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SAYAC Nathalie
DIDIREM (Paris 7), IUFM de Crteil (Paris 12)
12 bis rue des nfliers
93100 Montreuil
FRANCE
Tl: +33682828357/+33148583824
nsayac@5miranda.com/nathalie.sayac@creteil.iufm.fr
The question of the pre-service education and training in mathematics of primary school teachers is one of my main concerns as a trainer and researcher. This is why I was particularly interested in the topics of TSG 29 and its focus on forms, sites, contents, students, instruction methods, agents and aims. I must stress that this paper is based on a research in progress, started in September 2007, and that it will show some results. However it seemed relevant to try and contribute to TSG 29 since the problems my research raises are fully in tune with the theme of TSG 29.
Introduction: Pre-service Education and Training in France
General Training
In France, the pre-service education and training of primary school teachers is only one year long and aimed at students who have completed their first university degree or licence , in any subject, and who have passed the CERPE competitive examination, which includes compulsory examinations in maths, French, history, geography as well as optional subjects to be chosen between sciences, sports, music and visual arts. The training takes place in teacher training colleges or Instituts Universitaires de Formation des Matres (IUFM) which have been recently brought under the management of universities.
We must add that in France training in IUFMs is often criticized for being too theoretical or little suited to the expectations of trainees. Educators are often blamed for not being grounded in the realities of the classroom, for offering too theoretical a training which is then impossible to put into practice in schools.
The main aim of the pre-service teacher education is too allow trainee teachers to develop ten professional skills connected with their job as a teacher : to act as a responsible and ethical civil servant, to be fluent in the language of instruction and communication (French), to know and understand school subjects (including maths) and be well up on general knowledge, to know how to conceive and develop courses, to be skilled in classroom management, to know how to take into account the capabilities of learners, to be able to assess pupils, to be skilled in information and communication technology, to be able to work in a team and to cooperate with parents and other school members, and finally to be able to improve their practice and to innovate. It is quite obvious that mathematics play a fairly limited part, and are taught purely for professional purposes.
Training in Mathematics
The training in mathematics is done by specific full-time lecturers, based on a broad training curriculum defined nationally by the government but which can be interpreted on a local level by each IUFM (there are at present 31 IUFMs in France).
As a maths teacher educator for about ten years, I have observed with much interest the changes in the curricula introduced by successive Education Secretaries but as a researcher in maths didactics I could not remain a passive bystander. Nowadays the time spent by trainees in IUFMs has been shortened and more importance is given to training in the classroom and to practice analysis. This has consequences on the way training is organized. How exactly is training organized in France today?
In order to answer that question, I have decided to carry out, together with a small team of researchers, a study of the practices of IUFM teacher educators. It focuses on maths teacher educators in mathematics.
As far as the official directives about pre-service education are concerned, it is worth stressing that in maths the curriculum is developed in each training programme (see appendix) but that it remains quite vague because no precise indication is given on how the directives should be applied. My experience as a IUFM lecturer and educator allows me to assume that there is a wide diversity of practices among teacher educators in the pre-service education of primary school teachers. Such a diversity can be accounted for by a multiplicity of factors, both individual and circumstantial, which I will examine in my research. As a matter of fact, maths educators have varied professional backgrounds which can explain significant differences in their practices. Some of them are former primary school teachers who passed the CAPES in mathematics and went on to become maths teacher educators. Some are former secondary school teachers who tried to change career by becoming maths teacher educators for primary school teachers in IUFMs. Others have a purely academic background and have become trainers in their capacity of university lecturers and researchers.
Becoming a maths educator in charge of training primary school teachers requires a certain number of adaptations which are likely to generate distinct practices. The previous professional practice of a maths teacher does not necessarily match that of a maths IUFM educator. For the previous experience to be useful, it will have to be adapted first to an adult audience, and second to a course content which could be far removed from the trainers previous concerns (as an example, it can be unnerving to have to teach how to learn basic numbers when one was used to teaching logarithms). Learning this new job can also prove difficult because there is little training, if at all. In France, a non-profit organization called COPIRELEM plays a significant part in training maths educators, in organizing training seminars for junior educators and more senior ones, but it is difficult to assess the impact such extra-institutional training has on their practices. Other factors such as the lack of institutional standards in the training practice or the impossibility to assess ones own practice can also induce differences in practices which are difficult to identify.
