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Translation is a critical issue in international mathematics education studies but has seldom been carefully investigated. How can a theoretical approach be translated and subsequently used in different languages, and to what extent could the translation processes deepen the approach itself? This paper addresses such issues in the case of the Documentational Approach to Didactics (DAD). We explore possibilities of translating selected critical notions expressed in English terms into French, Arabic and Chinese, and developing insights from these possibilities. We further deal with the translation issues 'in situ', i.e. in an English mathematics teacher's lesson where we can identify the embodiments of the DAD concepts. The most challenging part in the translation is the embedding of the English terms in the English cultural sphere, and 're-bedding' them into another cultural sphere. It is claimed that examining the nuances between the different possibilities of translation for the same concept, in connection with their use 'in situ', and drawing inspiration from the educational, cultural and theoretical traditions in other cultural spheres, can help to deepen the theoretical constructs.

We are interested in understanding how university students learn to use programming as a tool for "authentic" mathematical investigations (i.e., similar to how some mathematicians use programming in their research work). The theoretical perspective of the instrumental approach offers a way of interpreting this learning in terms of development of schemes by students; these development processes are called instrumental geneses. Nevertheless, how these schemes evolve has not been fully explained. In this paper, we propose to enrich the theoretical frame of the instrumental approach by a model of scheme evolution and to use this new approach to investigate learning to use programming for pure and applied mathematics investigation projects at the university level. We examine the case of one student completing four investigation projects as part of a course workload. We analyze the productive and constructive aspects of the student's activity and the dynamic aspect of the instrumental geneses by identifying the mobilization and evolution of schemes. We argue that our approach constitutes a new theoretical and methodological contribution deepening the understanding of students' instrumented learning processes. Identifying instrumented schemes illuminates in particular how mathematical knowledge and programming knowledge are combined. The analysis in terms of scheme evolutions reveals which characteristics of the situations lead to such evolutions and can thus inform the design of teaching.

The study presented in this paper concerns the design and evaluation of curriculum material that supports mathematics teachers' understanding and enactment of reform curricula and innovative teaching practices. Our focus is on curriculum material supporting mathematics teachers' practices combining the use of digital technology and the development of student autonomy. We refer to the theoretical framework of the Documentational Approach to Didactics, which considers teachers' documentation work as a central lever for the evolution of teachers' practices. Our study took place in the context of curriculum reforms in France, which called on teachers to combine the use of digital technology with the development of student autonomy in their practices. We investigate in this paper the design of a meta-resource with the aim of supporting teachers' documentation work in this context. The documentation work ranged from choosing a lesson plan offered on a website to designing a completely new lesson. Using a design research approach, we conducted two design and evaluation cycles, involving different groups of researchers and teachers, and we analysed these design processes and their outcomes. The researchers used particular categories to distinguish between different forms of autonomy, and criteria concerning the articulation between student autonomy and digital technologies. The teachers provided elements concerning the features of a lesson plan facilitating its appropriation, and more generally related to their actual design work. Our results illustrate how a multidisciplinary team of researchers can collaborate with teachers to design 'meta-resources' supporting teachers' documentation work in a context of education reform.

In this paper we aim to contribute to a better understanding of the impact of digital resources on mathematics teachers' work and professional development. For this purpose we focus on the emblematic case of an experienced mathematics teacher at secondary level, Anna, who has also worked as a teacher educator in a university department. Using the lens of the Documentational Approach to Didactics (DAD), we investigate her case, with a particular interest in digital resources, including both digital curriculum resources (e.g., e-textbooks, online resources) and digital technologies (e.g., for communicating, sharing). Two notions appear essential for supporting this investigation: the notion of "resource system" for studying the teacher's activity as a whole, and the notion of documentational trajectory for studying the teacher's activity over the time. Methodologically, specific tools were developed for gaining deeper insights into the teacher's resource system, or her documentational trajectory. This study provides a window into mathematics teacher use and design of digital/non-digital resources in/for their teaching. Moreover, it helps us to develop better understandings of teacher professional learning over time, and of the ways the context of collaboration shapes their professional work and learning. More and also contrasting cases (e.g., of newly qualified teachers) would need to be studied to fully understand this field.

