Skip to main content

Advertisement

SpringerLink
Log in

Twenty years of research on technology in mathematics education at CERME: a literature review based on a data science approach

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their ability to summarize large amounts of unstructured text into coherent themes or topics allows researchers in any field to keep an overview of state of the art by creating automated literature reviews. In this article, we apply topic modeling in the context of mathematics education and showcase the use of this data science approach for creating literature reviews by training a model of all papers (n = 336) that have been presented in Thematic Working Groups related to technology in the first eleven Congresses of the European Society for Research in Mathematics Education (CERME). We guide the reader through the stepwise process of training a model and give recommendations for best practices and decisions that are decisive for the success of such an approach to a literature review. We find that research in this period revolved around 25 distinct topics that can be grouped into four clusters: digital tools, teachers and their resources, technology experimentation, and a diverse cluster with a strong focus on student activity. Finally, a temporal analysis of these topics reveals a correlation between technology trends and research focus, allowing for reflection on future research in the field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data availability

The material generated and analyzed during the current study are available in the Zenodo repository (CERN’s repository service for open science) in Herfort et al. (2022).

References

  • Asmussen, C. B., & Møller, C. (2019). Smart literature review: A practical topic modelling approach to exploratory literature review. Journal of Big Data, 6(1), 93. https://doi.org/10.1186/s40537-019-0255-7

  • Assude, T. (2007). Teachers’ practices and degree of ICT integration. In D. Pitta-Pantazi & C. Philippou (Eds.), European research in mathematics education V: Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME5, February 22–26, 2007) (pp. 1339–1348). University of Cyprus; ERME.

  • Bastian, M., Heymann, S., & Jacomy, M. (2009). Gephi: An Open Source Software for Exploring and Manipulating Networks. Proceedings of the International AAAI Conference on Web and Social Media, 3(1), 361–362. https://doi.org/10.1609/icwsm.v3i1.13937

  • Bikner-Ahsbahs, A., & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in mathematics education. Springer International Publishing. https://doi.org/10.1007/978-3-319-05389-9

  • Biton, Y., Hershkovitz, S., & Hoch, M. (2015). Peer learning in mathematics forum on facebook: A case study. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9, February 4 – 8, 2015) (pp. 2473–2479). Charles University in Prague, Faculty of Education and ERME.

  • Bittermann, A., & Fischer, A. (2018). How to identify hot topics in psychology using topic modeling. Zeitschrift Für Psychologie, 226(1), 3–13. https://doi.org/10.1027/2151-2604/a000318

    Article  Google Scholar 

  • Blair, S. J., Bi, Y., & Mulvenna, M. D. (2019). Aggregated topic models for increasing social media topic coherence. Applied Intelligence, 50(1), 138–156. https://doi.org/10.1007/s10489-019-01438-z

    Article  Google Scholar 

  • Blei, D. M. (2012). Probabilistic topic models. Communications of the ACM, 55(4), 77–84. https://doi.org/10.1145/2133806.2133826

    Article  Google Scholar 

  • Blei, D. M., & Lafferty, J. D. (2007). A correlated topic model of science. The Annals of Applied Statistics, 1(1), 17–35. https://doi.org/10.1214/07aoas114

    Article  Google Scholar 

  • Blei, D. M., Ng, A. Y., & Jordan, M. I. (2003). Latent Dirichlet Allocation. Journal of Machine Learning Research, 3, 993–1022.

    Google Scholar 

  • Borba, M. C., Askar, P., Engelbrecht, J., Gadanidis, G., Llinares, S., & Aguilar, M. S. (2017). Digital technology in mathematics education: Research over the last decade. In G. Kaiser (Ed.), Proceedings of the 13th International Congress on Mathematical Education, ICME-13 Monographs (pp. 221–233). Springer International Publishing. https://doi.org/10.1007/978-3-319-62597-3_14

  • Boyd-Graber, J., Hu, Y., & Mimno, D. (2017). Applications of topic models. Foundations and Trends ® in Information Retrieval, 11(2–3), 143–296. https://doi.org/10.1561/1500000030