As a maths teacher educator at the Livry-Gargan centre, I was also able to observe that the levels of achievement in maths of students and trainee teachers are usually quite poor and only a very small number of them have studied science subjects before taking the competitive exam to become a school teacher. And yet in the French system it is stated that the main aim of national competitive examinations, based on a national curriculum, is to guarantee that entrants are skilled in the subjects they are willing to teach. This quite clearly means that the skills and knowledge which entrants are supposed to acquire during their pre-service training must not be content skills in subjects but general skills used to construct professional practices. How can maths teacher educators both follow official directives and take into account the difficulties which their students experience in the subject? It is important to bear in mind that those difficulties are sometimes connected with painful memories from the days when they themselves were pupils at school. How can they be helped to get over such negative personal experience and teach maths with an open mind, focusing exclusively on their pupils achievement?
That is why I felt it necessary first to explore the practices of primary school maths teacher educators in IUFMs and identify similarities and differences in practices, and then to relate those practices to the diverse profiles of the educators and their personal and professional identity considered subjectively.
This research aims at exploring the way maths teacher educators interpret institutional training directives : what is the training content they provide? What part does pedagogy play in the training provisions? To what extent is the professional experience of the trainee teachers taken into account in their training? How are the characteristics of the trainee teachers taken into account in the training provisions?
References and Research Framework
As far as I know, there is very little literature on the practices of maths teacher educators. There is research on the various training schemes or on the skills and knowledge at stake in the learning process or on general maths training but none of it deals with the practices of maths teacher educators in the context of pre-service primary school teacher training.
Reference Works
In several studies on the training process in mathematics which were carried out a few years ago, some of the strategies adopted by maths teacher educators in IUFMs were identified (Kuzniak 1994, Houdement 1995, Peltier 1995).
- Monstration focuses on the transmission of a teaching model by observing how it is applied in primary schools (through videos for example). The idea is to transfer a practice by showing it to the trainee teachers and expecting them to imitate it.
- Homology is also based on imitation but of a more complex nature since the trainees must develop a teaching process drawn from the teaching they experienced as pupils (similar situations are presented to trainee teachers and primary school pupils). The maths teacher educator aims at transferring his understanding of teaching through the teaching provided during the pre-service training.
- Transposition differs from the other two strategies because it insists on theoretical distanciation, especially through the transmission of analysis tools developed by maths didactics (analysis of handbooks, of pupils mistakes, of teaching sessions).
Such strategies are used in varied and contextual ways by maths maths teacher educators in IUFMs, depending on the mathematical notions dealt with during the class (homology is used to teach notions ignored by the students, transposition and monstration for notions they should be more familiar with).
D. Butlen has investigated the practices of maths maths teacher educators in the context of training schemes developed to assist tenured teachers in their first appointments in a ZEP.
A recent study by A. Marchive on the way the results of research in math didactics were perceived and used by IUFM trainers has also emphasized the diversity of such practices.
Such studies were based on elements of self-declared practice. And yet it seems essential to work on the actual practice of trainers so as to understand the realities of the job and the varied ways in which the strategies identified by C. Houdement and others are adopted and modified.
Theoretical References
One of the main difficulties in assessing the practices of maths teacher educators lies in their complex professional identity:
- Being a maths teacher trainer in IUFM means teaching maths in a particular context. The various tools developed by maths didactics to analyse the practices of maths teachers teaching in primary or secondary schools can be useful to analyse the practices of IUFM trainers but they need to be adapted.
- Being a maths teacher trainer in IUFM means having a specific job which requires specific professional skills. It would be interesting to analyse such skills with concepts developed by professional didactics such as the notions of task/activity, conceptualisation, scheme, productive/constructive activity, discourse on activity, expertise, singularity of action as well as normative world.
- Being a maths teacher trainer in IUFM means having a singular personal and professional history which has implications on the way the job is perceived and the mission fulfilled. A specific study of the characteristics of trainers will be carried out to understand and analyse the practices of maths trainers who are part of the present research.
Therefore, in order to embrace the complexity and variability of the practices of maths teacher trainers in IUFM I have chosen to combine two complementary theoretical frameworks :
the framework of the twofold approach developed by A. Robert and J. Rogalski in maths didactics, which will allow me to take into account the mathematical content in the analysis of the practices of maths teacher trainers in IUFM
the framework of professional didactics which will allow me to assess teacher training as a profession and to analyse the notion of professional skill.