Volatile organic compounds (VOCs) contribute to air pollution through the formation of secondary aerosols and ozone and extend the lifetime of methane in the atmosphere. Tropospheric VOCs originate to 90 % from biogenic sources on a global scale, mainly from forests. Crops are also a potentially large yet poorly characterized source of VOCs (30 % of the VOC emissions in Europe, mostly oxygenated). In this study, we investigated VOC fluxes over a winter wheat field by eddy covariance using a PTR-Qi-TOF-MS with high sensitivity and mass resolution. The study took place near Paris over a 5-week period and included flowering, crop maturity and senescence. We found a total of 123 VOCs with fluxes 3 times above the detection limit. Methanol was the most emitted compound with an average flux of 63 µg m−2 h−1, representing about 52 % of summed VOC emissions on a molar basis (36 % on a mass basis). We also identified ethanol, acetone, acetaldehyde and dimethyl sulfide among the six most emitted compounds. The third most emitted VOC corresponded to the ion m/z 93.033. It was tentatively identified as furan (C6H4O), a compound not previously reported to be strongly emitted by crops. The average summed VOC emissions were about 173 ± 6 µg m2 h−1, while the average VOC depositions were about 109 ± 2 µg m−2 h−1 and hence 63 % of the VOC emissions on a mass basis. The net ecosystem flux of VOCs was an emission of 64 ± 6 µg m−2 h−1 (0.5 ± 0.05 nmol m−2 s−1). The most deposited VOCs were identified as hydroxyacetone, acetic acid and fragments of oxidized VOCs. Overall, our results reveal that wheat fields represent a non-negligible source and sink of VOCs to be considered in regional VOC budgets and underline the usefulness and limitations of eddy covariance measurements with a PTR-Qi-TOF-MS.

The instrumental approach is a useful theoretical lens for understanding students' learning processes with a main focus on the transformation of an artefact (a human design for a goal-directed activity) into a meaningful instrument (i.e. an artefact and schemes developed by the student). In this paper, we articulate the instrumental approach for computer programming technology use in the context of pure or applied mathematical investigation. We illustrate it by examining the engagement (scheme development) of an undergraduate student engaged in 'authentic' programming-based mathematical inquiry work, i.e. complete inquiry work as mathematicians would do. Two schemes are elaborated, namely the scheme of validating the programmed mathematics and the scheme of articulating in the programming language a mathematical process. Our discussion evidences some specific features of the programming language as artefact associated with a general aim of mathematical inquiry, in particular in terms of articulation between mathematics and programming.

How can future mathematics teachers be trained to combine the use of digital technologies with student autonomy? Referring to the documentational approach to didactics, we have designed and implemented an initial training course based on collective documentation work. Here we analyze the work of a team of trainees who designed a session on programming with Scratch, in terms of the potential of the lesson designed for the use of Scratch and student autonomy, and the professional knowledge mobilised. The analysis of this case highlights possibilities and limitations of such a training.

Objectives: To analyse the diagnostic performance of eosinopenia, alone or combined with polymorphonuclear neutrophils (PMN) and/or lymphocytes, as a marker of active COVID-19 in patients hospitalized for suspicion of SARS-CoV-2 infection. Methods: A prospective observational study including patients hospitalized for suspicion of COVID-19 in a COVID unit was performed from 20th March to 5th April 2020, in Perpignan, France. Patients for which there was a doubt upon diagnosis, who were recently under oral corticosteroids, had myeloid malignancy or human immunodeficient virus infection were excluded. SARS-CoV-2 detection was performed using an RT-PCR assay, from nasopharyngeal swab specimens. Complete blood count were performed for all patients. Results: One-hundred and twenty-one patient were included: 57 patients were diagnosed with COVID-19, 64 patients were not. Eosinophil count was lower in the COVID-19 group (median: 0/μL versus 70/μL, p

