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Can digital technology change the way mathematics skills are assessed?

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Abstract

Formative assessment strategies have been studied for a long time. Drawing on data from the FaSMEd (Formative Assessment in Science and Mathematics Education) project, this paper has the aim of contributing to research about formative assessment and the use of technology, in the field of mathematics education, by claiming that digital technology does modify classroom assessment processes when mastered by teachers, especially regarding the implementation of formative assessment strategies, but also by discussing how and to what extent this occurs, taking into account the different perspectives of the actors involved. The methodology of this research is founded in the design-based research paradigm, and the work with teachers is detailed in order to show the contributions of the project both in providing research results and in examples of practical use in the mathematics classroom.

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Notes

  1. The research leading to these results received funding from the European Community’s Seventh Framework Programme fp7/2007–2013 under grant agreement No [612337].

  2. https://research.ncl.ac.uk/fasmed/deliverables/.

References

  • Achiam, M., Sølberg, J., & Evans, R. (2013). Dragons and dinosaurs: directing inquiry in biology using the notions of ‘milieu’ and ‘validation’. Journal of Biological Education, 47(1), 39–45.

    Article  Google Scholar 

  • Ainley, J., & Margolinas, C. (2015). Accounting for student perspectives in task design. Task design in mathematics education, (pp. 115–141). Cham: Springer.

  • Aldon, G., & Panero, M. (2016). Une classe tablette en mathématiques, Mathematice, 50. Available at: https://revue.sesamath.net/spip.php?article857 (consulted on 13.04.20).

  • Aldon, G., Cusi, A., Morselli, F., Panero, M., & Sabena, C. (2017). Formative assessment and technology: Reflections developed through the collaboration between teachers and researchers. In G. Aldon, F. Hitt, L. Bazzini, & U. Gellert (Eds.), Mathematics and technology. Advances in mathematics education (pp. 551–578). Cham: Springer.

    Google Scholar 

  • Allal, L., & Lopez, L. M. (2005). Formative assessment of learning: A review of publications in French. In Centre for Educational Research and Innovation (Ed.), Formative assessment: Improving learning in secondary classrooms (pp. 241–264). Paris: OECD Publishing

  • Artigue, M. (2002). Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7(3), 245.

    Article  Google Scholar 

  • Artigue, M. (2009). Didactical design in mathematics education. In Nordic research in mathematics education (pp. 5–16). Leiden: Brill Sense.

  • Artigue, M., Haspekian, M., & Corblin-Lenfant, A. (2014). Introduction to the theory of didactical situations (TDS). In Networking of theories as a research practice in mathematics education (pp. 47–65). Springer, Cham.

  • Beatty, I. D., & Gerace, W. J. (2009). Technology-enhanced formative assessment: A research-based pedagogy for teaching science with classroom response technology. Journal of Science Education and Technology, 18(2), 146–162.

    Article  Google Scholar 

  • Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—An approach for exploiting the diversity of theoretical approaches. In B. Sriraman & L. English (Eds.), Theories of mathematics education. Advances in mathematics education. Berlin: Springer.

    Google Scholar 

  • Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational assessment, Evaluation and Accountability, 21(1), 5–31.

    Article  Google Scholar 

  • Bloch, I. (1999). L'articulation du travail mathématique du professeur et de l'élève dans l'enseignement de l'analyse en première scientifique. Recherches en Didactique des Mathématiques, 19(2), 135–194.

    Google Scholar 

  • Bloch, I., & Gibel, P. (2011). Un modèle d'analyse des raisonnements dans les situations didactiques. Étude des niveaux de preuves dans une situation d'enseignement de la notion de limite. Recherches en didactique des mathématiques, 31(2), 191–228.

    Google Scholar 

  • Brousseau, G. (1986). Théorisation des phénomènes d'enseignement des mathématiques. Thèse de l'Université de Bordeaux 1.

  • Brousseau, G. (1997) "Theory of Didactical situations in Mathematics". Recueil de textes de Didactique des mathématiques 1970–1990, traduction M. Cooper and N. Balacheff, R. Sutherland and V. Warfield. Dordrecht: Kluwer.

  • Brousseau, G. (2006). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (Vol. 19). Dordrecht: Springer Science and Business Media.

    Google Scholar 

  • Brousseau, G. (2010). Glossary of terms used in Didactique, online: https://faculty.washington.edu/warfield/guy-brousseau.com/biographie/glossaires/GLOSSARY_Eng.doc

  • Burns, M. (2017). Formative tech: Meaningful, sustainable, and scalable formative assessment with technology. New York: Corwin Press.

    Book  Google Scholar 

  • Buteau, C., Muller, E., Mgombelo, J., & Sacristán, A. I. (2019, July). Stages of students’ instrumental genesis of programming for mathematical investigations. In 43rd Annual Meeting of the International Group for the Psychology of Mathematics Education (vol. 4). Oral Communications and Poster.

  • Cerratto Pargman, T., Nouri, J., & Milrad, M. (2018). Taking an instrumental genesis lens: New insights into collaborative mobile learning. British Journal of Educational Technology, 49(2), 219–234.

    Article  Google Scholar 

  • Cusi, A., Morselli, F., & Sabena, C. (2017). Promoting formative assessment in a connected classroom environment: Design and implementation of digital resources. ZDM The International Journal on Mathematics Education, 49, 755–767.