    Article  Google Scholar 

  • Bray, A., & Tangney, B. (2015). Enhancing student engagement through the affordances of mobile technology: A 21st century learning perspective on realistic mathematics education. Mathematics Education Research Journal, 28(1), 173–197. https://doi.org/10.1007/s13394-015-0158-7

    Article  Google Scholar 

  • Buteau, C., Muller, E., Dreise, K., Mgombelo, J., & Sacristán, A. I. (2019). Students’ process and strategies as they program for mathematical investigations and applications. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6–10, 2019) (pp. 2796–2803). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

  • Chen, X., Zou, D., Cheng, G., & Xie, H. (2020). Detecting latent topics and trends in educational technologies over four decades using structural topic modeling: A retrospective of all volumes of computers & education. Computers & Education, 151, 103855. https://doi.org/10.1016/j.compedu.2020.103855

    Article  Google Scholar 

  • Denny, M. J., & Spirling, A. (2018). Text preprocessing for unsupervised learning: Why it matters, when it misleads, and what to do about it. Political Analysis, 26(2), 168–189. https://doi.org/10.1017/pan.2017.44

    Article  Google Scholar 

  • Emprin, F. (2007). Analysis of teacher education in mathematics and ict. In D. Pitta-Pantazi & C. Philippou (Eds.), European research in mathematics education V: Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME 5, February 22–26, 2007) (pp. 1399–1408). University of Cyprus; ERME.

  • Erren, T. C., Cullen, P., & Erren, M. (2009). How to surf today’s information tsunami: On the craft of effective reading. Medical Hypotheses, 73(3), 278–279. https://doi.org/10.1016/j.mehy.2009.05.002

    Article  Google Scholar 

  • Fabian, K. (2019). Student engagement in mobile learning activities: Breakdowns and breakthroughs. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6–10, 2019) (pp. 2815–2825). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

  • Foster, C., & Inglis, M. (2018). Mathematics teacher professional journals: What topics appear and how has this changed over time? International Journal of Science and Mathematics Education, 17(8), 1627–1648. https://doi.org/10.1007/s10763-018-9937-4

    Article  Google Scholar 

  • Fowler, S., Cutting, C., Kennedy, J., Leonard, S. N., Gabriel, F., & Jaeschke, W. (2021). Technology enhanced learning environments and the potential for enhancing spatial reasoning: A mixed methods study. Mathematics Education Research Journal, 34, 887–910. https://doi.org/10.1007/s13394-021-00368-9

    Article  Google Scholar 

  • Fuglestad, A. B. (2005). Students’ choice of tasks and tools in an ICT rich environment. In M. Bosch (Ed.), European Research in Mathematics Education IV: Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education (CERME 4, February 17 - 21, 2005) (pp. 1000–1009). ERME.

  • Fuglestad, A. B. (2007). Developing tasks and teaching with ICT in mathematics in an inquiry community. In D. Pitta-Pantazi & C. Philippou (Eds.), European Research in Mathematics Education V: Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME 5, February 22 - 26, 2007) (pp. 1409–1418). ERME.

  • Graham, S., Weingart, S., & Milligan, I. (2012). Getting started with topic modeling and MALLET (A. Crymble, Ed.). Programming Historian, 1(1). https://doi.org/10.46430/phen0017

  • Grant, M. J., & Booth, A. (2009). A typology of reviews: An analysis of 14 review types and associated methodologies. Health Information & Libraries Journal, 26(2), 91–108. https://doi.org/10.1111/j.1471-1842.2009.00848.x

    Article  Google Scholar 

  • Griffiths, T. L., & Steyvers, M. (2004). Finding scientific topics. Proceedings of the National Academy of Sciences, 101(1), 5228–5235. https://doi.org/10.1073/pnas.0307752101

    Article  Google Scholar 

  • Herfort, J. D. (forthcoming). Data as catalyst for mathematics teacher collaboration about digital tools [Manuscript in preparation]. Faculty of Science, University of Copenhagen.