Objectives We aimed to assess the level of prior SARS-CoV-2 infection in socially deprived neighbourhoods after the first wave of the pandemic, and to identify factors associated with seropositivity.Design A cross-sectional study.Setting Three socially deprived neighbourhoods of the city of Perpignan, in the south of France, where large settled Roma communities live.Participants People aged 6 years old or over, living in the study area. 700 people were included in the study using two-stage stratified sampling design.Interventions The study included a questionnaire and SARS-CoV-2 antibody testing by the Roche Elecsys immunoassay between 29 June and 17 July 2020.Primary and secondary outcome measures SARS-CoV-2 antibody seroprevalence was estimated from weighted data. Associated factors and reported symptoms were investigated using univariable and multivariable logistic regressions.Results The seroprevalence of anti-SARS-CoV-2 antibodies was 35.4% (95% CI 30.2% to 41.0%). People aged 15–64 years old had increased odds of being seropositive than those aged 65 years or over. Obese people had higher odds of being seropositive (adjusted OR (aOR)=2.0, 95% CI 1.1 to 3.8). The odds of being seropositive were higher in households with clinical COVID-19 cases (one case: aOR=2.5, 95% CI 1.3 to 5.0; several cases: aOR=6.9, 95% CI 3.1 to 15.2). In the neighbourhood with the highest measured seroprevalence, people living in a dwelling with one to two rooms had higher odds of being seropositive than those living in a four-room house (aOR=2.8, 95% CI 1.2 to 6.3). Working during the lockdown was associated with lower odds of being seropositive (aOR=0.2, 95% CI 0.03 to 1.0).Conclusion Transmission of SARS-COV-2 in this vulnerable population was very high during the COVID-19 pandemic’s first wave. Our results highlight the need to strengthen and adapt preventive measures taking into account all social determinants of health, especially housing conditions.

In this paper we introduce a link between the Theory of Didactical Situations and the Documentational Approach to Didactics, in order to study teaching/learning phenomena at the beginning of university mathematics studies. Specifically, we investigate the didactic contract at three levels: institutional, mathematical subject, and specific mathematical content level, and link it to the use of resources by students. Using this link, we analyse data stemming from two complementary case studies: one in the UK, and one in France. We identify didactic contract rules at the three levels for the students, and for the teachers. Moreover, we find discrepancies between students' and teachers' rules, and also between those and the explicit rules of the institution/s. These gaps may cause misunderstandings and prevent students from learning mathematics effectively at university level; we claim that these gaps can be reduced. Teachers could make their expectations more explicit in terms of resource use and support an appropriate use by students. The university institution could also contribute to a better alignment of the resources offered with actual student practices.

This paper is concerned with the development of e-textbooks. We claim that analysis (and design) of e-textbooks requires the development of a specific frame. Digital affordances provide particular opportunities (e.g. in terms of interactions between users) that require specific considerations for their analysis, as teachers and students use them for their individual and collective purposes. In this study, we develop a framework for mathematics e-textbook analysis, based on the notion of "connectivity." We introduce criteria to assess the different aspects of connectivity and build an analysis grid for e-textbooks. We illustrate the framework proposed by analyzing 2 commonly used French grade 10 mathematics e-textbooks. The results of the analyses show that there are major differences between the 2 e-textbooks in terms of connectivity, which can be related to differences in their design. Beyond these 2 examples, we claim that focusing on connectivity is a useful and relevant way of analyzing e-textbooks, as it can provide a window into issues of interactivity, both practically and cognitively.

