Recent One Decade Trends in Mathematical Representation Research: Systematic Mapping Study

Nizaruddin Nizaruddin(1*), Yanuar Hery Murtianto(2), Muhtarom Muhtarom(3)

(1) Universitas PGRI Semarang
(2) 
(3) 
(*) Corresponding Author

Abstract


Research can change over time and can be influenced by technological developments, educational trends, and current social issues. Developments on trends in mathematical representation research over the past 10 years are discussed in  this  systematic mapping study (SMS). The question of review research with the systematic mapping study method is how the trend of mathematical representation research over the last 1 decade and what new topics have the opportunity to be researched by future researchers related to the themes of mathematical representation. The method used in this review is the PRISMA method which includes 5 stages carried out: 1) defining eligibility criteria, 2) determining information sources, 3) data selection, 4) data collection, and 5) data collection. In  this systematic mapping study,  it starts from searching for articles on the topic of mathematical representation during the last 1 decade, namely the range of 2013-2023, articles obtained from the scopus database in July 2023 with the keywords "representations" AND : Mathematics" initial data obtained 1907 articles after the exclusion process obtained 120 articles which were then analyzed using R-Studio and Vos-Viewer tools. The results of SMS obtained the relationship of representation topics in the last 10 years of research with the topics of  visual, computer software, computer aid instruction, data mining, open source software, network architecture, natural language processing systems, intelligent systems and information analysis. In addition, research over the past 1 decade on the topic of representation has led more to  data mining, security of data and STEM. Artificial Intelligence or artificial intelligence is the latest topic that over the past 3 years has grown in various articles that deal with the theme of mathematical representation and accompanied by the theme of multi-representation. The evolution of research topics related to mathematical representations that used to be only related to visual representations and image representations now leads to computer programs, programming algorithms and artificial intelligence, this shows that over the past 1 decade there has been an evolution of research in the implementation of representations in technology.

Keywords


Mathematics, Representation, Systematic Mapping Study

Full Text:

PDF

References


Arakawa, T., Creutzig, T., & Feigin, B. (2022). Urod algebras and Translation of W-algebras. Forum of Mathematics, Sigma, 10. https://doi.org/10.1017/fms.2022.15

Aria, M., & Cuccurullo, C. (2017). bibliometrix: An R-tool for comprehensive science mapping analysis. Journal of Informetrics, 11(4), 959–975. https://doi.org/10.1016/j.joi.2017.08.007

Aria, M., Misuraca, M., & Spano, M. (2020). Mapping the Evolution of Social Research and Data Science on 30 Years of Social Indicators Research. Social Indicators Research, 149(3), 803–831. https://doi.org/10.1007/s11205-020-02281-3

Bai, C., Zhao, T., Wang, W., & Wu, M. (2015). An efficient indexing scheme based on K-Plet representation for fingerprint database (B. V., H. D.-S., & P. P. (eds.); Vol. 9225, pp. 247–257). Springer Verlag. https://doi.org/10.1007/978-3-319-22180-9_25

Bakar, K. A., Mohamed, S., Yunus, F., & Karim, A. A. (2020). Use of multiple representations in understanding addition: The case of pre-school children. International Journal of Learning, Teaching and Educational Research, 19(2), 292–304. https://doi.org/10.26803/IJLTER.19.2.18

Bille, P., Li Gørtz, I., & Vind, S. (2015). Compressed data structures for range searching (D. A.-H., M.-V. C., F. E., & T. B. (eds.); Vol. 8977, pp. 577–586). Springer Verlag. https://doi.org/10.1007/978-3-319-15579-1_45

Bomanson, J., Gebser, M., Janhunen, T., Kaufmann, B., & Schaub, T. (2016). Answer Set Programming Modulo Acyclicity. Fundamenta Informaticae, 147(1), 63–91. https://doi.org/10.3233/FI-2016-1398

Bouissou, M. (2020). Automatic translation from dynamic models to boolean representation suitable for i&ab quantification (B. P., D. M. F., & Z. E. (eds.); pp. 1868–1875). Research Publishing, Singapore. https://doi.org/10.3850/978-981-14-8593-0_4865-cd

Brazhnikova, Y. A. (2016). Innovative technique of working with music text by symmetry operations. Integration of Education, 20(4), 507–521. https://doi.org/10.15507/1991-9468.085.020.201604.507-521

Búrigo, E. Z., & Da Rosa, N. G. (2021). Machines and numbers: Translations of Nicole Picard’s texts in Porto Alegre during the 1970s . Educacao and Realidade, 46(2). https://doi.org/10.1590/2175-6236112151

Cao, J.-X., Yang, R.-H., & He, L.-M. (2019). Effect of subtitle presentation types on students’ learning outcome and cognitive load. 144–147. https://doi.org/10.1145/3369255.3369268

