Ons Oueslati
email: ons.oueslati@ba.irsa.cnr.it

A M De Girolamo

A Lo Porto

A Abouabdillah
email: aziz.abouabdillah@ba.irsa.cnr.

Trend detection in river runoff across Mediterranean river basins: evaluation of results from Moroccan case study

Keywords: Trend analysis, streamflow, Mann-Kendall, LOWESS, Morocco

Trend detection in river runoff across Mediterranean river basins: evaluation of results from Moroccan case study

Ons Oueslati, Anna Maria de Girolamo, Antonio Lo Porto, Aziz Abouabdillah

INTRODUCTION

Within the climate change debate, the subject of trend detection in hydrologic data has received greater attention during the last decades. Particularly, identification of trends in long term runoff is one of the important themes in hydrologic science (NRC, 1991). The reason is that the longterm runoff analysis is an important tool for detecting any modification in hydrological systems [START_REF] Chang | Comparative streamflow characteristics in urbanizing basins in the Portland Metropolitan Area, Oregon, USA[END_REF]. Trends in historic streamflow series might be caused by anthropogenic influences in the catchment, e.g. river regulation, dam construction or irrigation. Another reason for trends is climatic change. According to the most recent IPCC report (IPCC, 2007), annual average river runoff is projected to increase by 10-40 % at high latitudes and in some wet tropical areas, and decrease by 10-30% over some dry regions at mid-latitudes and in the dry tropics by midcentury. There is also high confidence that many semi-arid areas (e.g. the Mediterranean Basin, western United States, southern Africa and north-eastern Brazil) will suffer a decrease in water resources due to climate change (IPCC, 2007). Mediterranean-type ecosystems is likely to be especially affected by climate change because of reduction in rainfall (IPCC, 2007). Future climatic changes may have substantial impact on river discharge patterns, as well as on extreme events, their magnitude and probability of occurrence [START_REF] Krasovskaia | Frequency of extremes and its relation to climate fluctuations[END_REF]. River discharge time series have been extensively studied worldwide. For example, Svensson et al.

MATERIAL & METHODS

Study area

Trend analysis was done to a group of six flow gaging stations in Morocco (Figure 1). Annual and monthly mean flows time series were provided from the database of the Global Runoff Data Centre (GRDC) in Koblenz, Germany. The period of analysis is from 1960 to 1987. The selected stations (Table 1) belong to large important rivers in Morocco. These river basins are characterized by a semi-arid climate. The hydrological regime in these regions is then quite specific due to the high variability of rainfall regime. The differences between low and high water discharges can be extreme. This presents a major difficulty for the monitoring of rivers as well as for the analysis of the rainfall-runoff processes [START_REF] Drobinski | HYdrological cycle in the Mediterranean EXperiment (HYMEX). Towards a major field experiment in 2010-2020[END_REF]. Then hydrologic records remain sparse in semi-arid areas which handicap long-term trend studies in hydrologic data.

Rescaled Cumulative Departures

The rescaled cumulative departures of the monthly mean streamflow at each streamflow site were computed as the cumulative sum of the differences between the monthly value and the monthly mean for the period of record, divided by the monthly standard deviation for the period of record [START_REF] Garbrecht | Visualization of trends and fluctuations in climatic records[END_REF], the values are dimensionless. This procedure allows fluctuations and trends in flow to be visualized and was used to identify extended wet and dry periods and to compare general trends among the streamflow sites. Periods of negative slope indicate periods of monthly streamflow which are less than the mean; periods of positive slope indicate greater than normal streamflow conditions. The steepness of the slope indicates the magnitude of the deviations from normal conditions. Periods of relatively small changes in the rescaled cumulative departures, whether the slopes are positive or negative, indicate periods of near normal flows.

LOWESS technique

LOWESS is a locally weighted scatterplot smoothing [START_REF] Cleveland | Robust Locally Weighted Regression and Smoothing Scatterplots[END_REF]. LOWESS is a data analysis technique for producing a "smooth" set of values from a time series which has been contaminated with noise. LOWESS is useful in identifying trends in highly variable time-series data. This technique was used to smooth the monthly flows and to further identify possible trends. The degree of smoothing can be controlled by varying the value of the smoothness factor, f, which reflects the size of the window used to compute a value on the LOWESS curve [START_REF] Helsel | Statistical Methods in Water Resources[END_REF]. The smoothness factor can range from 0.01 to 0.99. Higher value of this factor means a larger window size resulting in smoother fitted curves but at the expense of loss of detail.

Mann-Kendall test

The Mann-Kendall trend test [START_REF] Mann | Non parametric tests against trend[END_REF][START_REF] Kendall | Rank Correlation Methods[END_REF] is one of the widely used non parametric tests to detect significant trends in time series. The Mann-Kendall trend test, being a function of the ranks of the observations rather than their actual values, is not affected by the actual distribution of the data and is less sensitive to outliers. On the other hand, parametric trend tests, although more powerful, require the data to be normally distributed and are more sensitive to outliers [START_REF] Hamed | Trend detection in hydrologic data: the Mann-Kendall test under the scaling hypothesis[END_REF]. The Mann-Kendall test, as well as other non parametric trend tests, is therefore more suitable for detecting trends in hidrological time series, which are usually skewed and may be contaminated with outliers [START_REF] Hamed | Trend detection in hydrologic data: the Mann-Kendall test under the scaling hypothesis[END_REF]. The Mann-Kendall trend test is based on the correlation between the ranks of a time series and their time order. For a time series X= (X1, X2, X3, ….., Xn), the test statisticis given by:

∑ < = j i ij a S (1)
where 1

( ) ( )= - = - = R R sign x x sign a i j i j ij 0 ( 2

a an nd d R Ri i a an nd d R Rj j a ar re e t th he e r ra an nk ks s o of f o ob bs se er rv va at ti io on ns s x xi i a an nd d x xj j o of f t th he e t ti im me es s s se er ri ie es s, , r re es sp pe ec ct ti iv ve el ly y. . C Co on ns si id de er ri in ng g H H 0 0 t th he e n nu ul ll l h hy yp po ot th he es si is s f fo or r t th he e t te es st t w wh he er re e t th he er re e i is s n no o t tr re en nd d i in n t th he e d da at ta a. . I If f t th he e n nu ul ll l h hy yp po ot th he es si is s H Ho o i is s t tr ru ue e, , t th he en n S S i is s a ap pp pr ro ox xi im ma at te el ly y n no or rm ma al ll ly y d di is st tr ri ib bu ut te ed d a an nd d t th he e m me ea an n a an nd d v va ar ri ia an nc ce e o of f t th he e S S s st ta at ti is st ti ic c a ar re e g gi iv ve en n b by y ( (K Ke en nd da al ll l, , 1 19 97 75 5) )

E(S)=0 V 0 = n(n-1)(2n+5)/18
The z-statistic is therefore (critical test statistic values for various significance levels can be obtained from normal probability tables):

z = | S | / V 0 ^0.5
A positive value of S indicates that there is an increasing trend and vice versa.

Linear regression test

This is a parametric test that assumes that the data are normally distributed. It tests whether there is a linear trend by examining the relationship between time (x) and the variable of interest (y).

The regression gradient is estimated by:

( )( ) ∑ - ∑ = = - - = n i n i i i x x y x i y x b 1 2 1 ) (
And the intercept is estimated as:

x b y a - =
The test statistic is:

σ b S = Where ( ) ) 1 )( 2 ( 12 2 1 - - - - = ∑ = n x y n n b a n i i i σ
The test statistic S follows a Student-t distribution with n-2 degrees of freedom under the null hypothesis (critical test statistic values for various significance levels can be obtained from Student's t statistic tables). The linear regression test assumes that the data are normally distributed and that the errors (deviations from the trend) are independent and follows the same normal distribution with zero mean.

