Abstract
The automated digital diagnostic assessment presented in this paper concerns the elementary algebra for students of secondary education (12–16 years) in France. The paper addresses the design of tasks for the test “Pépite ”, to favour students’ algebraic thinking. The selection of the tasks and the analysis of students’ responses are based on an epistemological reference of the algebraic domain. The information provided by “Pepite” enables identification of students’ consistent reasoning and calculation and assists teachers’ planning for differentiated instruction for groups of students. The paper reports some results on the integration of the tools in the usual teaching practices and on students’ learning, based on trialling with a group of teachers.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Pépite tools are available on LaboMep platform, developed by Sésamath, a French maths’ teachers association (http://www.labomep.net/) and on WIMS environment (an educational online learning platform spanning learning from primary school to the university in many disciplines).
- 2.
Praxeology originates from two Greek words praxis and logos.
- 3.
Contrary to usual practices in assessment , we do not attribute a code by technique for each task. This would lead to a multiplicity of codes on various tasks and would be unusable for a cross analysis on all the tasks of the test.
- 4.
Most of the non-coded answers are those in which the student uses natural language together with algebraic expressions, which disrupts the analysis; some are not coded because they are not predicted in the preliminary analysis of the answers. The basis of answers is regularly updated.
References
Artigue, M., Grugeon, B., Assude, T. & Lenfant, A. (2001). Teaching and learning algebra: Approaching complexity trough complementary perspectives. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The Future of the Teaching and Learning of Algebra, Proceedings of 12 th ICMI Study Conference, The University of Melbourne, Australia, December 9–14, 2001.
Bedja, S. (2016). Parcours différenciés d’apprentissage en algèbre élémentaire dans des systèmes de ressources en ligne: De l’usage des ressources par des communautés d’enseignants à leur évolution. Thèse de doctorat, université Paris Diderot.
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy and Practice, 5(1), 7–73.
Bolon, J. (2002). Pédagogie différenciée en mathématiques: Mission impossible ou défi? Grand N. Num, 69, 63–82 (IREM de Grenoble).
Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (ICME12) (pp. 51–69). Seoul, Korea, July 8–15, 2012.
Chevallard, Y. (1984). Le passage de l’arithmétique à l’algèbre dans l’enseignement des mathématiques au collège. Première partie. L’évolution de la transposition didactique. Petit x, 5, 51–94.
Chevallard, Y. (1989). Le passage de l’arithmétique à l’algébrique dans l’enseignement des mathématiques au collège—Deuxième partie: Perspectives curriculaires: La notion de madélisation. Petit x, 19, 43–72.
Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221–265.
Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the IV Congress of the European Society for Research in Mathematics Education (pp. 21–30). Barcelona, Spain: FUNDEMI-IQS.
Chenevotot-Quentin, F., Grugeon-Allys, B., Pilet, J., Delozanne, E., & Prévit, D. (2016). The diagnostic assessment Pépite and the question of its transfer at different school levels. In Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education CERME9 (pp. 2326–2332). Prague, République Tchèque, 4 au 8 février 2015.
Delozanne, É, Prévit, D., Grugeon, B., & Chenevotot, F. (2008). Automatic multi-criteria assessment of open-ended questions: A case study in school algebra. In Proceedings of ITS’2008, Montréal (pp. 101–110). LNCS 5091, Springer, June 2008.
Delozanne, E., Prévit D., Grugeon-Allys, B., & Chenevotot-Quentin, F. (2010), Vers un modèle de diagnostic de compétence. Revue Techniques et Sciences Informatiques, 29, 8–9 (Hermes-Lavoisier, Paris, pp. 899–938).
Douady, R. (1985). The interplay between different settings: Tool-object dialectic in the extension of mathematical ability—Examples from elementary school teaching. In International Conference of Psychology of Mathematics Education (PME) (pp. 33–52). Utrecht.
Garcia, F. J., Gascon, J., Higueras, L. R., & Bosch, M. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM Mathematics Education, 38(3), 226–246.