Castro-Alonso, J. C., Wong, R. M., Adesope, O. O., & Paas, F. (2021). Effectiveness of Multimedia Pedagogical Agents Predicted by Diverse Theories: a Meta-Analysis. Educational Psychology Review, 33(3), 989–1015. https://doi.org/10.1007/s10648-020-09587-1

Ceccherini-Silberstein, T., Scarabotti, F., & Tolli, F. (2022). Representations of Finite Group Extensions via Projective Representations. In Springer Monographs in Mathematics (pp. 189–228). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-13873-7_7

Dorrek, F. (2017). Minkowski Endomorphisms. Geometric and Functional Analysis, 27(3), 466–488. https://doi.org/10.1007/s00039-017-0405-z

Gao, W., & Chen, Y. (2020). Approximation analysis of ontology learning algorithm in linear combination setting. Journal of Cloud Computing, 9(1). https://doi.org/10.1186/s13677-020-00173-y

Greiner-Petter, A., Schubotz, M., Breitinger, C., Scharpf, P., Aizawa, A., & Gipp, B. (2023). Do the Math: Making Mathematics in Wikipedia Computable. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4), 4384–4395. https://doi.org/10.1109/TPAMI.2022.3195261

Gülk?l?ka, H., U?urlub, H. H., & Yürükc, N. (2015). Examining students’ mathematical understanding of geometric transformations using the pirie-kieren model. Kuram ve Uygulamada Egitim Bilimleri, 15(6), 1531–1548. https://doi.org/10.12738/estp.2015.6.0056

Guo, D., Ren, S., Lu, S., Feng, Z., Tang, D., Liu, S., Zhou, L., Duan, N., Svyatkovskiy, A., Fu, S., Tufano, M., Deng, S. K., Clement, C., Drain, D., Sundaresan, N., Yin, J., Jiang, D., & Zhou, M. (2021). GRAPHCODEBERT: PRE-TRAINING CODE REPRESENTATIONS WITH DATA FLOW. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85139426637&partnerID=40&md5=887d147a2eac53b296f7973e2bb16380

Helingo, D. D. Z., Amin, S. M., & Masriyah, M. (2019). Translation process of mathematics representation: From graphics to symbols and vice versa (P. P.W. (ed.); Vol. 1188, Issue 1). Institute of Physics Publishing. https://doi.org/10.1088/1742-6596/1188/1/012055

Iancu, M., Kohlhase, M., Rabe, F., & Urban, J. (2013). The Mizar mathematical library in OMDoc: Translation and applications. Journal of Automated Reasoning, 50(2), 191–202. https://doi.org/10.1007/s10817-012-9271-4

Ikeda, T., & Stephens, M. (2015). Reconsidering the Roles and Characteristics of Models in Mathematics Education. In International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 351–361). Springer Science and Business Media B.V. https://doi.org/10.1007/978-3-319-18272-8_29

Istadi, Kusmayadi, T. A., & Sujadi, I. (2017). Students’ mathematical representations on secondary school in solving trigonometric problems. 855(1). https://doi.org/10.1088/1742-6596/855/1/012021

Kohlhase, M., Müller, D., Owre, S., & Rabe, F. (2017). Making PVS accessible to generic services by interpretation in a universal format: Vol. 10499 LNCS (M. C.A. & A.-R. M. (eds.); pp. 319–335). Springer Verlag. https://doi.org/10.1007/978-3-319-66107-0_21

Lemus, E., Bribiesca, E., & Garduño, E. (2015). Surface trees - Representation of boundary surfaces using a tree descriptor. Journal of Visual Communication and Image Representation, 31, 101–111. https://doi.org/10.1016/j.jvcir.2015.06.004

Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1), 1–21. https://doi.org/10.46328/ijemst.1111

Mazo, L., & Baudrier, É. (2017). Study on the digitization dual combinatorics and convex case: Vol. 10502 LNCS (K. W.G., A. N.M., & J. I. (eds.); pp. 363–374). Springer Verlag. https://doi.org/10.1007/978-3-319-66272-5_29

Mbusi, N. P., & Luneta, K. (2021). Mapping pre-service teachers’ faulty reasoning in geometric translations to the design of Van Hiele phase-based instruction. South African Journal of Childhood Education, 11(1). https://doi.org/10.4102/sajce.v11i1.871

Munthe-Kaas, H. Z. (2016). Groups and symmetries in numerical linear algebra. In Lecture Notes in Mathematics (Vol. 2173, pp. 319–406). Springer Verlag. https://doi.org/10.1007/978-3-319-49887-4_5

Nitsch, R., Fredebohm, A., Bruder, R., Kelava, A., Naccarella, D., Leuders, T., & Wirtz, M. (2015). STUDENTS’ COMPETENCIES IN WORKING WITH FUNCTIONS IN SECONDARY MATHEMATICS EDUCATION—EMPIRICAL EXAMINATION OF A COMPETENCE STRUCTURE MODEL. International Journal of Science and Mathematics Education, 13(3), 657–682. https://doi.org/10.1007/s10763-013-9496-7