RESULTS AND DISCUSSION

Rescaled Cumulative Departures

The rescaled cumulative departures (RDCs) of monthly flows for the selected rivers exhibit the same general patterns for the period of record (Figure 2). For the period 1960-1962 flows were average for all the rivers expect for the Bab Ouender station where flows were greater than average in 1960 and less than average in 1961. From 1962 to 1966 flows were greater than case study -Ons OUESLATI

LOWESS-Smoothed records

The 1960-1987 records of monthly mean flows for the selected stations were smoothed using the LOWESS technique with a smoothness factor of 0.5 to identify trends in monthly streamflows (Figure 3). LOWESS-smoothed monthly mean flows have the same general pattern for the period of record. Flows exhibited a generally decreasing trend which is more obvious from early 1970s. However, a net increasing trend can be observed in the second half of the 1960s particularly in: Pont du Mdez, Bab Ouender and Azib Soltane stations.

Trends in annual runoff

The Mann-Kendall trend test and linear regression analysis were used to determine if a statistically significant monotonic trend was present in annual mean flows (Tables 2 and3).

Long-term annual runoff trend using both statistics showed that all stations have a statistically significant decreasing trend at 5% and 1% confidence level expect for the Ourtzagh station where the linear regression analysis suggests that there is a decreasing trend at 10% siginificance level.

CONCLUSIONS

Identification of changes in streamflow records is challenging. As presented in this work a set of different procedures can be used to search for changes in streamflow conditions. The rescaled cumulative departures time series of monthly flows exhibit a long drought starting from 1980 to 1987 in all sites. LOWESS-smoothed monthly mean flows have the same general pattern during the period of record . Flows exhibited a generally decreasing trend which is more obvious from early 1970s. Statistical testing using the Mann-Kendall test and linear regression analysis show a significant decreasing trend in annual runoff.

Figure 1 :

 1 Figure 1: Location of streamflow stations

  this period, the RCDs present steep slopes reflecting high magnitudes floods. From 1966 until April 1967 flows were less than normal in all the stations. From Mai 1967 to mid 1972 flows were greater than average as indicated by the positive slope in the RDCs (Figure2). From autumn 1972 until late 1975 flows were average or less than average. Then a new wet period is observed until mid 1976. From Summer 1976 until 1980, different pattern can be observed. Finally the period 1980-1987 was one of less-than-normal runoff. This drought appears to have been the longest on record) at all sites.

Figure 2 :

 2 Figure 2: Recaled Cumulative Departures of montlhly mean streamflow, 1960-1987

  (2005) studied trends in 21 stations worldwide with flow records of up 100 years, while[START_REF] Kundzewicz | Trend detection in river flow series: 1. Annual maximum flow[END_REF] studied trends in 195 worldwide daily flow time series.

	8th World Wide Workshop for Young Environmental Scientists WWW-YES 2009: Urban waters: resource
	or risks? (2-5 June 2009)
	2 2 / / 8 8

Table 1 : Streamflow stations used in analysis

 1

	grdc_no	River	Station	Area	Altitude
				Km 2	m
	1308110	ANSGEMIR	ANSEGMIR	960	450
	1308600 MOULOUYA DAR EL CAID	24422	325
			AZIB
	1309700	SEBOU	SOLTANE	17250

LOWESS-Smoothed plots of monthly mean flow, 1960-1987

	Trend detection in river runoff across Mediterranean river basins: Evaluation of results from Moroccan
			case study -Ons OUESLATI
	Figure 3:
	Wet	Dry	Wet	Wet
				Dry
				Line of zero cumulative
				departure
			7 7 / / 8 8

Table 2 : Mann-Kendall trend test results

 2

	Station	Test statistic	Critical values (Statistical table)	Result
			a=0.1	a=0.05	a=0.01
	Anzegmir	-3.095	1.645	1.96	2.576	S (0.01)
	Dar El Caid	-2.498	1.645	1.96	2.576	S (0.05)
	Azib Soltane	-3.433	1.645	1.96	2.576	S (0.01)
	Ourtzagh	-1.962	1.645	1.96	2.576	S (0.05)
	Pont du Mdez	-2.34	1.645	1.96	2.576	S (0.05)
	Bab Ouender	-2.087	1.645	1.96	2.576	S (0.05)

Table 3 : Linear regression analysis results

 3

	Station	Test statistic	Critical values (Statistical table)	Result
			a=0.1	a=0.05	a=0.01
	Anzegmir	-3.155	1.703	2.052	2.771	S (0.01)
	Dar El Caid	-2.896	1.699	2.045	2.756	S (0.01)
	Azib Soltane	-3.668	1.703	2.052	2.771	S (0.01)
	Ourtzagh	-1.916	1.69	2.031	2.727	S (0.1)
	Pont du Mdez	-2.654	1.696	2.04	2.745	S (0.05)
	Bab Ouender	-2.134	1.689	2.029	2.722	S (0.05)

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Denis Gillet
email: denis.gillet@epfl.ch

Sandy El Helou

Marie Joubert

Rosamund Sutherland
email: ros.sutherland@bristol.ac.uk

Science 2.0: Supporting a Doctoral Community of Practice in Technology Enhanced Learning using Social Software

Introduction

The STELLAR European network of Excellence (NoE) (http://www.stellarnet.eu) represents the effort of leading European institutions and projects in Technology Enhanced Learning (TEL) to unify their diverse and sometimes fragmented community. The Network is executed via a series of integration instruments designed to increase the research capacity of European TEL at all levels. One level is that of early career researchers, and in particular doctoral candidates, who are seen as key in establishing sustainable research capacity in TEL.

This paper focuses on the ways in which STELLAR supports doctoral candidates through the establishment of a Doctoral Community of Practice (CoP) in Technology Enhanced Learning as a STELLAR doctoral integration instrument for the doctoral stakeholder community. This TEL Doctoral CoP (DoCoP), officially established in Autumn 2009, is also instrumental in bringing together actors of engineering education research in academic institutions, as proposed in the USA by Streveler [START_REF] Streveler | Enhancing engineering education research capacity through building a community of practice[END_REF]. The paper discusses possible ways in which the DoCoP could be developed through the innovative use of Web 2.0 technologies, by outlining the characteristics of one such technology and describing the ways in which an imaginary PhD candidate might use the technology in their PhD journey.

Doctoral Community of Practice in TEL

In STELLAR a high priority is given to PhD candidates, i.e. early career researchers conducting their PhD research in higher education institutions and typically being enrolled in a doctoral program. PhD education is a key issue for strengthening TEL research, shaping the domain and preparing the next generation of researchers and TEL entrepreneurs. This is especially true in European countries where the majority of PhD candidates, particularly those involved in the more technical aspects of TEL, move immediately to companies after graduation. As such, the integration of PhD candidates into STELLAR creates the conditions for the long-term sustainability of TEL research and TEL impact on the economy.

The first instrument to support the doctoral community in TEL is the STELLAR Doctoral Academy, which includes selected face-to-face events that bring the community together for doctoral courses, workshops and seminars. Such events typically last between a few days and one week. The organized workshops and lectures focus on theoretical, methodological and technological issues of relevance to TEL research (for example activity theory, embodied cognition, individual, social & organizational learning processes, human computer interaction, Web mash-up, adaptive and personal learning environments, as well as knowledge and competence management). Organization committees can apply to get an event sponsored by STELLAR. Upon acceptance, the sponsorship acts as a quality label (STELLAR accreditation) recognizing excellence and attracting participants who may be awarded STELLAR scholarships for participation. Sponsorships are granted to events gathering the top experts in the field and showing a high potential for the integration of the multidisciplinary and multicultural TEL community. Experts, PhD advisors and PhD candidates meet in such events that rely on Science 2.0 infrastructure to be established and for sustaining further interaction between the participants. Science 2.0 infrastructure stands for Web 2.0 solutions applied for scientific purposes and enabling interaction between peers, as well as sharing of resources offered by the community for the community.

