Main Article Content

Abstract

Digital task design is an important issue when integrating technology into mathematics education. However, existing frameworks often are not fine-grained enough for supporting teachers in designing tasks or they only focus on geometric topics. In this paper, we share a case study as the first cycle of our design-based research study that aims to extend and adapt the well-known Dynamic Geometry Task Analysis framework for analyzing further digital materials. The adapted framework is named Digital Task Analysis (DTA) model and can be utilized to analyze, modify, and design digital materials from other mathematical topics. The model focuses on supporting teachers in integrating two essential aspects within digital materials, namely creating cognitively stimulating tasks and exploiting added value of technology. In this paper, we present the first analyses of three cases representing digital materials including visualizations addressing lower secondary mathematics following the DTA model. The results show that the presented DTA model is suitable to analyze such digital materials and has the potential to support teachers in designing, assessing, and modifying digital tasks that support learners in focusing their attention on mathematically relevant aspects of digital resources, and in deepening their awareness of how to formulate targeted tasks for learners.

Keywords

Digital Materials Lower Secondary Education Mathematics Education Task Quality

Article Details

How to Cite
Lindenbauer, E., Infanger, E.-M., & Lavicza, Z. (2023). Developing the Digital Task Analysis (DTA) framework to enable the assessment and redesign of digital resources in mathematics education. Journal on Mathematics Education, 14(3), 483–502. https://doi.org/10.22342/jme.v14i3.pp483-502