Grapin, N. (2015). Étude de la validité de dispositifs d’évaluation et conception d’un modèle d’analyse multidimensionnelle des connaissances numériques des élèves de fin d’école. Thèse de doctorat, université Paris Diderot.
Grugeon-Allys, B. (2015). Réguler l’enseignement en algèbre élémentaire: Une approche multidimensionnelle. D. A. C. Mathé & E. Mounier (Eds.), Actes du séminaire national de Didactique des mathématiques 2015. Paris, France: IREM Paris 7.
Grugeon-Allys, B., Pilet, J., Chenevotot-Quentin, F., & Delozanne, E. (2012). Diagnostic et parcours différenciés d’enseignement en algèbre élémentaire. In L. Coulange, J. P. Drouhard, J. L. Dorier, & A. Robert (Eds.), Recherche en Didactique des Mathématiques Enseignement de l’algèbre élémentaire, Bilan et perspectives Hors-série (pp. 137–162). Grenoble: La pensée sauvage.
Kahn, C. (2007). Pédagogie différenciée. Bruxelles: De Boeck.
Ketterlin-Geller, L. R., & Yovanoff, P. (2009). Diagnostic assessment in mathematics to support instructional decision making. Practical Assessment Research & Education, 14(16).
Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester (Eds.), Second handbook of research on mathematics teaching and learning (Chapter 16, pp. 707–762).
Pilet, J. (2012). Parcours d’enseignement différencié appuyés sur un diagnostic en algèbre élémentaire à fin de la scolarité obligatoire: Modélisation, implémentation dans une plateforme en ligne et évaluation (Thèse de doctorat). Université Paris-Diderot. Available online http://tel.archives-ouvertes.fr/tel-00784039.
Pilet, J. (2015). Réguler l’enseignement en algèbre élémentaire par des parcours d’enseignement différencié. Recherches en didactique des mathématiques, 35(3), 273–312.
Pilet, J. Chenevotot, F., Grugeon, B., El-Kechaï, N., & Delozanne, E. (2013). Bridging diagnosis and learning of elementary algebra using technologies. In Proceedings of the Eighth Congress of the European society for Research in Mathematics Education. CERME 8. Antalaya, Turquie, 6 au 10 février 2013. 10 p.
Ruiz-Munzón, N., Matheron, Y., Bosch, M., & Gascón, J. (2012). Autour de l’algèbre: les entiers relatifs et la modélisation algébrico-fonctionnelle. In L. Coulange, & J. P. Drouhard (Eds.), Enseignement de l’algèbre élémentaire. Bilan et perspectives, Recherches en didactique de mathématiques. Grenoble: La Pensée Sauvage.
Sirejacob, S. (2016). Les organisation de savoirs mathématiques à enseigner: Les équations au college. Petit x, 102, 27–55.
Sirejacob, S., Chenevotot-Quentin, F., & Grugeon-Allys, B. (to coming) Pépite online automated assessment and student learning: The domain of equations for grade 8th. In Proceedings of the Tenth Congress of the European society for Research in Mathematics Education CERME10. Dublin, Irlande, 1er au 5 février 2017.
Vergnaud, G. (1986). Psychologie du développement cognitif et didactique des mathématiques. Un exemple: Les structures additives. Petit x, 22, 51–69.
Wiliam, D., & Thompson, M. (2007). Integrating assessment with learning: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–82). Mahwah, NJ: Erlbaum.
Acknowledgement
We warmly thank Elisabeth Delozanne for her valuable contribution to the project.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Grugeon-Allys, B., Chenevotot-Quentin, F., Pilet, J., Prévit, D. (2018). Online Automated Assessment and Student Learning: The PEPITE Project in Elementary Algebra. In: Ball, L., Drijvers, P., Ladel, S., Siller, HS., Tabach, M., Vale, C. (eds) Uses of Technology in Primary and Secondary Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-76575-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-319-76575-4_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76574-7
Online ISBN: 978-3-319-76575-4
eBook Packages: EducationEducation (R0)