The second instrument is the Doctoral Community of Practice (DoCoP). Its purpose is to bring or keep together PhD candidates working on TEL research, offering them opportunities to share, discuss, and receive feedback on their research by peers and experts. In this respect, as the doctoral candidates ('newcomers') interact with each other and with expert researchers ('oldtimers'), they are learning how to become TEL researchers [START_REF] Lave | Situated Learning, Legitimate Peripheral Participation[END_REF]. As Wenger [START_REF] Wenger | Communities of practice: a brief introduction[END_REF] has explained, a community of practice has three characteristics, firstly a shared domain of interest (in this case TEL research), secondly a community in which members interact and learn from each other, and thirdly the practice "members of a community of practice are practitioners). They develop a shared repertoire of resources: experiences, stories, tools, ways of addressing recurring problems-in short a shared practice. This takes time and sustained interaction". The DoCoP is supported by an on-line platform specifically designed for exchanges between doctoral candidates and researchers in the TEL field as part of the STELLAR Science 2.0 portal. The STELLAR Science 2.0 portal is presented in Section 3 below. A social software that could be integrated in the portal as an interaction space for the DoCoP is introduced in Section 4 and detailed in Section 5.

In creating and sustaining a doctoral community, the DoCoP has the potential to support doctoral candidates in three key ways. First, it can support researchers who may feel isolated, who work in small labs without a critical mass of PhD candidates or without staff with interdisciplinary skills, by integrating them into the STELLAR community in particular, and the TEL community in general. Second, the DoCoP could also serve as a platform for doctoral candidates and their advisors to find informal or formal co-advisors or jury members for the PhD thesis. Third, it is possible that, through engaging in the DoCoP, PhD candidates will be able to identify key research groups and companies whom they might want to visit as part of a mobility programme brokered by STELLAR. Such visits will help doctoral candidates to integrate collaborative research or testbed validation in their PhD thesis, and will also contribute to STELLAR's aim of developing capacity beyond institutional boundaries.

STELLAR Science 2.0 Framework

STELLAR adopts the perspective that in establishing effective communities of practice and stronger research communities in TEL, mutual learning of the participants is enhanced by supporting knowledge sharing and facilitating the advancement of one's own competences and knowledge while researching in TEL. In order to scaffold these processes, STELLAR uses the STELLAR "Science 2.0" concept which federates a variety of communication channels to ease internal exchanges within the scientific STELLAR network as well as beyond it to reach the general TEL community. These communication channels also aim to make research results known to the European and international TEL community. STELLAR opens its framework and instruments to interlink with relevant scientific communities and people, and to support knowledge construction within the TEL research area. For this purpose, it aims at providing efficient access to the research outcomes of colleagues and peers in one's own and related disciplines, using Web 2.0 approaches that leverage the links between people as well as the links between documents, using a combination of pull and push techniques.

The STELLAR Science 2.0 portal is grounded within the context of the above objectives, integrating Web 2.0 tools, services and social software publically available or offered by the STELLAR community members. The Web of the second generation adds collaboration and communication mechanisms to scientific research resources by designing and implementing tools to support, follow and track discussions, argumentations and the whole history of a process which participates in the building of science. Blogs, forums, Wiki-pages and RSS feeds have become popular means for lightweight exchange, discussion and syndication of knowledge and opinions. Advanced TEL-oriented social networking or communication tools will be integrated together with analysis tools that will enable evaluation of the usage of the portal and the evolution of the community.

As mentioned in Section 2, the doctoral stakeholder community and its related doctoral community of practice are central to reducing fragmentation of research in technology enhanced learning in Europe. As a consequence, special components of the Science 2.0 portal have to be designed and dedicated to the DoCoP. These components aim at virtually complementing and sustaining interaction between face-to-face events such as TEL doctoral schools, workshops, and doctoral consortia.

An informal survey carried out during the 2009 Joint Summer School on TEL (a doctoral event sponsored by STELLAR) has demonstrated that the doctoral community members in TEL use a huge variety of tools, resources and repositories. It has also highlighted the needs for better integration and sharing in contexts and on purposes. STELLAR does not aim to create an additional tool to meet this need, but to adapt solutions developed in previous European projects to integrate in a space of the Science 2.0 portal all the digital and social ingredients of a successful PhD recipe in TEL. For example, the Graaasp social software developed for supporting Communities of Practice in the framework of the European PALETTE research project under the eLogbook name appears to fulfill simultaneously the need to have a single aggregation place for global resources and to have a unique personalization mean to organize such aggregated resources by contexts and by purposes. In addition, Graaasp also supports workflow management as requested when implementing and conducting doctoral school events or visits supported by mobility scholarships. It may be that STELLAR will adapt this software for use by the DoCoP. The remainder of this paper explores how Graaasp might fit with STELLAR's agenda.

Constructing a Web 2.0 DoCoP interaction space

Successful Web 2.0 solutions result from the implementation of a proper participatory design approach and also from the recognition that the Darwin theory of evolution applies to them. In other words, only the Web 2.0 tools and services (species) that fit to the environment (user's contexts, expectations, and adoption thresholds) can survive and spread. They spread thanks to mass adoption, open source licensing, shared features or APIs (as the DNA of the best individuals).

Preliminary participatory design results can be derived from the analysis of the practice in the target community; in our case the community of PhD candidates and advisors in TEL. The objective is to define and construct an interaction space (component) of the Science 2.0 portal for supporting the DoCoP, as well as to improve the features of the Graaasp social software, which is a candidate solution as Web 2.0 DoCoP interaction space. The robustness of the Science 2,0 portal to the natural evolution of the Web 2.0 solutions is not considered here. It is supported practically by relying on standards and choosing solutions as open as possible, either for being integrated as component or feeds in other platforms, or for integrating other components or feeds. In effect, in the Web 2.0 realm, people and platforms are simultaneously consumers and providers.

For design purpose in our Science 2.0 context, it is important to reflect on the practice of PhD candidates in TEL, in terms of social networking, communication and online resources. As a seed for reflection, one can ask if PhD research in TEL is different from PhD research in general, and, if yes, in what sense and what are the consequences in terms of practice. There are at least two distinctive features of TEL research. First, its youth and second its interdisciplinary nature.

One impact of the youth of TEL research in terms of practice is that it is difficult to find and to assess relevant scholarly resources and experts. Workshops, conferences and journals are not yet fully established, indexed and recognized; thus putting more burden on the candidates' shoulders and their communities to point out relevant material of good quality. In view of this difficulty, the STELLAR Science 2.0 portal should direct PhD candidates towards the proper scholarly places to find references and also to publish their work. As a matter of fact, collaborative recommendation driven by the TEL community through the portal should give access to the most relevant scientific contributions in the field. Also, best practices on what a PhD thesis in TEL is have still to be fully established. The portal should point to all published PhD thesis in TEL and enable interaction and communication with TEL researchers, TEL experts, TEL PhD advisors, and TEL Research Alumni.

The impact of the interdisciplinary nature of TEL research is quite deep [START_REF] Pallas | Preparing Education Doctoral Students for Epistemological Diversity Educational Researcher[END_REF]. First of all, it is still difficult to carry out research tagged as TEL in most academic institutions. Moving from "Thesis in Computer Science with Application to TEL" or "Thesis in Education with Application to TEL" towards "Thesis in TEL with Application to … Education in Computer Science (as example)" requires the full leveraging of the TEL research community. In that sense, supporting a strong visibility of the DoCoP senior and successful faculty members through the STELLAR portal is instrumental to enabling high-level PhD research in TEL. As TEL research requires multidisciplinary competences infrequently owned by a single individual, the role of the community as a coach to PhD advisors can be seen as stronger in TEL than in other research fields. This shows again the importance of supporting the DoCoP properly and highlights the importance of interaction in the community, as well as peer or expert recommendation, possibly supported through the Science 2.0 portal.

Research in TEL is a niche that can be expanded considering the closeness between TEL and modern knowledge management practices. Currently, as a niche, in most institutions there is not the critical mass to establish a doctoral program in TEL. As a matter of fact, we claim that it should be avoided to fully build on the interdisciplinary nature of TEL. Hence, the DoCoP and the STELLAR science 2.0 portal should enable the operation of a virtual, distributed and informal doctoral program in TEL. This should integrate the existing face-to-face doctoral events only accessible to a subset of the DoCoP members and the associated resources. This program should be informal in the sense that it should not be built as a competitor of institutional programs, but as an additional resource for which the client institutions should grant ECTS credits themselves. Associated resources offered through the STELLAR Science 2.0 portal include pointers to YouTube or FlashMeeting videos of talks, seminars and lectures, as well as the associated slides and handouts available for example on SlideShare, where they can be tagged and rated.