  • Herfort, J. D., Tamborg, A. L., Meier, F., Allsopp, B. B., & Misfeldt, M. (2022). Topic model of cerme (Version 4). Zenodo. https://doi.org/10.5281/zenodo.7351992

  • Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education? In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 323–349). Springer Netherlands. https://doi.org/10.1007/978-94-010-02738_11

  • Inglis, M., & Foster, C. (2018). Five decades of mathematics education research. Journal for Research in Mathematics Education, 49(4), 462–500. https://doi.org/10.5951/jresematheduc.49.4.0462

    Article  Google Scholar 

  • Johnstone, W. (1990). The role of computer algebra systems in mathematics teaching at upper secondary school (Doctoral dissertation). Edith Cowan University. https://ro.ecu.edu.au/theses_hons/178

  • Jones, K., Lagrange, J.-B., & Lemut, E. (2002). Tools and technologies in mathematical didactics. In J. Novotná (Ed.), European Research in Mathematics Education II: Proceedings of the Second Conference of the European Society for Research in Mathematics Education (pp. 125–127). Charles University, Faculty of Education; ERME.

  • Khoo, C. S. G., Na, J.-C., & Jaidka, K. (2011). Analysis of the macro-level discourse structure of literature reviews. Online Information Review, 35(2), 255–271. https://doi.org/10.1108/14684521111128032

    Article  Google Scholar 

  • Kissane, B., McConney, A., & Ho, K. F. (2015). Review of the use of technology in mathematics education and the related use of CAS calculators in external examinations and in post school tertiary education settings (tech. rep.). School Curriculum and Standards Authority.

  • Kolovou, A., & Kynigos, C. (2017). Teachers designing e-books to foster creative mathematical thinking: The case of curvature. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1–5, 2017) (pp. 2422–2429). DCU Institute of Education and ERME

  • Kristinsdóttir, B., Hreinsdóttir, F., & Lavicza, Z. (2019). Silent video tasks: Towards a definition. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6–10, 2019) (pp. 2709–2710). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

  • Laborde, C., & Laborde, J.-M. (1995). The case of cabri-géomètre: Learning geometry in a computer based environment. In D. Watson & D. Tinsley (Eds.), Integrating information technology into education (pp. 95–106). Springer US. https://doi.org/10.1007/978-0-387-34842-1_10

  • Lagrange, J.-B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Second international handbook of mathematics education (pp. 237–269). Springer Netherlands. https://doi.org/10.1007/978-94-010-0273-8_9

  • Lau, J. H., Newman, D., & Baldwin, T. (2014). Machine reading tea leaves: Automatically evaluating topic coherence and topic model quality. In S. Wintner, S. Goldwater, & S. Riezler (Eds.), Proceedings of the 14th conference of the european chapter of the association for computational linguistics (pp. 530–539). Association for Computational Linguistics, Gothenburg, Sweden

  • Lavicza, Z., Juhos, I., Koren, B., Fenyvesi, K., Csapodi, C., Kis, M., & Mantecón, J.-D. (2015). Integrating technology into primary and secondary school teaching to enhance mathematics education in Hungary. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9, February 4–8, 2015) (pp. 2430–2431). Charles University in Prague, Faculty of Education and ERME.

  • Lim, K. W., & Buntine, W. (2014). Twitter opinion topic model. Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management, 1319–1328. https://doi.org/10.1145/2661829.2662005

  • Maier, D., Niekler, A., Wiedemann, G., & Stoltenberg, D. (2020). How document sampling and vocabulary pruning affect the results of topic models. Computational Communication Research, 2(2), 139–152. https://doi.org/10.5117/ccr2020.2.001.maie

    Article  Google Scholar 

  • Maier, D., Waldherr, A., Miltner, P., Wiedemann, G., Niekler, A., Keinert, A., Pfetsch, B., Heyer, G., Reber, U., Häussler, T., Schmid-Petri, H., & Adam, S. (2018). Applying LDA topic modeling in communication research: Toward a valid and reliable methodology. Communication Methods and Measures, 12(2–3), 93–118. https://doi.org/10.1080/19312458.2018.1430754

    Article  Google Scholar 

  • Mann, H. B. (1945). Nonparametric tests against trend. Econometrica, 13(3), 245. https://doi.org/10.2307/1907187