En este trabajo estudiamos las interacciones entre dos profesoras de matemáticas de secundaria y los recursos utilizando el marco teórico de la aproximación documental. Este marco propone que estas interacciones producen documentos asociados a los recursos y a los esquemas de uso. Los esquemas comprenden el conocimiento profesional en términos de invariantes operatorios. Las profesoras trabajan colectivamente organizando su enseñanza en torno a los intervalos de fluctuación. Mostramos que, a pesar del trabajo colectivo, los documentos desarrollados por cada una comprenden diferentes elementos: los invariantes operatorios iniciales no evolucionan lo suficiente como para conducir a documentos comunes.

The goal of this conceptual paper is to develop enhanced understandings of mathematics teacher design and design capacity when interacting with digital curriculum resources. We argue that digital resources in particular offer incentives and increasing opportunities for mathematics teachers' design, both individually and in collectives. Indeed they require increased design expertise because of the changing nature of the resources. Drawing on the literature (1) we suggest ten questions providing a tool to study teacher design processes; and (2) we propose three components for exploring teacher design capacity. Building on two main theoretical areas (i.e. teaching as design; documentational approach to didactics) we propose to deepen understandings of the notions of "teacher design" and "teacher design capacity." Drawing on two different collective environments and two individual teacher cases working within these environments, we investigate and illustrate teachers' design processes and design capacity building across a range of contexts and curriculum formations, with the focus on how digital resources can help to develop teacher design capacity. We claim that the evolutions of digital resources in particular require an elaboration and refinement of the concept of teacher design capacity, which we develop and illustrate. Indeed, interacting with digital resources, it is claimed, might be a fruitful vehicle for developing teachers' design capacity, in particular when working in collectives.

Mathematics teachers interact with resources of various kinds in their work in and out of class. The documentational approach of didactics is a theoretical approach that has been elaborated to investigate these interactions and their consequences in terms of teachers' practice and teachers' beliefs in particular. According to this approach, using resources teachers develop documents, encompassing these resources and a scheme of use; they also develop structured documents systems and resources systems. I interviewed six university teachers in France and collected the resources they used and designed. Drawing on these data I analyzed their documents and their resources systems, focusing on the features of resources use that appear specific to the university (rather than secondary school) context. I observed that lecturers can develop important agency in the design and use of teaching resources. On the other hand, PhD students starting to teach seem to conform their teaching to ready-made resources; nevertheless, their personal resources and beliefs intervened in their documentation work. Resources and beliefs deriving from the lecturers' research can also influence the development of documents and thus contribute to shaping the mathematics taught.

In this study, we investigated design processes in teacher collectives, which have been made possible by new "digital" opportunities: platforms, discussion lists, etc. The object of our study is the French Sésamath teacher association and its design of a grade 10 e-textbook, more precisely the design of the "functions" chapter. We analysed it with two theoretical lenses: the documentational approach and cultural-historical activity theory. We studied the activity system of a community of teachers designing an e-textbook. At macro-level, we observed a change of objects of the activities: from designing a "toolkit" for mathematics teachers; to interactive exercises; and finally to a more "classical e-textbook". At micro-level, we analysed the development of collective documents by the community, combining resources and schemes.

This study reports NO, NO2 and O3 mixing ratios and flux measurements using the eddy covariance method during a 7-month period over an oilseed-rape field, spanning an organic and a mineral fertilisation event. Cumulated NO emissions during the whole period were in agreement with previous studies and showed quite low emissions of 0.26 kg N ha−1 with an emission factor of 0.27 %, estimated as the ratio between total N emitted in the form of NO and total N input. The NO emissions were higher following organic fertilisation in August due to conditions favouring nitrification (soil water content around 20 % and high temperatures), while mineral fertilisation in February did not result in high emissions. The ozone deposition velocity increased significantly after organic fertilisation. The analysis of the chemical and turbulent transport times showed that reactions between NO, NO2 and O3 below the measurement height occurred constantly throughout the 7-month period. Following organic fertilisation, the NO ground fluxes were 30 % larger than the NO fluxes at the measurement height (3.2 m), while the NO2 fluxes switched from deposition to emission during certain periods, being negative at the surface and positive at the measurement height. This phenomenon of apparent NO2 emissions appears to be significant during strong NO emissions and high O3 ambient mixing ratios, even on a bare soil during August.