References

  1. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241.
  2. Ball, L., & Stacey, K. (2019). Technology-supported classrooms: New opportunities for communication and development of mathematical understanding. In A. Büchter, M. Glade, R. Herold-Blasius, M. Klinger, F. Schacht, & P. Scherer. (Eds) Vielfältige Zugänge zum Mathematikunterricht (pp. 121-129). Springer Fachmedien Wiesbaden. https://doi.org/10.1007/978-3-658-24292-3_9
  3. Biesta, G. J. J., & Burbules, N. C. (2004). Pragmatism and educational research. Rowman & Littlefield.
  4. Borba, M. C. (2021). The future of mathematics education since COVID-19: humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics, 108, 385-400.
  5. Bozkurt, G., & Yiğit Koyunkaya, M. (2022). Supporting prospective mathematics teachers’ planning and teaching technology-based tasks in the context of a practicum course. Teaching and Teacher Education, 119, 103830. https://doi.org/10.1016/j.tate.2022.103830
  6. Bruner, J. S., Oliver, R. S., & Greenfield, P. M. (1971). Studien zur kognitiven Entwicklung. Kohlhammer.
  7. Büchter, A., & Leuders, T. (2009). Mathematikaufgaben selbst entwickeln: Lernen fördern - Leistung überprüfen (4th ed.). Cornelsen Scriptor.
  8. Bundesministerium für Unterricht und Kunst. (2021). Gesamte Rechtsvorschrift für Lehrpläne -- allgemeinbildende höhere Schulen. https://www.ris.bka.gv.at/GeltendeFassung.wxe?Abfrage=Bundesnormen&Gesetzesnummer=10008568
  9. Clark-Wilson, A., & Hoyles, C. (2017). Dynamic digital technologies for dynamic mathematics: Implications for teachers’ knowledge and practice (Issue April). UCL Institute of Education Press, University College.
  10. Clark-Wilson, A., Robutti, O., & Thomas, M. (2020). Teaching with technology. ZDM Mathematics Education, 52(7), 1223–1242. https://doi.org/10.1007/s11858-020-01196-0
  11. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13. https://doi.org/10.3102/0013189X032001009
  12. Dick, T. P. (2008). Keeping the faith: Fidelity in technological tools for mathematics education. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 2. Cases and perspectives (pp. 333–339). Information Age.
  13. Donevska-Todorova, A., Trgalová, J., Schreiber, C., & Rojano, T. (2021). Quality of task design in technology-enhanced resources for teaching and learning mathematics. In A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalova, & H.-G. Weigand (Eds.), Mathematics Education in the Digital Age (pp. 23–41). Routledge. https://doi.org/10.4324/9781003137580-3
  14. Drijvers, P. (2015). Digital technology in mathematics education: Why it works (or doesn’t). In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 135–151). Springer International Publishing. https://doi.org/10.1007/978-3-319-17187-6_8
  15. Drijvers, P. (2018). Tools and taxonomies: A response to Hoyles. Research in Mathematics Education, 20(3), 229–235. https://doi.org/10.1080/14794802.2018.1522269
  16. Drijvers, P., Ball, L., Barzel, B., Heid, M. K., Cao, Y., & Maschietto, M. (2016). Uses of technology in lower secondary mathematics education. Springer International Publishing.
  17. Drijvers, P., Boon, P., & Van Reeuwijk, M. (2011). Algebra and technology. In P. Drijvers (Ed.), Secondary algebra education. Revisiting topics and themes and exploring the unknown (pp. 179–202). Sense.
  18. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103–131.
  19. Fahlgren, M., Szabo, A., & Vinerean, M. (2022). Prospective teachers designing tasks for dynamic geometry environments. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 2526–2533). Free University of Bozen-Bolzano and ERME. https://hal.science/hal-03747493/
  20. Gueudet, G., & Trouche, L. (2009). Towards new documentation systems for mathematics teachers? Educational Studies in Mathematics, 71(3), 199–218. https://doi.org/10.1007/s10649-008-9159-8
  21. Hughes, J., Thomas, R., & Scharber, C. (2006). Assessing technology integration: The RAT - replacement, amplification, and transformation - framework. In C. Crawford, R. Carlsen, K. McFerrin, J. Price, R. Weber, & D. Willis (Eds.), Proceedings of SITE 2006 - Society for Information Technology & Teacher Education International Conference (pp. 1616–1620). Association for the Advancement of Computing in Education. http://www.editlib.org/p/22293/
  22. Kimeswenger, B. (2017). Identifying and assessing quality of dynamic materials for teaching mathematics [Doctoral dissertation, Johannes Kepler Universität Linz]. https://epub.jku.at/obvulihs/content/titleinfo/2581881
  23. Leacock, T. L., & Nesbit, J. C. (2007). A framework for evaluating the quality of multimedia learning resources. Journal of Educational Technology & Society, 10(2), 44–59.
  24. Lindenbauer, E. (2018). Students’ conceptions and effects of dynamic materials regarding functional thinking [Doctoral dissertation, Johannes Kepler Universität Linz]. https://epub.jku.at/obvulihs/content/titleinfo/3548223
  25. Lindenbauer, E. (2020). Interactive worksheets assisting students’ functional thinking conceptions in lower secondary education. Mathematica Didactica, 43(1), 1-23.
  26. Lindenbauer, E., Lavicza, Z., & Weinhandl, R. (2022). Initiating the development of a pre-service teacher training course based on research on students’ digital resource and teaching designs. In J. Hodgen, E. Geraniou, G. Bolondi, & F. Ferretti (Eds.), Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME12) (pp. 2570–2577). Free University of Bozen-Bolzano and ERME. https://hal.archives-ouvertes.fr/hal-03747531
  27. McCulloch, A., Leatham, K., Bailey, N., Cayton, C., Fye, K., & Lovett, J. (2021). Theoretically framing the pedagogy of learning to teach mathematics with technology. Contemporary Issues in Teacher Education, 21(2), 325–359.
  28. Roth, J. (2017). Computer einsetzen: Wozu, wann, wer & wie? Mathematik lehren, 205, 35–38.
  29. Sherman, M., & Cayton, C. (2015). Using appropriate tools strategically for instruction. The Mathematics Teacher, 109(4), 306–310. https://doi.org/10.5951/mathteacher.109.4.0306
  30. Sinclair, M. P. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289–317. https://doi.org/10.1023/A:1024305603330
  31. Smith, M. S., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350.
  32. Stake, R. E. (1995). The art of case study research. Sage Publications.
  33. Thomas, A., & Edson, A. J. (2019). A framework for teachers’ evaluation of digital instructional materials: Integrating mathematics teaching practices with technology use in K-8 classrooms. Contemporary Issues in Technology and Teacher Education, 19(3), 351–372. https://citejournal.org/volume-19/issue-3-19/mathematics/a-framework-for-teachers-evaluation-of-digital-instructional-materials-integrating-mathematics-teaching-practices-with-technology-use-in-k-8-classrooms/
  34. Trgalova, J., & Jahn, A. P. (2013). Quality issue in the design and use of resources by mathematics teachers. ZDM Mathematics Education, 45(7), 973–986. https://doi.org/10.1007/s11858-013-0525-3
  35. Trocki, A. (2014). Evaluating and writing dynamic geometry tasks. The Mathematics Teacher, 107(9), 701–705. https://doi.org/10.5951/mathteacher.107.9.0701
  36. Trocki, A. (2015). Designing and examining the effects of a dynamic geometry task analysis framework on teachers’ written Geometer’s Sketchpad tasks. Raleigh: North Carolina State University. Unpublished doctoral dissertation.
  37. Trocki, A., & Hollebrands, K. (2018). The development of a framework for assessing dynamic geometry task quality. Digital Experiences in Mathematics Education, 4(2–3), 110–138. https://doi.org/10.1007/s40751-018-0041-8
  38. Watson, A, & Ohtani, M. (2015). Themes and issues in mathematics education concerning task design. In: A. Watson, & M. Ohtani (Eds.), Task design in mathematics education: An ICMI study (pp. 3–15). Springer.
  39. Yin, R. K. (2009). Case study research: Design and methods (4th ed.). Sage Publications.

Most read articles by the same author(s)