    Article  Google Scholar 

  • Marks, R., Foster, C., Barclay, N., Barnes, A., & Treacy, P. (2020). A comparative synthesis of UK mathematics education research: What are we talking about and do we align with international discourse? Research in Mathematics Education, 23(1), 39–62. https://doi.org/10.1080/14794802.2020.1725612

    Article  Google Scholar 

  • McCallum, A. K. (2002). Mallet: A machine learning for language toolkit. http://www.cs.umass.edu/mccallum/mallet

  • Mimno, D. (2012). Computational historiography. Journal on Computing and Cultural Heritage, 5(1), 1–19. https://doi.org/10.1145/2160165.2160168

    Article  Google Scholar 

  • Mimno, D., Wallach, H., Talley, E., Leenders, M., & McCallum, A. (2011). Optimizing semantic coherence in topic models. Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processing, 262–272. https://aclanthology.org/D11-1024

  • Papadopoulos, I., Diamantidis, D., & Kynigos, C. (2017). Meaning-generation through an interplay between problem solving and constructionism in the c-book technology environment. In T. Dooley & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1–5, 2017) (pp. 2619–2626). DCU Institute of Education and ERME

  • Papert, S. (1982). Mindstorms. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-5357-6

    Article  Google Scholar 

  • Paul, M., & Girju, R. (2009). Topic modeling of research fields: An interdisciplinary perspective. Proceedings of the International Conference RANLP-2009, 337–342. https://aclanthology.org/R09-1061

  • Quinn, K. M., Monroe, B. L., Colaresi, M., Crespin, M. H., & Radev, D. R. (2010). How to analyze political attention with minimal assumptions and costs. American Journal of Political Science, 54(1), 209–228. https://doi.org/10.1111/j.1540-5907.2009.00427.x

    Article  Google Scholar 

  • Ramage, D., Rosen, E., Chuang, J., Manning, C. D., & McFarland, D. A. (2009). Topic modeling for the social sciences. In Y. Bengio, D. Schuurmans, J. Lafferty, C. Williams, & A. Culotta (Eds.), Advances in neural information processing systems (nips): Workshop on applications for topic models: Text and beyond (Vol. 5, pp. 1–4). Stanford University.

  • Roberts, D. L., Leung, A. Y. L., & Lins, A. F. (2012). From the slate to the web: Technology in the mathematics curriculum. Third international handbook of mathematics education (pp. 525–547). Springer. https://doi.org/10.1007/978-1-4614-4684-2_17

  • Roberts, M. E., Stewart, B. M., Tingley, D., Lucas, C., Leder-Luis, J., Gadarian, S. K., Albertson, B., & Rand, D. G. (2014). Structural topic models for open-ended survey responses. American Journal of Political Science, 58(4), 1064–1082. https://doi.org/10.1111/ajps.12103

    Article  Google Scholar 

  • Ronau, R. N., Rakes, C. R., Bush, S. B., Driskell, S. O., Niess, M. L., & Pugalee, D. K. (2014). A survey of mathematics education technology dissertation scope and quality. American Educational Research Journal, 51(5), 974–1006. https://doi.org/10.3102/0002831214531813

    Article  Google Scholar 

  • Routitsky, A., & Tobin, P. (2001). Graphics calculators use in mathematics victorian secondary schools. In J. Novotná (Ed.), European Research in Mathematics Education II: Proceedings of the Second Conference of the European Society for Research in Mathematics Education (pp. 227–240). Charles University, Faculty of Education; ERME.