    Article  Google Scholar 

  • Dunn, K. E., & Mulvenon, S. W. (2009). A critical review of research on formative assessment: The limited scientific evidence of the impact of formative assessment in education. Practical Assessment, Research and Evaluation, 14(7), 1–11.

    Google Scholar 

  • Kidron, I., Artigue, M., Bosch, M., Dreyfus, T., & Haspekian, M. (2014). Context, milieu, and media-milieus dialectic: A case study on networking of AiC, TDS, and ATD. Networking of theories as a research practice in mathematics education (pp. 153–177). Cham: Springer.

    Chapter  Google Scholar 

  • Lee, H., Feldman, A., & Beatty, I. D. (2012). Factors that affect science and mathematics teachers’ initial implementation of technology-enhanced formative assessment using a classroom response system. Journal of Science Education and Technology, 21(5), 523–539.

    Article  Google Scholar 

  • Määttänen, P. (2016). The concept of the scheme in the activity theories of Ilyenkov and Piaget. The Practical Essence of Man (pp. 154–166). Brill: Leiden.

    Google Scholar 

  • Margolinas, C. (1995). La structuration du milieu et ses apports dans l'analyse a posteriori des situations. Les débats de didactique des mathématiques, 89–102.

  • Margolinas, C., Coulange, L., & Bessot, A. (2005). What can the teacher learn in the classroom?. In Beyond the Apparent Banality of the Mathematics Classroom (pp. 205–234). Boston: Springer.

  • C Margolinas 2004 Points de vue de l'élève et du professeurHabilitation à diriger des recherches de l'Université de Provence-Aix-Marseille I Essai de développement de la théorie des situations didactiques

  • Panero, M., & Aldon, G. (2016). How teachers evolve their formative assessment practices when digital tools are involved in the classroom. Digital Experiences in Mathematics Education, 2(1), 70–86.

    Article  Google Scholar 

  • Pape, S., Irving, K., Owens, D., Boscardin, C., Sanalan, V., Abrahamson, L., et al. (2013). Classroom connectivity in Algebra I classrooms: Results of a randomized control trial. Effective Education, 4(2), 169–189.

    Article  Google Scholar 

  • Perrin-Glorian, M. J. (March). From producing optimal teaching to analysing usual classroom situations. Development of a fundamental concept in the theory of didactic situations: the notion of milieu. The first century of the International Commission on Mathematical Instruction (1908–2008), March 2008, Rome, Italy. Abstract page 308. hal-01660872

  • Rabardel, P. (1995). Les hommes et les technologies; Approche cognitive des instruments contemporains. Paris: Armand Colin.

    Google Scholar 

  • Rabardel, P. (1999). Eléments pour une approche instrumentale en didactique des mathématiques. Actes de l'école d'été de didactique des mathématiques, 18(21), 203–213.

    Google Scholar 

  • Roorda, G., Vos, P., Drijvers, P., & Goedhart, M. (2016). Solving rate of change tasks with a graphing calculator: A case study on instrumental genesis. Digital Experiences in Mathematics Education, 2(3), 228–252.

    Article  Google Scholar 

  • Roschelle, J., & Pea, R. (2002). A walk on the WILD side: How wireless handhelds may change computer-supported collaborative learning. International Journal of Cognition and Technology, 1(1), 145–168.

    Article  Google Scholar 

  • Ruchniewicz, H., & Barzel, B. (2019). Technology supporting students’ self assessment in the field of functions: A design based research study. In G. Aldon & J. Trgalova (Eds.), Technology in mathematics education (pp. 49–74). Cham: Springer.

    Google Scholar 

  • Sensevy, G. (2012). About the joint action theory in didactics. Zeitschrift für Erziehungswissenschaft, 15(3), 503–516.

    Article  Google Scholar 

  • Spector, J. M., Ifenthaler, D., Samspon, D., Yang, L., Mukama, E., Warusavitarana, A., et al. (2016). Technology enhanced formative assessment for 21st century learning. Educational Technology & Society, 19(3), 58–71.

    Google Scholar 

  • Stroup, W., Kaput, J. J., Ares, N., Wilensky, U., Hegedus, S. Roschelle, J., Mack, A., Davis, S.M., & Hurford, A. (2002). The nature and future of classroom connectivity: The dialectics of mathematics in the social space (pp. 195–203). Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education—North American Chapter, Athens, Georgia.

  • Swan, M. (2014). Design research in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 148–151). Dordrecht: Springer.

    Google Scholar 

  • Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized learning environments: guiding students’ command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281–307.

    Article  Google Scholar 

  • Vergnaud, G. (2009). The theory of conceptual fields. Human Development, 52(2), 83–94.

    Article  Google Scholar 

  • Vergnaud, G. (2016). Forme opératoire et forme prédicative de la connaissance. Investigações em Ensino de Ciências, 17(2), 287–304.

    Google Scholar 

  • Wang, F., & Hannafin, M. J. (2005). Design-based research and technology-enhanced learning environments. Educational Technology Research and Development, 53(4), 5–23.

    Article  Google Scholar 

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Aldon, G., Panero, M. Can digital technology change the way mathematics skills are assessed?. ZDM Mathematics Education 52, 1333–1348 (2020). https://doi.org/10.1007/s11858-020-01172-8

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