In this article we present an "instrumental approach" in mathematics education, which focuses on the interactions between students, teachers, and "artefacts." This approach analyses "mediations" attached to the use of a given artefact and "instruments" developed by the subjects from this artefact along "instrumental geneses." We draw on three "Research Cases" at university to illustrate the use of this approach: the first is about students' geneses with a programming technology; the second about students' and teachers' geneses with a virtual learning environment; and the third about textbooks and teachers professional development. We also introduce the "documentational approach," which draws on the instrumental approach, but takes into account the broader range of available "resources." It distinguishes resources and "documents" developed by teachers from these resources, and studies teachers' "documentation systems." We present a fourth "Research Case" concerning the documentation system of a mathematics teacher, and focusing on the place of technologies within this system.

The abundant digital resources on the Internet are leading to profound changes in teachers’ activity. We refer to the theoretical framework and methodology of the documentational approach to didactics to investigate these changes. We compare two case studies: an English teacher, and a mathematics teacher, both working in the same upper secondary school in France. We have observed significant use of digital resources in both cases, but of a different nature. We present and discuss these differences that shed light upon teachers’ documentational work. We use these cases to draw more general conclusions on designing, using and sharing digital teaching resources.

We study in this article mathematics teachers' "documentation work": looking for resources, selecting/designing mathematical tasks, planning their succession, managing available artifacts, etc. We consider that this documentation work is at the core of teachers' professional activity and professional development. We introduce a distinction between available "resources" and "documents" developed by teachers through a "documentational genesis" process, in a perspective inspired by the "instrumental approach." Throughout their documentation work, teachers develop "documentation systems," and the digitizing of resources entails evolutions of these systems. The approach we propose aims at seizing these evolutions, and more generally at studying teachers' professional change.

The study we present here concerns the consequences of integrating online resources into the teaching of mathematics. We focus on the interaction between teachers and specific online resources they draw on: e-exercise bases. We propose a theoretical approach to study the associated phenomena, combining instrumental and anthropological perspectives. For given didactical tasks, we observe teachers' instrumental geneses, and the didactical techniques they develop. We exemplify our approach with the analysis of a case study of trigonometry in grade 9.

The secondary-tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also institutional phenomena are considered with different perspectives. Each perspective yields a particular view of transition. The association and comparison of these views makes it possible to build an organized outline of this complex object, combining several kinds of ruptures and long-term evolutions.

The aim of this paper is to contribute to the understanding of the possible influence of the use in class of Internet resources which offer mathematical exercises for the students' activity and learning processes. I present an exploratory study grounded on a teaching design set up in two French grade six classes about proportional reasoning involving an e-exercise resource. We adopted a teaching design which used free access for the student to a wide range of exercises, and many written reports associated with the work on the computer. We observe that the students' activity during the experiment is much richer than drill. Students develop different working patterns on the computer. These patterns can be interpreted as consequences of the different roles implicitly attributed by the student to the resource within the didactical contract. We also observe the construction of new mathematical abilities. At the end of the teaching, the students were able to use several kinds of strategies to solve proportionality problems. However the didactical contract is modified by the Internet resource and generates specific difficulties, in particular insufficient written work. (Contains 1 tables and 2 figures.)

E-Exercise Bases (EEB) are now used in the teaching of mathematics, especially at university. We discuss here the consequences of their use on the students' activity during computer lab sessions. Results stem from observations of several teaching designs organised in different French universities with three e-exercise bases. The analysis focuses on new tasks and on specific solving strategies, which appear using these resources. Moreover, specific didactic contract clauses are studied.