Padalkar, S., & Hegarty, M. (2015). Models as feedback: Developing representational competence in chemistry. Journal of Educational Psychology, 107(2), 451–466. https://doi.org/10.1037/a0037516

Parta, I. N., Sa’dijah, C., Sirajuddin, & Sukoriyanto. (2021). How do prospective teachers solve the algebra problem as a broad measure (S. H., H. H., & R. D. (eds.); Vol. 2330). American Institute of Physics Inc. https://doi.org/10.1063/5.0043738

Peng, F., Li, J., & Long, M. (2015). A lossless watermarking algorithm for STL model using entity rearrangement based on average coding tree. Journal of Computational Information Systems, 11(8), 2895–2904. https://doi.org/10.12733/jcis14064

Sandie, Purwanto, Subanji, & Hidayanto, E. (2019). Process thinking of students in translating representation of covariational dynamic events problems. International Journal of Scientific and Technology Research, 8(10), 1405–1408. https://www.scopus.com/inward/record.uri?eid=2-s2.0-85074175739&partnerID=40&md5=3ca4072de2b037887fd5e46b1b299bf1

Selkälä, A., Callegaro, M., & Couper, M. P. (2020). Automatic versus manual forwarding in web surveys - a cognitive load perspective on satisficing responding: Vol. 12194 LNCS (M. G. (ed.); pp. 130–155). Springer. https://doi.org/10.1007/978-3-030-49570-1_10

Shestakova, M. (2018). Visualization of the philosophical and conceptual foundations of modern natural sciences in renaissance painting. Praxema, 186(4), 263–272. https://doi.org/10.23951/2312-7899-2018-4-263-272

Tan, S., Clivaz, S., & Sakamoto, M. (2022). Presenting multiple representations at the chalkboard: bansho analysis of a Japanese mathematics classroom. Journal of Education for Teaching. https://doi.org/10.1080/02607476.2022.2150538

Taxipulati, S., & Lu, H.-D. (2021). The Influence of Feedback Content and Feedback Time on Multimedia Learning Achievement of College Students and Its Mechanism. Frontiers in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.706821

Tomita, K. (2018). Does the Visual Appeal of Instructional Media Affect Learners’ Motivation Toward Learning? TechTrends, 62(1), 103–112. https://doi.org/10.1007/s11528-017-0213-1

Tugtekin, U., & Odabasi, H. F. (2022). Do Interactive Learning Environments Have an Effect on Learning Outcomes, Cognitive Load and Metacognitive Judgments? Education and Information Technologies, 27(5), 7019–7058. https://doi.org/10.1007/s10639-022-10912-0

Uysal, M. P. (2016). Evaluation of learning environments for object-oriented programming: measuring cognitive load with a novel measurement technique. Interactive Learning Environments, 24(7), 1590–1609. https://doi.org/10.1080/10494820.2015.1041400

Van Den Eynde, S., Van Kampen, P., Van Dooren, W., & De Cock, M. (2019). Translating between graphs and equations: The influence of context, direction of translation, and function type. Physical Review Physics Education Research, 15(2). https://doi.org/10.1103/PhysRevPhysEducRes.15.020113

Waisman, I., Brunner, C., Grabner, R. H., Leikin, M., & Leikin, R. (2023). (Lack of) neural efficiency related to general giftedness and mathematical excellence: An EEG study. Neuropsychologia, 179. https://doi.org/10.1016/j.neuropsychologia.2022.108448

Waisman, I., Leikin, M., Shaul, S., & Leikin, R. (2014). Brain Activity Associated With Translation Between Graphical And Symbolic Representations Of Functions In Generally Gifted And Excelling In Mathematics Adolescents. International Journal of Science and Mathematics Education, 12(3), 669–696. https://doi.org/10.1007/s10763-014-9513-5

Waite, A., & Byrne, W. (2015). The geometry of statistical machine translation. 376–386. https://doi.org/10.3115/v1/n15-1041

Yu, M., Bai, C., Yu, J., Zhao, M., Xu, T., Liu, H., Li, X., & Yu, R. (2022). Translation-Based Embeddings with Octonion for Knowledge Graph Completion. Applied Sciences (Switzerland), 12(8). https://doi.org/10.3390/app12083935




DOI: http://dx.doi.org/10.30998/formatif.v14i2.21652

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Formatif: Jurnal Ilmiah Pendidikan MIPA

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Publisher:
Institute for Research and Community Services
(LPPM) Universitas Indraprasta PGRI
Kampus A Building 3, 2nd Floor | Jl. Nangka No. 58 C (TB. Simatupang), Kel. Tanjung Barat, Kec. Jagakarsa, Jakarta Selatan 12530, Jakarta, Indonesia. 


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

View My Stats