The Graaasp Web 2.0 social software and an imaginary PhD journey through it

The Graaasp social software envisioned as an interaction space for the DoCoP can be described as a Web 2.0 application that can serve simultaneously as an aggregation, contextualization, discussion, and networking platform, a shared asset repository, as well as an activity management system.

Graaasp is built on the 3A interaction model [START_REF] El Helou | Software for Sustaining Interaction, Collaboration and Learning in Communities of Practice[END_REF] which is particularly focused on describing and designing social and collaborative environments. It was developed in the framework of the Palette European Project (http://palette.ercim.org/) following a participatory design approach: interviews and questionnaires with communities of practice such as Learn-Net, Doctoral Program Lancaster, InCorPorate and Adira helped identify their needs and translate them into design requirements. The 3A model accounts for three main constructs or entities: Actors are entities capable of initiating an event in a collaborative environment. They can be humans as well as virtual agents. Actors create collaboration spaces where they conduct Group Activities to reach specific objectives. In each of these activities, actors can take different roles, each of which consisting of a label and an associated set of rights. Furthermore, Actors produce, edit, share and annotate Assets in order to meet activities objectives. Assets can consist of simple text files, RSS feeds, wikis, videos or audio files. In addition, an activity can possibly have a well-defined planning of expected assets with concrete submission and evaluation deadlines, predefined evaluators and submitters. This is particularly useful in project-based learning communities and online educational environments. The model accounts for Web 2.0 features: entities can be tagged, shared, commented, linked together and rated. By design, Graaasp can serve not only as a networking platform, a repository of assets and an activity management system, but also as an aggregator bringing together content and services from other Web 2.0 applications. Internal tracking and notification features enable Graaasp to provide awareness to users on ongoing activities and participation.

To understand the potential role of Graaasp in enhancing the learning experience of PhD candidates in TEL, their interaction with one another as well as with senior researchers, we examine a scenario about an imaginary person, namely Pat, who has just started her PhD in the TEL field. Pat is invited by her PhD advisor and/or colleagues to register to Graaasp. Just like any other Web 2.0 social software, Graaasp has a low entry barrier; registration only requires a valid email and a password, or an OpenID. With time, Pat's profile can be gradually built up.

As initial action, Pat types in the search field "trust and reputation in Web 2.0 applications", which will be the subject of her thesis. As a response, the system relies on content and linked-based analysis techniques to propose a list of relevant group activities, assets and actors. For example, Graaasp proposes a LinkedIn group entitled "Trust & reputation in Web 2.0". Pat decides to join the group. Consequently, Graaasp uses the LinkedIn application programming interface (API) to send an adequate Web service request on her behalf. As assets, the system returns relevant documents, archived discussions threads saved and annotated in Graaasp, embedded YouTube videos such as conference talks on trust and reputation in Web 2.0, external papers from the IEEE and ACM digital libraries and the STELLAR open archive (http://www.telearn.org), as well as aggregated new feeds relevant to Pat's query. It also recommends a list of actors that are keen on the requested topic, ordered by relevancy and reputation. Actors include appropriate PhD candidates and senior researchers that are already Graaasp users, as well as external people that have written relevant papers and/or participated in relevant group activities. For actors who are logged in to Graaasp, the system shows presence awareness to encourage interaction. Since actors do not only consist of people but also of agents and tools, Graaasp also suggests to Pat useful online systems related to TEL. The system also asks Pat if she wishes to be notified about the creation of any new activities and assets relevant to "Trust and Reputation in Web 2.0". Pat responds in the affirmative.

In the mean time, a professor from Germany creates a group space called "Privacy, trust and reputation challenges in Web 2.0" in order to conduct collaborative activities related to the subject. The activity space is public and anyone can become a member. Pat is notified of the creation of the space, and decides to join it. She takes the role "PhD candidate". Her membership is announced to other members. Another senior "PhD candidate" takes the initiative of opening a conversation with her and gives her hints on how to start learning about the field as well as references to assets (i.e. discussions, papers, online course notes) and group activities that can best introduce to the field. They also speak about the PhD process in general. Seeing that the discussion is interesting, Pat decides to save it as an asset, post it in the activity space and tag it "tips for beginners", "TEL", "PhD in TEL". It will serve as a reference to her and other new PhD candidates. Afterwards, Pat is notified of the creation of a new sub-activity space within "Privacy, trust and reputation challenges in Web 2.0" dedicated to a summer school whose topics and application process are described in the space wiki. A plan for expected assets is created, specifying submission and evaluation deadlines. By a simple click, Pat downloads the submission deadline to her calendar. She intends to work hard to be able to develop her knowledge in the field, submit a position paper and eventually participate in the summer school.

After a discussion with Pat, her thesis advisor decides to create an activity in Graaasp that helps his candidate progress her PhD in TEL and facilitates follow-up. They define for this activity a plan of expected assets. First, Pat is expected to read material related to TEL, raise and discuss the challenges that she thinks are important to consider and solve. These discussions are to be submitted as assets for the thesis advisor. Once the submission is done, the advisor is notified by the system. He then reviews and comments the submitted asset before a scheduled face-to-face meeting. After the meeting, Pat uploads minutes of meeting report and links it to the asset that triggered the discussion.

It is worth mentioning that the system allows users to enforce an order in the submission and evaluation of expected assets. This means, for example, that the research plan cannot be submitted before the submission and the successful evaluation of the asset discussing TEL challenges. Some time later, and always with respect to her PhD progress, Pat types in the search field "PhD dissertation". Graaasp proposes AWSOME Dissertation, an online project that other users have registered as a tool and tagged with the keywords "PhD dissertation" [START_REF]Academic Writing Empowered by Social Online Mediated Environments[END_REF].

Last but not least, as Pat uses Graaasp more regularly and visits other actors' profiles, she starts seeing the added value of completing her own profile information. She fills in information related not only to her academic background and current position, but also to the skills and competencies that she already has and the ones that she aims to acquire or develop. Pat also augments the profile of other actors she interacted with by giving personal feedback through comments and ratings. As is the case for tags, the system suggests skills and competencies that have already been added by other actors, to Pat. This helps her discover skills worth developing, build a common TEL vocabulary, and/or reach people with similar learning objectives. As Pat's profile is gradually completed, and as she uses the collaboration platform more frequently, the recommendations rendered by the system become more and more personalized. As a matter of fact, as the system suggests resources, actors and group activities to Pat depending on her working context, it draws on information about Pat's previous interactions to discover her preferences, her trusted network of actors, and the kind of actors, resources and group activities that are best fitted to her learning needs and goals.

Figure 1 below provides a mock up of the Graaasp interface, showing with a large orange banner and as current context the activity created by Pat. It is entitled "Pat's PhD Research Follow up" (central left-hand side) and integrates a wiki with the description of the activity and a field for free comments that could be added by users having sufficient rights to access it. The current context is selected from the Favorites or the Clipboard area by clicking on the desired color rectangle. It could also be chosen among the results of a search query. Once an entity is selected as current context, related personal entities explicitly associated to the current context by the user are automatically displayed in three dedicated columns (central right-hand side). Hence, Graaasp can be seen as a contextual browser showing in a single screen all the relevant information aggregated by the user in the current context. Feeds relevant for Pat's PhD research are only visible in this context, not in her other space dedicated to the theatric performance she is organizing with friends. In addition to these preselected entities, recommendation of external ones can be provided taking into account their existing relations with the current context and their relative importance in it (bottom left-hand side) [START_REF] El Helou | The 3A Contextual Ranking System: Simultaneously Recommending Actors, Assets, and Group Activities[END_REF]. By clicking on any rectangle, the user automatically trigger a change in context and all the interface components are updated. New relations can be created by dragging and dropping entities or by clicking on the relevant grey rectangles.