The studies by DeBlois et Squalli on the epistemological postures of future teachers (the posture of former pupil, the posture of student and the posture of teacher) will also be used to grasp teacher trainers relationship to the trainee teachers since a teacher trainer doesnt address a trainee as a teacher addresses a pupil.
I shall also borrow some elements from education science researchers who have also studied teacher training as a profession (Perrenoud, Altet, Schulman, Blanchard-Laville).
Methodology
In order to carry out an in-depth investigation, I have chosen to lead a qualitative study based on a small number of maths teacher educators who all work in the same training college, the Livry-Gargan centre of the Crteil IUFM. I have neutralized the working place as a contextual factor because I want to focus on the personal factors which could explain differences in practice between educators.
Six maths teacher educators in mathematics at the Livry-Gargan centre have agreed to take part in the research, which means that they will have to :
Answer a questionnaire
The questionnaire deals with their personal and professional backgrounds, the way the conceive pre-service training for primary school teachers, their training priorities, the main elements in their training provisions and other pieces of information which could help us analyse their practices.
Be filmed during a training session at the IUFM
The session will be videoed during the year of training, one camera being focused on the trainer and another one being located at the back of the classroom to get a general view of what happens during the session.
Take part in an interview about the videoed session
An analysis of the action of the trainer will be based on a series of self-confrontation or debriefing interviews, which should allow us to grasp the singular dimension of the trainers actions during the filmed sessions. The trainers will thus be able to go over their actions again, to comment upon them, to justify or to regret them, which, on the one hand, will help us understand their choices and analyse their activity from the work analysis perspective, and on the other hand will allow the trainers to develop a reflective and retroactive analysis of their own actions. The trainers will this be able to reconstitute the meaning of the events which occurred during the session and to understand what happened. They will also be able to analyse their actions retrospectively, free from the pressures and constraints of the teaching situation
This type of analysis requires the mediation of a third person, in this case one the members of the research team I have gathered together on the project, who will present the educator with a hypothetical analysis of what happened based on the three dimensions of the didactical analysis described below. The educator will then be able to confirm or infirm the interpretation.
Analysing the Training Sessions
The sessions will be analysed with the help of analysis grids derived from maths didactics but adapted to training sessions. Three dimensions will be examined :
A dimension connected with the general session outline chosen by the trainer, the content of the session and the general dynamics between the different stages of the session
A dimension connected with the different tasks (quantity, order, type) in the proposed activities
A dimension connected with the way the session unfolded, the nature of the organized work, the working conditions of the trainee teachers and with the duration of the different stages in the session.
Initial results
This year was spent drawing up tools likely to help in the analysis of maths teacher educatorspractices and in refinding a research methodology. I came up against the problem of transposing tools from the field of mathematics didactic enabling teacherspractices to be analysed to tools for analysing the maths teacher educatorspractices. As I have already indicated the maths teacher educator cannot be considered as special case, while he must transmit knowledge within an educational framework, his role and functions go beyond certain aspects of the job of teacher. Likewise, the question of professional training knowledge took up a lot of my time given the inextricable interlinking of different knowledge which comes into play during a raining session.
I have therefore striven this year to make changes to and refine the research methodology in respect of these various elements to be able to obtain convincing and constructive results.
In order to move the project forward I used a training session by an expert maths teacher educator at the Livry-Gargan Center, filmed at the beginning of the year. This choice initially proved problematic then finally very constructive. In fact, the trainer being filmed was, in practice terms, for removed from a secondary school teacher which made the transposition I had envisaged difficult but, for that very reason, I was able to understand the job of maths teacher educator.
Concerning professional knowledge
The issue of professional knowledge was clarified on the basis of different interpretative from the viewpoint of my experience as a trainer and the specific study of the filmed session.
After extensive research, the idea of PCK put forward by Shulman (1986- 1987) struck me as relevant for specifying the mathematical content of the initial training of primary school teachers as is corresponds better, in my opinion, to the professional knowledge transmitted during training. In fact, the skills worked on during the disciplinary sessions are only done so with a view to them being learned by the future pupils who will be entrusted to the trainee teachers. The trainees have to carry out a transformation of the knowledge to move from their own understanding of it, to understanding it for others (Shulmans model describes six processes required for this transformation). In working on teacher training content from various angles the aim is for the trainee to adopt it professionally, so as to be able to teach it as effectively as possible.
