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The ‘Resource’ Approach to Mathematics Education pp 257–321Cite as

Analyzing Teachers’ Work with Resources: Methodological Issues

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Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Studying teachers’ work with resources leads to wide-ranging research questions requiring diverse theoretical frameworks and, consequently, various methodologies. Characterizing the dialectical relation between theoretical and methodological choices is critical. Teachers’ work with resources and professional development appear intertwined, opening new avenues for research and methodological developments. After developing the main methodological issues raised in Re(s)sources International Conference, four texts illustrate research that challenge these issues. Rocha studies the long-term evolution of interactions between teachers and resources. She proposes two new notions—documentational trajectory and documentational experience—and develops methodologies adapted to their study. Glasnović Gracin and Courtney present contrasting studies on teachers’ work with resources, concerning lesson planning from two distinct countries (Croatia and the USA). They develop a methodology aimed at expounding on what occurs within teachers’ resource systems in different environments. Aldon, Front, and Gardes study proximity between teacher’s intentions and those of resource designers. They present a method of collaborative design and define an indicator of convergence to analyze the conjunction between intentions of the resources’ authors and teacher’s classroom achievement. Taranto, Arzarello, and Robutti examine teachers’ professional learning in Massive Open Online Courses (MOOCs). They elaborate a theoretical framework, MOOC-MDT, which allows for analysis of the interactive nature of MOOCs and their influence on teachers’ professional learning.

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Notes

  1. 1.

    Our translation.

  2. 2.

    Our translation.

  3. 3.

    Our translation.

  4. 4.

    https://www.merriam-webster.com/dictionary/map

  5. 5.

    We present here more details about five acronyms (see more in Rocha 2018, p. 245): (1) The collective APMEP (Association des Professeurs de Mathématiques de l’Enseignement Public, https://www.apmep.fr/) “where teachers teaching mathematics from pre-primary schools to University and promoting teacher’s training”; (2) The collective IREM (Institut de Recherche sur l’Enseignement des Mathématiques, http://www.univ-irem.fr/) in which members “articulated work between research and practice looking for diffusing research results and promoting teacher’s training”; (3) Sésames (Science Education: Modeling Activities, Assessment, Simulation (Sésames, Situations d’Enseignement Scientifique: Activités de Modélisation, d’Évaluation, de Simulation)) teachers and researchers thinking about resources for teaching Algebra and promoting teacher’s training; (4) IFÉ (Institut français d’éducation, http://ife.ens-lyon.fr/ife) responsible by promote research and training in France; (5) the network LéA (Lieux d’éducation associés à l’IFÉ—Associated educational Places at the French Institute for Education, http://ife.ens-lyon.fr/lea/lea-english-version) putting together researchers and teachers in a network of schools linked to IFÉ to improve teaching.

  6. 6.

    http://www-irem.ujf-grenoble.fr/spip/IMG/pdf/fiche_prof_crepier_psychorigide.pdf

  7. 7.

    https://pixees.fr/

  8. 8.

    This problem comes from the more general mathematical situation: obtaining 1 in the sum of Egyptian fractions that is to say fractions with numerator 1. This situation is one of the EXPRIME situations.

  9. 9.

    With this expression, we mean in-service teachers who have long teaching experience and who have obtained a 2-year master’s degree to become trainers in mathematics education.

  10. 10.

    The choice of this term to refer to teachers’ education programs is in tune with Simon definition of Learning Trajectory: “The Hypothetical learning trajectory consists of the goal for the students’ learning, the mathematical tasks that will be used to promote students’ learning and hypothesis about the process of the students’ learning” (Simon 1995).

  11. 11.

    Hybridization is a very specific type of networking of theories (Bikner-Ahsbahs and Prediger 2014). In networking of theories, researchers use different theories (generally from mathematics education) to study the same problem, possibly producing different levels of combination/integration of the different theories. We have a hybridization of a theory T0 when a more or less extensive fragment of another theory T1(possibly also from a different theoretical field) is introduced coherently, operatively, and productively into the theory T0 but only partially altering its principles and methodology. Typically, researchers hybridize a theory when they realize that their working theory gives only a partially satisfactory answer to the research question they are facing; so, they introduce some new theoretical fragments, coherent with the starting frame, in order to develop a more satisfactory analysis.

  12. 12.

    So far, the first three have been delivered and the fourth one is a work in progress. They are called, respectively, MOOC Geometria (based on geometry contents, from October 2015 to January 2016), MOOC Numeri (based on arithmetic and algebra contents, from November 2016 to February 2017), and MOOC Relazioni e Funzioni (based on changes and relations concepts, from January 2018 to April 2018).

  13. 13.

    If the MOOC-teachers liked them; if MOOC-teachers were explaining at that time topics close to those proposed in their own classes

  14. 14.

    In the terminology of the Moodle forum, a discussion is defined as the set of posts that are grouped in response to an original post, which opened the topic of the discussion.

  15. 15.

    Note, moreover, E.L.I posts in a discussion already started: see in Table 10.3 the presence of ellipsis before the E.L.I line. This also denotes that E.L.I has carried out an information self-organization.

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Authors and Affiliations

  1. École normale supérieure de Lyon, Lyon, France

    Catherine Loisy, Katiane Rocha & Gilles Aldon

  2. University of Reims Champagne-Ardenne, Grand Est, France

    Hussein Sabra

  3. Kent State University, Kent, OH, USA

    Scott A. Courtney

  4. University of Zagreb, Zagreb, Croatia

    Dubravka Glasnović Gracin

  5. University of Lyon, Lyon, France

    Mathias Front & Marie-Line Gardes

  6. University of Turin, Turin, Italy

    Eugenia Taranto, Ferdinando Arzarello & Ornella Robutti

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  3. Eindhoven School of Education- ESoE, Eindhoven University of Technology- TU/e, Eindhoven, The Netherlands

    Birgit Pepin

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Loisy, C. et al. (2019). Analyzing Teachers’ Work with Resources: Methodological Issues. In: Trouche, L., Gueudet, G., Pepin, B. (eds) The ‘Resource’ Approach to Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-20393-1_10

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