Concluding remarks

This paper has argued that TEL doctoral candidates have a particular need for support, and has described the structure of STELLAR's organizational commitments to provide this support in the form of doctoral events and a Doctoral Community of Practice (DoCoP). It further argued that the DoCoP should support its members through mutual learning and knowledge building, introducing the Graaasp social software, and explaining through an illustrative example how Web 2.0 features could be used to meet the aims of the DoCoP.

As a matter of fact, supporting a Doctoral Community of Practice (DoCoP) in Technology Enhanced Learning (TEL) is more a question of pointing to the right resources, services and people from a single place than a question of platform and technology. However, because of the large set and the variety of the digital assets and online communities involved, the way these entities are integrated plays a key role for adoption, appropriation and identification. In effect, building a strong community identity is also a must to position TEL in the worldwide research arena and to strengthen exchange in its multidisciplinary community. A single Web 2.0 interaction space bringing together the most relevant people and resources is instrumental in that perspective.

We believe that Graaasp, or similar social software, could provide an online environment that would support doctoral candidates and would provide the 'space' where the members of the DoCoP would interact, building on their relationships initiated and consolidated at face-to-face doctoral events. We believe it is important to work towards developing this software so that it becomes the first choice of the members of the DoCoP, so that the space becomes well populated with group activities, actors and assets. We recognize, however, that populating such a tool depends on the commitment of the individuals involved and perhaps the greatest challenge for the STELLAR network is to encourage committed doctoral candidates and academics (such as their supervisors) to 'get the ball rolling'. We suggest that once the 'ball is rolling', the value of the tool will grow and be recognized by all individuals in the DoCoP, in STELLAR and in the network of stakeholders.

Figure 1 .

 1 Figure 1. Recent Mock-up of the Graaasp interaction space.

Acknowledgements

This paper integrates parts of the STELLAR project description with contributions from (in alphabetic order) of N. Balacheff, S. Barnes, R.M. Bottino, D. Burgos Solans, U. Cress, P. Dillenbourg, E. Duval, F. Fischer, D. Gillet, E. Herder, B. Kieslinger, M. Kravcik, S. Lindstaedt, W. Nejdl, M. Ney, P. Scott, M. Sharples, H. Spada, M. Specht, R. Sutherland, P. Tchounikine, C. Windrum, and K. Wodzicki. The STELLAR project is partially funded by the Seventh Framework Programme for Research and Technological Development (FP7) of the European Union in Information and Communication Technologies.


V Singh

A K Mittal
email: akmittal@civil.iitd.ernet.in

Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of Okhla Landfill, Delhi

Keywords: Landfill leachate, contaminants, acute toxicity, bioassay, public health

Uncontrolled landfilling is predominant in developing countries like India. Leachate generated from these landfills contains variety of contaminants, which even at trace levels can cause health problems of unknown dimensions and magnitude. Unchecked release of these leachates into the environments poses a substantial risk to the origins of potable water. Toxicity analysis can be used as an important tool to assess the leachate contamination potential. In the present study, Okhla municipal landfill leachate was subjected to acute toxicity tests using fish bioassay. The toxicity varied substantially with time of sampling. The leachates were found to be highly toxic to the test organisms, indicating significant risk to public health. Results from this study, demonstrate the importance of conducting such toxicity tests to assess the potential impact of a pollutant discharge on aquatic resources and demand for the proper management of solid waste in Delhi.

INTRODUCTION

In developing countries like India, landfilling is the most commonly practiced form of municipal solid waste (MSW) disposal due to its economic advantages. However, the leachate arising from such landfills is now being recognized as a potential health risk to both surrounding ecosystems and human populations.

Delhi, capital of India, generates approximately 7,000 metric tons of MSW daily. The monthly production of leachate has been estimated to be 81.5 m 3 [START_REF] Kumar | Threat to the Groundwater from the municipal landfill sites in Delhi[END_REF]. At present, there are three landfill sites in Delhi -Bhalsawa, Gazipur and Okhla (Figure 1). All the three are unlined and fall under the category of uncontrolled solid waste disposal facility. The leachate generated mostly percolated down the ground surface and the excess quantity gets collected in some low lying areas and sometimes gets mixed up with sewer and drainage systems thereby polluting ground water and surface water sources. A number of incidences have been reported in the past where leachate had contaminated the surrounding soil and polluted the underlying ground water aquifer or nearby surface water [START_REF] Mor | Leachate characterization and assessment of groundwater pollution near municipal solid waste landfill site[END_REF][START_REF] Zafar | Landfill runoff and its effects on river water quality[END_REF].

Around 30 % of population in Delhi watershed depends upon groundwater. Due to the presence of toxic constituent in leachate, its unchecked release into the environment poses a substantial risk to local resource users. Research has shown that many leachates do contain toxic and sometimes carcinogenic compounds [START_REF] Baun | Toxicity testing of organic chemicals in groundwater polluted with landfill leachate[END_REF][START_REF] Brown | An estimation of the risk associated with the organic constituents of hazardous and municipal waste landfill leachate, Hazard, Waste Hazard[END_REF] studies have shown that leachate from a municipal solid waste landfill can be more toxic than leachate from hazardous waste landfill [START_REF] Brown | An estimation of the risk associated with the organic constituents of hazardous and municipal waste landfill leachate, Hazard, Waste Hazard[END_REF][START_REF] Clement | Estimation of the hazard of landfills through toxicity testing of leachates. 1. Determination of leachate toxicity with a battery of acute tests[END_REF][START_REF] Schrab | Acute and genetic toxicity of municipal landfill leachate[END_REF]. Chemical analysis can identify the presence of specific compounds, but the identification is not enough to assess the potential danger [START_REF] Baun | Toxicity testing of organic chemicals in groundwater polluted with landfill leachate[END_REF][START_REF] Clement | Estimation of the hazard of landfills through toxicity testing of leachates. 1. Determination of leachate toxicity with a battery of acute tests[END_REF][START_REF] Cheung | Toxic effect of landfill leachate on microalgae[END_REF]. In addition chemical analysis only detects a small percentage of the toxic compounds present. Bioassay toxicity tests that measure effects on organisms and can detect toxicity even when the contaminants are not identified by chemical analysis. They reflect the cumulative and synergistic effects of all the compounds [START_REF] Baun | Toxicity testing of organic chemicals in groundwater polluted with landfill leachate[END_REF][START_REF] Lambolez | The environmental risks of industrial waste disposal: an experimental approach including acute and chronic toxicity studies[END_REF].

Toxic compounds can have two different effects on living organisms: acute toxicity, which is possible to evaluate in the short term, and chronic toxicity, whose evaluation takes longer since, in this case sub-lethal effects must be analyzed. In this work acute toxicity was studied in the samples of Okhla municipal landfill leachate with a view to determining the degree of pollution and contamination in this wastewater. A freshwater fish Poecilia reticulata (Guppy) was used in the toxicity tests.

MATERIALS & METHODS

Site details

The Okhla landfill site was commissioned in 1996. The waste dumped at this site includes domestic waste, e.g. kitchen waste; paper, plastic, glass, cardboard and cloths; construction waste, and unauthorized industrial waste. A high waste density of 1200 kg/m 3 may be attributed to the high content of construction and demolition waste and inert waste.

Leachate characteristics

The leachate used in the study was collected from the Okhla landfill site, Delhi. The collected leachate was stored in the laboratory at 4 o C for further analysis. The following parameters were employed to evaluate characteristics of leachate: analyzed for Chemical Oxygen Demand (COD), hardness, chloride, ammoniacal nitrogen (NH 3 -N), pH, alkalinity, Total Suspended Solids (TSS), Total Dissolved Solids (TDS), Total Solids (TS) and metals. All analysis was performed in accordance with the Standard Methods for the Examination of Water and Wastewater 20 th Edition (1998).