I have adapted this concept to the initial training of primary school teachers in France and have drawn up three specific entries for PCK :
- PCK1 which enables the idea to be worked on from a strictly mathematical angle
- PCK2 which enables the transposition from prescribed knowledge to knowledge for teaching to be worked on : when studying handbooks or digital resources from a didactical viewpoint, when working on the idea of conceptual field (Vergnaud), of operating invariants and signifiers (symbols, designations).
- PCK3 which is more concerned with the organisation of the knowledge to be taught : how to device a progression? A prep sheet ? How to manage a problem situation?
I have also defined another, more transversal, axis of professional knowledge also comprising three specific entries :
- an entry centred on institutional knowledge : officinal guidelines, teaching syllabuses
- an entry centred on knowledge of pupils : sociological, psychological, cognitive approaches of pupils : when stages of learning are distinguished (Piaget), when speaking of ZPD (Vigotsky), when looking at ZEP
- an entry centred on basic professional gestures : how to manage a class? Group-work? Returning to peace and quiet?
These skills are not worked on alternately or one after the other, they sometimes overlap and are difficult to distinguish but seemed to me to cover the different contents proposed in pre-service training by maths teacher trainers in our training center.
Concerning the trainees
The new rule in France requiring all trainees to have a class, one day a week, during their year of training has forced maths teacher educators to take work in the field into account more. The problem for the trainee is finding himself in different postures without this being clearly defined institutionally.
Drawing on the works of DeBlois & Squalli, (2002, 2007) into the notion of the epistemological postures of future teachers for inspiration, I have picked out three postures in which the trainee is involved by the trainer. In fact, while studying the different activities proposed, in pre-service training, I noticed that during a same class the trainees could be placed alternately in different postures by the trainer, depending on what they had to do:
the pupil posture : when trainee is assigned tasks he has to solve as a pupil in educational system. For example, when he is faced with activities he has to do in the way a pupil would, whatever the level (play a game, reproduce a geometrical figure, solve a problem)
the student posture : when trainee is subjected to activities which are going to allow him to train as a future teacher to reflect on a teaching approach. For example, when he asked to rank activities according to their difficulties or when procedures in which pupils are faced with a mathematical problem are being studied.
the teacher posture : when trainee is addressed as a teacher. For example, when he is asked which teaching choice he would make for such and such notion, when he is asked what he does in his class.
for each proposed task, the trainer addresses either a pupil, a student or a teacher and expects the trainee to settle into the posture chosen for him (consciously or unconsciously). The trainee can accept this positioning or oppose it, which can create tensions in the DeBlois & Squalli (1997) sense or incidents in Roditi sense.
C Blanchard-Laville has drawn a very relevant parallel in my view, between initial teacher training and the crisis period of adolescence. The incessant posture changes the trainer requires of his trainees show the difficulties encountered in pre-service training.
Conclusion
Based on these elements, I feel able, not only to grasp the practices of maths trainers, but also to envisage the impact of these practices on the trainees since I will be able to look at :
what rate of posture change over does the trainer impose on his trainees during a class? Is an efficient trainer one who puts his trainees in various postures or one who favours one posture over another?
Is the professional knowledge linked to specific postures? is there professional knowledge which is more efficiently transmitted in one posture than in another?
I am therefore now going to widen my research to a greater number of maths trainers in order to check my hypothesis about the wide variety of trainer practices and attempt to better understand whats at stake in pre-service training, from the point of view of contents and trainees.
The stakes are high if one assumes that the practices of maths teacher educators have direct or indirect implications for the practices of primary school teachers of mathematics. This impact will not be assessed in the present research, but if one wishes to assess it in the future, then it will be necessary to know and understand the practices of IUFM educators. This research could also lead to the development of training schemes for educators, which would be based on the effective practices of maths teacher educators, and to the development of training tools which new trainers could adopt more easily.
BIBLIOGRAPHY
ASTIER Philippe, en collaboration avec Paul Olry (matre de confrences universit de Paris Nord), numro 165 et 166 de la revue Education Permanente Analyses du travail et formation (dcembre 2005; mars 2006).