  • Schofield, A., Magnusson, M., & Mimno, D. (2017). Pulling out the stops: Rethinking stopword removal for topic models. Proceedings of the 15th Conference of the European Chapter of the Association for Computational Linguistics: Volume 2, Short Papers, 432–436. https://doi.org/10.18653/v1/e17-2069

  • Schofield, A., & Mimno, D. (2016). Comparing apples to apple: The effects of stemmers on topic models. Transactions of the Association for Computational Linguistics, 4, 287–300. https://doi.org/10.1162/tacl_a_00099

    Article  Google Scholar 

  • Schofield, A., Thompson, L., & Mimno, D. (2017). Quantifying the effects of text duplication on semantic models. Proceedings of the 2017b Conference on Empirical Methods in Natural Language Processing, 2737–2747. https://doi.org/10.18653/v1/d17-1290

  • Sievert, C., & Shirley, K. (2014). LDAvis: A method for visualizing and interpreting topics. Proceedings of the Workshop on Interactive Language Learning, Visualization, and Interfaces, 63–70. https://doi.org/10.3115/v1/w14-3110

  • Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014). Dropout: A simple way to prevent neural networks from overfitting. The Journal of Machine Learning Research, 15(1), 1929–1958.

    Google Scholar 

  • Tapan, S. (2003). Integration of ICT in the teaching of mathematics in situations for treatment of difficulties in proving. In M. A. Mariotti (Ed.), European research in mathematics education III: Proceedings of the Third Conference of the European Society for Research in Mathematics Education (CERME3, February 28–March 3, 2003) (pp. 1–8). University of Pisa; ERME.

  • Trgalova, J., Fuglestad, A. B., Maracci, M., & Weigand, H.-G. (2011). Introduction to the papers of wg15. In M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (CERME7, February 9–13, 2011) (pp. 2144–2147). University of Rzeszów; ERME.

  • Trgalová, J., Clark-Wilson, A., & Weigand, H.-G. (2018, April). Developing research in mathematics education. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven (Eds.), Developing research in mathematics education. Routledge. https://doi.org/10.4324/9781315113562

  • Ulm, V. (2010). Systemic innovations of mathematics education with dynamic worksheets as catalysts. In V. Durand-Guerrier, S. Soury-Lavergne, & F. Arzarello (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (CERME6, January 28–February 1, 2009) (pp. 1280–1289). Institut National de Recherche Pédagogique; ERME.

  • Vega-Carrasco, M., O’Sullivan, J., Prior, R., Manolopoulou, I., & Musolesi, M. (2020). Modelling grocery retail topic distributions: Evaluation, interpretability and stability. arXiv preprint arXiv:2005.10125. https://doi.org/10.48550/ARXIV.2005.10125

  • Wallach, H. M., Murray, I., Salakhutdinov, R., & Mimno, D. (2009). Evaluation methods for topic models. Proceedings of the 26th Annual International Conference on Machine Learning – ICML, 09, 1105–1112. https://doi.org/10.1145/1553374.1553515

    Article  Google Scholar 

  • Williams, J., & Goos, M. (2012). Modelling with mathematics and technologies. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 549–569). Springer. https://doi.org/10.1007/978-1-4614-4684-2_18

  • Wörler, J. F. (2019). How to distinguish simulations? development of a classification scheme for digital simulations for teaching and learning mathematics. In U. T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6–10, 2019) (pp. 2757–2764). Freudenthal Group & Freudenthal Institute, Utrecht University and ERME.

  • Zbiek, R. M., Heid, M. K., Blume, G. W., & Dick, T. P. (2007). Research on technology in mathematics education: A perspective of constructs. In K. Lester Frank (Ed.), Second handbook of research on mathematics teaching and learning: A project of the national council of teachers of mathematics (pp. 1169–1207). IAP.

Download references

Author information

Authors and Affiliations

  1. University of Copenhagen, Copenhagen, Denmark

    Jonas Dreyøe Herfort, Andreas Lindenskov Tamborg & Morten Misfeldt

  2. Aalborg University, Copenhagen, Denmark

    Florian Meier & Benjamin Brink Allsopp

Authors
  1. Jonas Dreyøe Herfort
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Lindenskov Tamborg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Florian Meier
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benjamin Brink Allsopp
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Morten Misfeldt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonas Dreyøe Herfort.

Ethics declarations

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Herfort, J.D., Tamborg, A.L., Meier, F. et al. Twenty years of research on technology in mathematics education at CERME: a literature review based on a data science approach. Educ Stud Math 112, 309–336 (2023). https://doi.org/10.1007/s10649-022-10202-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-022-10202-z

Keywords

Search

Navigation