Analysis of leachate toxicity

Leachate toxicity was determined using static 96-h fish bioassays. Poecilia reticulata, commonly known as guppy fish, was used as test organism. The fish were exposed to varying percentage of the leachate diluted with tap water. Fish mortality was observed at frequent time intervals for the determination of toxicity values. Dead fish were removed immediately from the test vessels. Toxicity was expressed as the leachate concentration (% v/v) that causes death for 50% of fish (LC50). For all the tests LC50 were calculated using the Spearman-Karber method [START_REF] Hamilton | Trimmed Spearman-Karber method for estimating median lethal concentrations in toxicity bioassays[END_REF].

RESULTS AND DISCUSSION

Leachate characteristics

Leachate samples were collected in the month of June and December of the year 2007. Leachate was always collected from two different places of the landfill site. The wide range of values for various parameters presented in table 1 shows, that the characteristics of leachate varied significantly with space and time.

Leachate toxicity

The studies were aimed to assess acute toxicity (96-h LC50) of leachate by estimating the rate of mortality in Poecilia reticulata. Prior to the 96-h toxicity tests, range finding tests were conducted in order to determine the appropriate dilution range for leachate. The leachate collected in the month of December was found to be more toxic with 96-h LC50 less than 3% for L1 (Figure 4) and less than 4% for L2 (Figure 5), compared to the June leachate with LC50 less than 13% for L1 (Figure 2) and less than 12 % for L2 (Figure 3).

Though, toxicological and physico-chemical analysis was done simultaneously, no correlation could be established between leachate toxicity and its physico-chemical characteristics, as reported by previous studies. [START_REF] Clement | The contribution of ammonia and alkalinity to landfill leachate toxicity to duckweed[END_REF][START_REF] Atwater | Experiments using daphnia to measure landfill leachate toxicity[END_REF][START_REF] Cameron | Toxicity of landfill leachates[END_REF]. The toxicity of the complex leachate matrix may be due to the synergetic interaction between the various pollutants. High concentration of heavy metals, organic matter and nitrogen (Table 1) are known to contribute to extreme elevation of toxicity levels in any environment. These classes of compounds are a risk to the ecosystems and public health.

-

96-h LC50 = <4%

Metals in the leachate

Mobilization of heavy metals from the landfill into leachate usually occurs both when hydrated ions are formed and by complexation with organic substrates with low molecular weight (amino acids and sugars), with polymers (fulvic and humic acids), and with colloids of high molecular weight [START_REF] Zoumis | Demobilization of heavy metals from mine waters[END_REF]. Significant amount of heavy metals can also bond with both inorganic and organic particulate matter. These constitute important means for leachate transportation.

In the leachate samples studied, various metals deemed as hazardous to the environment and public health were detected. Lead (Pb), Cadmium (Cd), Chromium (Cr), Nickel (Ni), and Cobalt (Co) have been implicated for various human health problems even at trace levels.

Pb is potentially carcinogenic and its toxic effects on humans can be detected via symptoms originated in the nervous system, such as muscle tremor, convulsions, paralysis, and coma [START_REF] Wang | Health risks of heavy metals to the general public in Tianjin, China via consumption of vegetables and fish[END_REF]. In the present study lead ranged between 0.9-1.5 mg/L. Cd, which was Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of Okhla Landfill, Delhi -Vijaya SINGH and A.K. MITTAL 6 / 8 detected in the range of 0.2-0.3 mg/L, also has been reported to cause agonistic and antagonistic effects on hormones and enzymes leading to lots of malformations like renal damage [START_REF] Lewis | Hazardous chemicals desk reference 2 nd Eds[END_REF][START_REF] Donalson | Trace element toxicity[END_REF]. These two metals have affinity for SH groups in proteins, haemoglobin, enzymes/ hormones [START_REF] Manahan | Toxicological chemistry[END_REF]. Likewise, Ni and Cd are classified as carcinogens [START_REF] Pekey | The distribution and sources of heavy metals in Izmit Bay surface sediments affected by a polluted stream[END_REF]USEPA 1999). Other metals, investigated in this study, were Co, Cr, Zn and Cu, each of which has been reported for various health problems being non-biodegradable and with the possibility of accumulation in the food web [START_REF] Langston | Toxic effects of metals and the incidence of metal pollution in marine coastal ecosystem[END_REF]. Fe and Mn which are commonly detected in water, were also detected in leachate and at very high concentrations. Fe and Ni showed the highest concentrations in all the four leachate samples. Fe ranged between 4-9 mg/L whereas Ni ranged between 1-5 mg/L.

Bioavailability of organic compounds and toxicity

The structure of organic compounds is a determining factor in toxicity analysis. Organonitrogenated substances for instance have a highly polluting potential, especially due to its metabolites, among which is ammonia. High concentrations of ammoniacal nitrogen were detected in leachate (Table 1). Concentrations exceeding 1,000 mg/L could be observed throughout the monitoring period. Studies have shown that municipal landfill leachates do contain high concentrations of organo-halogenated compounds, which can cause great concern since they can persist in aquatic environments and cause bioaccumulation [START_REF] Araujo | Application of toxicity identification evaluation to sediment in a highly contaminated water reservoir in southeastern Brazil[END_REF]. The effects of toxicity of organic compounds on the aquatic organisms as well as humans can range from mortality to hepatoxicity, immunotoxicity, carcinogenicity, and metabolic alterations that can lead to a decrease in the rates of reproduction and other activities [START_REF] Agundiran | Assessment of the physicochemical parameters and heavy metals toxicity of leachates from municipal solid waste open dumpsite[END_REF][START_REF] Araujo | Application of toxicity identification evaluation to sediment in a highly contaminated water reservoir in southeastern Brazil[END_REF][START_REF] Nilsson | Increased reproductive toxicity of landfill leachate after degradation was caused by nitrite[END_REF]. Organonitrogenated compounds as well as heavy metals remain highly toxic, with a high potential of bioavailability, especially when they are water soluble. The pH values and the ion exchange capacity are important factors that interfere with the relation between adsorption and de-adsorption in compounds as it may render the species either more or less available. pH values of leachate were found to be slightly alkaline. These is due to the methanogenic phase of solid waste degradation at the landfill and contribute to reduce toxicity levels since these alkaline values can favor the precipitation of metals by making them less bioavailable (Table 1).

CONCLUSIONS

The toxicity assays of the leachate highlight the high pollution potential of the Okhla landfill leachate. In India there is scant information available on deleterious effects of leachate. Ecotoxicological evaluation of wastewater from such a source is fundamental for assessing the risk posed to environment and public health in municipalities where waste is not adequately treated. Consequently, it is absolutely necessary to introduce the monitoring of toxicity of leachates flowing from municipal landfills. Presence of heavy metals in the leachate supports the toxicity data. There is a clear cut case of potential environmental pollution as indicated by the toxicity of the leachate.

Figure 1 :

 1 Figure 1: Location of Okhla and other landfill sites in Delhi (adopted from Zafar and Alappat, 2004)

Figure 5 :

 5 Figure 5: Toxicity assay L2 December 2007

  . Additional Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of Okhla Landfill, Delhi -Vijaya SINGH and A.K. MITTAL

	2 / 8

TABLE 1 : Characteristics of Okhla landfill leachates used in the fish bioassays Parameters Range of values a

 1 Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of Okhla Landfill, Delhi -Vijaya SINGH and A.K. MITTAL

	pH	7.6 -8.2
	Alkalinity	12,000 -32,000
	Hardness	9,000 -25,000
	Chloride	16,000 -23,000
	COD	6,000 -20,000
	NH 3 -N	1,000 -3,000
	TSS	20,000 -35,000
	TDS	2,000 -19,000
	TS	24,000 -54,000

a All in mg/l except pH

<13% Figure 2: Toxicity assay L1 June 2007

	Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of
				Okhla Landfill, Delhi -Vijaya SINGH and A.K. MITTAL
		120	96-h LC50 = <3%
		100
	Mortality %	40 60 80
		20
		0
		-20
			0.5%	1.5%	3.0%	4.5%	6.0%	7.5%
					Dilution of sam ples
	Figure 4: Toxicity assay L1 December 2007
	Mortality % Mortality % Mortality %	20 0 20 40 60 80 100 0 20 40 60 80 100 120 -20 0 20 100 120 96-h LC50 = -20 7.5% 9.0% 96-h LC50 = <12% 12.0% Dilution of sam ples 13.5% 1.0% 2.0% 3.0% 4.0% Dilution of sam ples 40 60 80	15.0% 5.0%	16.5% 6.0%
			10.0%	11.5%	13.0%	14.5%	15.5%	16.0%
					Dilution of sam ples
	Figure 3: Toxicity assay L2 June 2007
							5 / 8