ASTIER Philippe, Actions de formation, rencontres dactivits Education permanente N 166, mars 2006, pp. 137-146.
ASTIER Philippe, Dynamique de la transmission des comptences dans les organisations. Colloque international Union Europenne de systmique. Paris, ENSAM, 21 septembre 2005 (actes du colloque sur CD-Rom).
BLANCHARD-LAVILLE, C. (2000). Malaise dans la formation des enseignants, LHarmattan, Paris
BLANCHOUIN Aline, PFAFF Nathalie,Formation denseignants: Quels scnarios? Quelles valuations?, un dispositif de formation pour engager les PE du C2 dans un lien EPS/mathmatiques
CYR, S. & DEBLOIS, L (2007) tude de la comprhension des composantes de la notion de corrlation chez les futurs matres du secondaire Revue Petit x n75, p50-73
DEBLOIS, L. & SQUALLI, H. (1997) lanalyse des erreurs des lves en mathmatiques par des tudiantes et des tudiants en formation initiale lenseignement La formation initiale, entre continuit et ruptures, Presses de lUniversit de Laval, Qubec, p 125 - 143
DEBLOIS, L. & SQUALLI, H. (2002) Implication de lanalyse de production dlves dans la formation des maitres Educational Studies in Mathematics 50, p 212- 237
HOROKS Julie, "Examples of tasks to make mathematics teachers work on student's activities in the classroom : texts, management and the links between them", avec Aline Robert, JMTE special issue 2006
HOROKS Julie, Les triangles semblables en classe de seconde : des enseignements aux apprentissages. tude de cas, Doctorat en Didactique des Disciplines, option mathmatiques, (2006) Universit de Paris 7,
KUZNIAK Alain, tude des stratgies de formation en mathmatiques utilises par les formateurs de matres du premier degr頻 Thse de Doctorat, Universit Paris 7 (1994)
MALO Annie, savoirs de formation et savoir dexprience: un processus de transformation, Revue Education et francophonie, Vol XXVII, n2, 2000
MARCHIVE Alain, Recherches en didactique et formation des enseignants : analyse dentretiens biographiques auprs denseignants dun IUFM franais Actes du Colloque international EMF 2006, Sherbrooke, Canada, mai 2006.
MAUBANT Philippe et al, La didactique professionnelle, un nouveau regard pour analyser les pratiques denseignement, Colloque quest-ce quune formation professionnelle universitaire des enseignants? Arras, mai 2007
PELTIER Marie-Lise, La formation initiale, en mathmatiques, des professeurs d'cole: "entre conjoncture et ternit " Thse de Doctorat, Universit Paris 7 (1994)
PERRENOUD P., la formation des enseignants. Entre thorie et pratique Editions lHarmattan, 1994.
PFAFF Nathalie, Processus de conceptualisation autour du thorme de Thals Thse en Sciences de l'ducation, Universit Paris V (1991)
RODITI E. (2005), Les pratiques enseignantes en mathmatiques. Entre contraintes et libert pdagogique, 196 p., Paris : L'Harmattan.
SAYAC Nathalie, Les pratiques des professeurs de mathmatiques de lyce: une approche croise des influences du sexe, de lge et du cursus, Doctorat de didactique des mathmatiques, Paris, IREM Paris 7 (2003)
SAYAC Nathalie, A scheme for the initial education of teachers: analysing practicesduring professional workshops ICMI-15, Brsil (2005).
SAYAC Nathalie, Un dispositif de formation initiale pour professeurs des coles, en France prenant en compte des constats de formateurs et de chercheurs.Actes du Colloque international EMF 2006, Sherbrooke, Canada, mai 2006.
SAYAC Nathalie, tude a grande chelle sur les pratiques des professeurs de mathmatiques de lyce : rsultats lis des variables spcifiques et typologie sommaire, Recherche en didactique des mathmatiques 26-3, Grenoble, La Pense Sauvage (2006).
SHULMAN, L. (1986b). Those who understand : knowledge growth in teaching. Educational Researcher, 57 (2), 4-14
SHULMAN, L. (1987). Knowledge and teaching : Foundation of a new reform. Harvard Review, 57 (1), 1-22.