Resumo Este texto é a tradução em Português (com uma atualização das referências) de um artigo publicado em 2007 em francês[1]. Nós escolhemos publicá-lo aqui, pois este artigo apresenta as bases da abordagem documental que alimenta várias contribuições desta revista. A abordagem documental estuda o trabalho dos professores a partir de suas interações com os recursos. A documentação designa simultaneamente este trabalho e o que nele é produzido. O artigo propõe uma abordagem teórica para o estudo dessa documentação e introduz, em particular, a noção de gênese documental. Estas gêneses têm aspectos individuais, mas também coletivos, particularmente, no seio das comunidades de prática. Elas desempenham um papel essencial no desenvolvimento profissional dos professores. O artigo apresenta a abordagem documental da didática e exemplos de sua aplicação no caso dos professores de Matemática. Depois de 2008, esta abordagem documental conheceu novos desenvolvimentos ao ter contato com outras abordagens a nível nacional e internacional interessadas, particularmente, pelo trabalho coletivo dos professores[2]. Ela foi também trabalhada na Escola de Altos Estudos financiada pela CAPES em janeiro de 2015. A tradução em Português foi realizada por Katiane de Moraes Rocha, que iniciou em 2014 uma tese financiada pelo CNPq com base nesta abordagem essa tradução se insere, portanto, neste processo de transmissão-desenvolvimento. [1]GUEUDET, G., TROUCHE, L. Du travail documentaire des enseignants: genèses, collectifs, communautés. Le casdes mathématiques. Education et didactique, Rennes,2, 3, 7-33. 2008. [2]As três obras apresentadas a seguir marcam as principais etapas destes desenvolvimentos: - GUEUDET, G. TROUCHE, L. Ressources vives. Le travail documentaire des professeurs en mathématiques. In Gueudet, G., Trouche. Rennes: Paideia, 2010. p.372. p. - GUEUDET, G., PEPIN, B., & TROUCHE, L. (eds.) From Textto ‘Lived’ Resources: Mathematics Curriculum Materialsand Teacher Development, New York:Springer, 2012. 365 p. - Pepin, B., Gueudet, G., Trouche, L. Re-sourcing teacher workandinteraction: new perspectives onresource design, use and teacher collaboration, special issueofZDM.The InternationalJournalon Mathematics Education, London: Springer,45, 7, 929-943. 2013.