TABLE 2 : Heavy metals detected in the Okhla landfill leachate Metals Range of values a

 2

	Lead (Pb)	0.9 -1.5
	Cadmium (Cd)	0.2 -0.4
	Copper (Cu)	0.2 -1.5
	Manganese (Mn) 0.2 -0.5
	Zinc (Zn)	0.8 -1.5
	Chromium (Cr)	0.8 -2.2
	Iron (Fe)	4.0 -9.5
	Nickel (Ni)	1.0 -5.0
	Cobalt (Co)	0.3 -1.0

a All in mg/L

  Toxicity Analysis and Public Health Aspects of Municipal Landfill Leachate: A Case Study of Okhla Landfill, Delhi -Vijaya SINGH and A.K. MITTAL

	7 / 8


Giuliana Dettori
email: dettori@itd.cnr.it

Francesca Morselli
email: morselli@dima.unige.it

ELICITING BELIEFS WITH A NARRATIVE ACTIVITY IN MATHEMATICS TEACHER EDUCATION

In a teacher training course for mathematics teachers, a narrative activity was assigned to elicit participants' beliefs on proof. Proof is a very important topic in mathematics education, crucial to develop mathematical thinking, and therefore worth special attention. Individual narrations of one's relation with proof were collected, posted on the web and discussed. This allowed a number of different aspects and views to emerge and to be compared, providing a good opportunity for the trainees to become aware of their own beliefs and shortcomings. The positive outcomes of this experience suggest that narrative can be a suitable tool to address beliefs in teacher education.

INTRODUCTION AND BACKGROUND

Beliefs about mathematics and its teaching and learning are recognized to deeply influence teachers' instructional practice [START_REF] Philipp | Mathematics teachers' beliefs and affect[END_REF][START_REF] Thompson | Teachers' beliefs and conceptions: a synthesis of the research[END_REF], as much as the social context and the teachers' level of thought and reflection [START_REF] Ernest | The impact of beliefs on teaching[END_REF].

Teachers' beliefs are therefore an object of study of the research in mathematics education. Three different perspectives can be found in the literature, as emerges from Thompson's survey (1992) and the contributions collected by Leder, Pehkonen and Törner (2002): attention to teachers' beliefs, with particular reference to the construction of a suitable theoretical framework; focus on the dialectic relationship between teachers' beliefs and instructional practice; study of situations and experiences that may change teachers' beliefs. This last stream is directly linked to the emerging field of research in mathematics teacher education [START_REF] Adler | Reflections on an emerging field: researching mathematics teacher education[END_REF]Tirosh & Wood, 2008).

As widely reported in the literature [START_REF] Llinares | Mathematics (student) teachers teacher educators as learners[END_REF], pre-service teachers join the teacher education program with beliefs about mathematics and mathematics teaching and learning which influence not only what kind of teachers they will become, but also how they attend the teacher education program. Two kinds of beliefs should be taken into account: about mathematics and about mathematics teaching and learning. Both of them are linked to content knowledge and to pedagogical content knowledge [START_REF] Shulman | Those who understand: Knowledge growth in teaching[END_REF].

Explicitly addressing prospective teachers' beliefs, therefore, aims to help them "learn to do something different from -and better than-what they experienced in mathematics classes" (Ball, 1990, p. 11). To this end, educators have two responsibilities: "to judge what prior learning can contribute to future growth and which may impede it" as well as "to construct the conditions for experiences which can foster future growth" (ibid, p.12).

Transforming teachers' beliefs is not an easy task because they are rooted in life experience and often unconscious, so much that [START_REF] Thompson | Teachers' beliefs and conceptions: a synthesis of the research[END_REF] underlines that "teachers treat their beliefs as knowledge" (p. 127). According to Thompson (ibid.), good results are obtained by making prospective teachers doubt about their own beliefs. [START_REF] Llinares | Mathematics (student) teachers teacher educators as learners[END_REF] note that some pre-service education programs concentrate on making prospective teachers aware of beliefs by means of reflection on action, regarded as a way for teachers to construct the meaning and knowledge that guide their actions. In this perspective, the work on teachers' beliefs is linked to the importance of preparing reflective teachers [START_REF] Schön | The reflective practitioner. How professionals think in action[END_REF], able to challenge their own practice and beliefs.

In our opinion, an effective way to tackle this issue is to help beliefs emerge with a narrative activity and then address them by means of comparison and discussion with peers. This is the approach that we adopted in the described experience.

Narrative has been gaining increasing attention in the educational field in the past couple of decades, thanks to its cognitive and motivational potential [START_REF] Dettori | Narrative learning in technology-enhanced environments[END_REF], and is increasingly used also in mathematics education, both as a teaching tool [START_REF] Zazkis | Teaching Mathematics as Storytelling[END_REF], and as a methodology of study [START_REF] Kaasila | Using narrative inquiry for investigating the becoming of a mathematics teacher[END_REF]. Stories and narrations are an expressive form that is natural, informal and pleasant for people of any culture and age [START_REF] Bruner | Acts of meaning[END_REF][START_REF] Schank | Tell Me a Story: Narrative and Intelligence[END_REF]. The narrative form suggests (possibly implicit) temporal and causal connections among the presented facts [START_REF] Bruner | Acts of meaning[END_REF][START_REF] Herman | Stories as a tool for thinking[END_REF]. This transforms a sequence of events in what is called a configuration [START_REF] Ricoeur | Hermeneutics and the Human Sciences[END_REF], i.e. a coherent whole in which each part contributes to the global meaning and at the same time takes meaning from its position within it [START_REF] Bruner | Making Stories[END_REF]. This leads the narrator, and those who read or listen a narrative, to become aware of more or less implicit relations, hence favouring thought organization and content understanding.

For these reasons, narrative can constitute an excellent starting point to foster selfawareness and reflection. Reflections are thoughts, mostly abstract and often mooddependent, and beliefs are often unconscious and therefore difficult to retrieve. Narrations can aid to overcome both problems since they can help ground reflection in concrete, personal experience and let beliefs emerge from the narrated facts, events and feelings. It is not surprising, therefore, that narrative activities are increasingly used to support reflection on a variety of aspects, including beliefs, in the training of both pre-service and in-service teachers.

As pointed out by [START_REF] Zaslavsky | Professional Development in Mathematics Education: Trends and Tasks[END_REF], the narrative approach leads mathematics teachers to elicit experiences they lived in the classroom, helping them to reflect on the complex domain of teaching practice and by this means fostering professional growth. [START_REF] Dolk | Narratives in teacher education[END_REF], for instance, challenge small groups of teachers to collaboratively build stories of classroom situations presented by means of videos, with the aim to improve their ability to observe and correctly identify learning difficulties.

Oriented to the study of beliefs is the use of narrative made by [START_REF] Chapman | Stories of practice: a tool in preservice secondary teachers education[END_REF]2008a;2008b) to implement pre-service teachers' self-study and hence detect beliefs possibly conflicting with the views of mathematics education promoted in the training program. In her teacher education intervention, trainees write stories of both actual teaching (from their schooldays or the running practicum), and ideal, best practice teaching. These stories are shared with the other trainees and used as starting point for self-reflection, then revised and made once again object of reflection. Trainees are also given theoretical means to analyse narratives so that this approach can become part of their professional competence and also used in future work.