APPENDIX
Training programme in Mathematics
IUFM De Crteil, France 2007
1) Matriser les disciplines et avoir une bonne culture gnrale
Matrise un niveau satisfaisant pour le domaine mathmatiques de toutes les comptences en matire de connaissances, capacits et attitudes figurant pour le professeur des coles dans cette entre.
Connaissances
Des contenus mathmatiques enseigns lcole primaire et des enjeux dapprentissage, notamment:
La numration de la maternelle au CM2
Les notions de grandeur et mesure
Un exemple de champ conceptuel
Lapprentissage des oprations enseignes lcole lmentaire (techniques opratoires, calcul mental, calcul rflchi etc.)
La gomtrie: de la gomtrie perceptive la gomtrie instrumente: continuits et ruptures.
La rsolution de problmes sera un thme transversal tous les points cits ci-dessus.
Capacits
Organiser les diffrents enseignements en les articulant entre eux dans le cadre de la polyvalence
Attitudes
Avoir une attitude de rigueur scientifique
Participer la construction dune culture commune des lves.
2) Concevoir et mettre en uvre son enseignement
Connaissances
Connatre les objectifs atteindre pour un niveau donn dans le cadre de son enseignement
Capacits
Capable de dfinir des objectifs dapprentissage partir des rfrences des textes officiels
Capable de mettre en uvre une progression et une programmation sur lanne et sur le cycle en mathmatiques
Capable de prendre en compte en mathmatiques les rsultats des valuations dans la construction dune progression pdagogique, notamment les valuations CE2 et 6e.
Etre capable dutiliser les programmes denseignement et les documents daccompagnement concernant tous les niveaux denseignement du premier degr pour les mathmatiques .
Attitudes
Construire des activits permettant dacqurir la mme comptence par le biais de plusieurs disciplines
Apprcier la qualit des documents pdagogiques ( manuels scolaires et livres du professeurs associs, ressources documentaires, logiciels denseignement)
Comptence: organiser le travail de la classe
organiser les diffrents moments dune squence
adapter les formes dintervention et de communication aux types de situations et dactivits prvues (posture, place, intervention, vrification des consignes etc.)
Attitudes: dans toute situation denseignement le professeur veille instaurer un cadre de travail permettant lexercice serein des activits.
3) Prendre en compte la diversit des lves
Capacits
Capacit de prise en compte de la diversit des lves, en proposant notamment des cheminements cognitifs et des parcours adapts dventuelles difficults diagnostiques.
Capacit danalyse des erreurs dlves, en les reliant des stratgies ou des conceptions errones en mathmatiques.
4) valuer les lves
Capacits
Capacit de concevoir des valuations en mathmatiques aux diffrents moments de lapprentissage, caractre plus ou moins diagnostique, formatif ou sommatif.
The Licence is equivalent to a Bachelors Degree, received after 3 years of study after the A-levels.
Competitive examination for the recruitment of primary school teachers
The change was enforced after 1st January 2007. It is therefore too early to assess the impact of that change on teacher training but this political decision is not neutral and will certainly have visible consequences.
They are maths teacher educators at the Crteil IUFM: PFAFF Nathalie (PhD in Education sciences), HOROKS Julie (PhD in maths didactics), BLANCHOUN Aline (completing a PhD at CNAM) and as an external colloborator: ASTIER Philipe (University Professor, Lyon II CNAM)
Secondary school teaching certificate, equiv. PGCE.
Commission Permanente des IREM pour lenseignement des mathmatiques lcole lmentaire.
During their training period, trainee teachers have to go on several school placements : one follow-up placement where they spend one day a week at the same school; two three-week grouped placements, where they are in charge of pupils on a different level from the previous placement.
On that subject, Annie Malos Savoirs de formation et savoir dexprience : un processus de transformation is very interesting.
Zone dEducation Prioritaire or a deprived area with special educational needs
In the article entitled La didactique professionnelle, un nouveau regard pour analyser les pratiques denseignement, P. Maubant explains very accurately why the theoretical framework of professional didactics is a relevant framework for professional training.
Pedagogical content knowledge, Shulman 1986
" the capacity of a teacher to transform the content knowledge he or she possesses into forms that are pedagogically powerful" Shulman, 1986
TSG 29: paper SAYAC ICME 11- 2008
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