Resumo Em numerosos países os livros didáticos são, em Matemática, recursos centrais para os professores; todavia esses têm sofrido importantes evoluções ligadas ao digital. Nós estudamos estas evoluções e suas consequências em relação ao processo de designer de livros didáticos, pautados em um perspectiva de abordagem documental. Nós propomos de re-conceitualizar a noção de qualidade dos livros didáticos, introduzindo duas dimensões: a conectividade e a coerência dos livros. Nós analisamos dois livros didáticos franceses destinados ao sexto ano do ensino fundamental, um criado por um pequeno grupo de especialistas (Hélice) e outro por uma grande equipe de professores (Sésamath). Nós aplicamos a estes livros nossas proposições teóricas e ilustramos para sua análise (em particular o tema área) o tipo de fenômenos que podemos identificar em termos de instrumentalização e instrumentação; a conectividade, a coerência e a qualidade dos livros. Nós mostramos que o livro produzido pelos especialistas é de uma grande qualidade didática, mas estática, voltada para a instrumentação dos usuários, enquanto que o livro produzido pelo coletivo e professores é de uma qualidade dinâmica, voltada para a instrumentalização. Palavras-Chave: Abordagem documental para didática, coerência de livros didáticos, produção de e livros didáticos, conectividade de e livros didáticos, qualidade de e livros didáticos Abstract In many countries textbooks remain to be the main resources for mathematics teachers. However, textbooks have changed over time, likely due to developments in information technology. In this paper we report on an investigation of how two French mathematics textbooks are conceived by their authors, analysing the effects of different conceptualisations reflected in the books. For the analysis we chose two commonly used French textbooks at grade 6 (topic of “area”): one authored by a small group of experts (Helice); and one by a large group of mathematics teachers (Sesamath). In addition, we drew evidence from interviews with the textbook authors. Using the documentational approach, we analysed the textbooks with respect to quality and their usages (instrumentation-instrumentalisation). In particular, we propose to re-conceptualise the notion of quality of textbooks by introducing two dimensions for analysis: connectivity; and coherence of textbooks. Based on our analysis, we argue that (1) the “expert book” is of “didactic quality”, albeit static and oriented towards an “instrumentation usage”; whereas (2) the “teacher collective book” was of “dynamic quality” oriented towards processes of “instrumentalisation”. Keywords: Documentational approach to didactics, textbook coherence, textbook design, textbook connectivity, textbook quality. Résumé Dans de nombreux pays, les manuels scolaires restent en mathématiques des ressources centrales pour les professeur ; toutefois ils connaissent d’importantes évolutions liées au numérique. Nous étudions ces évolutions et leurs conséquences, en ce qui concerne la conception de manuels, avec une perspective d’approche documentaire. Nous proposons de re-conceptualiser la notion de qualité des manuels, en introduisant deux dimensions : la connectivité et la cohérence des manuels. Nous avons retenu deux manuels français pour la classe de 6e, l’un conçu par un petit groupe d’experts (Hélice) et l’autre par une large équipe de professeurs (Sésamath). Nous appliquons à ces manuels nos propositions théoriques, et illustrons par leur analyse (en retenant en particulier le thème de « l’aire ») le type de phénomènes que l’on peut identifier en termes d’instrumentalisation et d’instrumentation ; de connectivité, de cohérence et de qualité des manuels. Nous montrons que le manuel conçu par des experts est d’une plus grande qualité didactique, mais statique, et tourné vers l’instrumentation pour les utilisateurs, tandis que le manuel conçu par un collectif de professeurs est d’une qualité dynamique et tourné vers l’instrumentalisation. Mots-clés: Approche documentaire du didactique, cohérence des manuels scolaires, conception des manuels scolaires, connectivité des manuels scolaires, qualité des manuels scolaires.

Ammonia concentration and fluxes were measured above a growing triticale field for two months during May and June 2010 at the NitroEurope crop site in Grignon (Fr-Gri) near Paris, France. The measurement campaign started 15 days following a 40 kg N ha−1 application of an ammonium nitrate solution. A new mini-wedd (Wet Effluent Denuder) flow injection analyser with three channels (ROSAA, RObust and Sensitive Ammonia Analyser) was used to measure NH3 fluxes using the aerodynamic gradient method. The measured ammonia concentrations varied from 0.01 to 39 μg NH3 m−3 and were largely influenced by advection from the nearby farm. The ammonia fluxes ranged from –560 to 220 ng NH3 m−2 s−1 and averaged –29 ng NH3 m−2 s−1. During some periods the large deposition fluxes could only be explained by a very small surface resistance, which may be partly due to the high concentrations of certain acid gases (HNO3 and SO2) observed in this suburban area. Ammonia emissions were also observed. The canopy compensation point Cc was around 1.5 μg NH3 m−3 on average. The canopy emission potential Γc (Cc normalised for the temperature response of the Henry equilibrium) decreased over the course of the measurement campaign from Γc = 2200 to Γc = 450, the latter value being close to the median stomatal emission potential (Γs) and lower than the median ground emission potential (Γg) for managed ecosystems reported in the literature. The temporal dynamics of the measured NH3 flux compared well with the Surfatm-NH3 model using fitted parameters. The subjectivity of the model fitting is discussed based on a sensitivity analysis.

Mathematics didactics invites to consider inquiry-based teaching as a particular form of didactic contract, leaving an important responsibility to the students, regarding the knowledge at stake and its evolution in class. Does the use of technology support the development of such a contract? Under which conditions, concerning the mathematical situations, or the role of the teacher, or the use of technology? In this article, we discuss these questions, drawing on the literature, and on different research projects concerning mathematics at secondary school. We analyze the contract, considering how the teacher and the students share the responsibility concerning three dimensions: posing initial questions, producing answers, advancing knowledge.