012064. https://doi.org/10.1088/1742-6596/1806/1/012064

Ozmantar, M. F., & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112. https://doi.org/10.1007/BF03217457

Phan, T. T., Do, T. T., Trinh, T. H., Tran, T., Duong, H. T., Trinh, T. P. T., Do, B. C., & Nguyen, T.-T. (2022). A bibliometric review on realistic mathematics education in Scopus database between 1972-2019. European Journal of Educational Research, 11(2), 1133-1149. https://doi.org/10.12973/eu-jer.11.2.1133

Reinboth, T., & Farkaš, I. (2022). Ultimate grounding of abstract concepts: A graded account. Journal of Cognition, 5(1), 1-26. https://doi.org/10.5334/JOC.214

Saefudin, A. A., Wijaya, A., & Dwiningrum, S. I. A. (2023). Mapping research trends in mathematical creativity in mathematical instructional practices: A bibliometric analysis. Journal of Pedagogical Research, 7(4), 439-458. https://doi.org/10.33902/JPR.202322691

Simon, M. A. (2020). Elaborating reflective abstraction for instructional design in mathematics: Postulating a second type of reflective abstraction. Mathematical thinking and learning, 22(2), 162-171. https://doi.org/10.1080/10986065.2020.1706217

Simon, M. A., Kara, M., Norton, A., & Placa, N. (2018). Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the learning through activity research program. The Journal of Mathematical Behavior, 52, 151-173. https://doi.org/10.1016/j.jmathb.2018.03.002

Simon, M. A., Kara, M., & Placa, N. (2018). Promoting reinvention of a multiplication-of-fractions algorithm: A study of the learning through activity research program. The Journal of Mathematical Behavior, 52, 174-187. https://doi.org/10.1016/j.jmathb.2018.03.007

Simon, M. A., Placa, N., Kara, M., & Avitzur, A. (2018). Empirically-based hypothetical learning trajectories for fraction concepts: Products of the learning through activity research program. The Journal of Mathematical Behavior, 52, 188-200. https://doi.org/10.1016/j.jmathb.2018.03.003

Skemp, R. R. (1987). The psychology of learning mathematics. Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203396391

Suseelan, M., Chew, C. M., & Chin, H. (2022). Research on mathematics problem solving in elementary education conducted from 1969 to 2021: A bibliometric review. International Journal of Education in Mathematics, Science and Technology, 10(4), 1003-1029. https://doi.org/10.46328/ijemst.2198

van Oers, B., & Poland, M. (2007). Schematising activities as a means for encouraging young children to think abstractly. Mathematics Education Research Journal, 19(2), 10-22. https://doi.org/10.1007/BF03217453

Yilmaz, R., & Argun, Z. (2018). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6(1), 41-57.

Zupic, I., & Čater, T. (2015). Bibliometric methods in management and organization. Organizational Research Methods, 18(3), 429-472. https://doi.org/10.1177/1094428114562629