In the experience described in this paper, we relied on narrative to address trainees' beliefs on a particular aspect of mathematics learning, i.e., proof and proving. These are very important concepts in mathematics, at the very core of mathematical thinking, and should therefore be central in mathematics education.

The interest for this topic is underlined by the big amount of literature on the subject (see e.g. the international newsletter www.lettredelapreuve.it and the proceedings of the ICMI Study 19 "Proof and proving in Mathematics Education" (Lin et al., 2009)).

Among the authors who underline the importance of proof, we recall De Villiers (1990) and [START_REF] Hanna | Some pedagogical aspects of proof[END_REF], who advocate that the function played by mathematical proofs and theorems within mathematics should be stressed in the classroom in order to motivate students to get engaged in proving and to make them grasp the meaning and importance of proof. Hanna discusses proofs that (only) prove and proofs that (also) explain. De Villiers singles out different functions of proof in mathematics: verification/conviction, explanation, systematization, discovery, communication.

As concerns how to introduce it in school, Balacheff (1982) points out that the teaching of proofs and theorems should aim both to make students understand what is a proof, and learn to produce it. [START_REF] Weber | Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in proof construction[END_REF] dealing with the proving process of undergraduate students, argues that it may be seen as a problem solving activity and discusses what kind of learning is fostered by different ways of proving. [START_REF] Selden | Unpacking the logic of mathematical statements[END_REF] point out that many difficulties related to mathematical proof, especially at tertiary level, rely on the fact that students are used to see it as final product to be reproduced rather than as a process they should be able to work out.

All these considerations highlight the importance to include proof in mathematics teachers' preparation, considering it both as a product (that must meet some standard requirements) and as a process (intentionally aimed at the construction of such products). The different roles that proofs can play in mathematics learning and the need to see proofs not only as products but also as processes underline the importance of explicitly addressing proof-related beliefs in teacher training. This was the focus of the described experience.

A NARRATIVE ACTIVITY TO ELICIT BELIEFS

In this paper we discuss a narrative activity that was planned and carried out during the academic year 2007-2008, in the context of a course in Mathematics Education for pre-service teachers of secondary school (PSTs). This 49-hour course, which took place in the first year of a two-year training program of the University of Genoa (Italy) and was taught by one of the authors (FM), had a special focus on the teaching and learning of proof.

We planned a narrative activity at two different points in the course, with different aims. The first of them, which is reported in this paper, aimed to make the PSTs become aware of their own beliefs, connecting them with their previous experience and comparing them with their colleagues', so as to boost reflection on the teaching and learning of mathematical proof. This is in line with our idea of working on preservice teachers' beliefs by capitalizing on PST's different backgrounds as a source of shared reflection. At the same time, we aimed to deepen the use of narrative as a tool to elicit beliefs and contribute to explore the learning potential of narrative.

Methodology

In total, 16 PSTs took part in the course.

During the first class, an open narrative task was proposed:

Write down the story of your relationship with proof (it is important that you write a story, rather than considerations; your story will be the starting point for a collective reflection).

The individual stories were collected and posted, in anonymous form, in the course's online space. The PSTs were then asked to read all the stories and comment them in a forum created on purpose:

In the virtual space of the course, you find a word document that contains in anonymous form all the stories of your relationships with proof. Reading this document, you will read again your own story, together with the stories written by your colleagues. After reading all the stories, do you feel you would like to add something to your own story? Are there other episodes that would like to narrate? Other stories?

For our analysis, therefore, we have at disposal the written individual narrations of the PSTs' experiences with proof, as well as the comments posted in the forum.

ANALYSIS Individual stories about proof

The short stories written by the trainees report difficulties and strengths, inclinations and dispositions, from which it is possible to spot beliefs and other affective factors. Looking at individual stories, we can single out two main types: "evolution stories" (6 in total) and "permanence stories" (5 in total). The other contributions do not contain a clear temporal dimension and relate single episodes or general opinions.

Evolution stories narrate the positive evolution of the relationship with proof, or the shift from difficulty in understanding and building proofs to succeding in both of them. We may note that negative evolution stories (from a positive to a negative attitude, from success to difficulty) are not present. This is not surprising, considering which special population was involved in this experience.

An example of "evolution story" is given by Anna's narration:

At the beginning I had difficulties in understanding how to proceed, especially in proofs by contradiction, but once I understood the logical-deductive method, over the time I learned, thanks to a good teacher I had.

Permanence stories, on the other hand, show the stability over time of a relationship with proof. Here, we find not only positive but also negative situations, as some PSTs report feelings of uneasiness and anxiety, or even difficulties, when proving. Such difficulties and negative dispositions should not be considered as indicators that those PSTs would never become good teachers; quite on the contrary, experiencing in person difficulties and negative affects with proof can help a teacher to better understand students' troubles, without taking understanding for granted, provided these negative aspects are suitably addressed and overcome. Discussing with the class such negative relationships is useful also to those PSTs who, on the contrary, always had a good relationship with proof, since this opens for them a different perspective and can hence help them to be in a better position to understand the difficulties of their future students.

An example of positive "permanence story" is Betta's narration:

Being very rational, I always loved proofs (even the most boring ones!), because they allow me to verify theses that I would be unwilling to accept otherwise.

An example of negative "permanence story" is given by Biagio:

My relationship with proof was always a turmoil. In mathematics, even if I knew that this was wrong, I have always seen proof as something "boring". Something where someone smarter than me had been able to find the way to reach his goal.

Analysing the stories, a number of causal links emerge. In the evolution stories it is interesting to see which factors are perceived as causes of the evolution. In some cases, it was fostered by the intervention of a teacher (see Anna's quotation above), in other cases, the evolution took place as a consequence of personal growth. Alessio, e.g., explains:

As regards the first part of my life, that ended with the start of my university studies, my idea of proof was linked to argumentative and discursive forms, certainly of logicaldeductive nature, sometimes axiomatic; in few cases also to inductive reasoning. In a second phase of my life I started to understand the "sense" of proof from a mathematical point of view: on one side, I started to catch its inner and deep sense when studying it at the university; on the other side, I used proof to clarify, justify, explain, memorize and give meaning to the topics that I had to teach to my students.

In a third phase, I started to reflect on the philosophical and mathematical meaning of proof, looking back at the questions that emerged spontaneously during the preceding phases. Important suggestions came from studying Mathematical Logic.

Also in the permanence stories some factors are seen at the basis of permanence, which is described as linked to one's personal characteristics, as well as to the very idea of proof. An example is Betta's excerpt reported above, where interest for proof is seen as an expression of personal rationality.

The crucial role of the teacher is also underlined; Caterina, for example, writes: "My relationship with is essentially linked to the teachers who taught me it". Explicitly stating facts like this is very important in teacher training, because, even though PSTs are very much aware of the importance of good teaching, it is anyway useful for them to remind the positive and negative influences they had from teachers in their school days.

The relationship with proof is often described in a strong "affective" way, independently of the author's attitude towards it: "I always loved proofs" (very good relationship; Betta), "I loved those proofs that were taught me by teachers who loved mathematics" (partially good, conditioned relationship; Caterina), "My relationship to proof was always a turmoil" (difficult relationship; Biagio). The stories brought to the fore the issue of affective involvement during the proving process or during the study of a proof: "Usually I don't remember the final proof, what I like is proving" (Clara); "When I worked on proofs by myself at home and I managed to understand and to reach the end, I felt very satisfied" (Brigitta). Such stories provided an opportunity to raise the point of the importance of affective factors in the teaching and learning of mathematics, and in particular in the teaching and learning of proof.

Beliefs about the nature of proof also emerged. Most of the PSTs focus on proof as a mathematical object: "Proof is an important and necessary tool in mathematics, otherwise you risk to do philosophy" (Claudio); "In a proof, each step must be a natural consequence of the hypothesis or of the preceding steps, or an obvious application of theorems that were proved before" (Cecilia). Others focus on the roles of proof in the teaching and learning of mathematics: "I always used proof to better understand the theorems" (Bianca); "in order to frame the theorems, rather than memorizing them, I understood that it was easier to prove them, by means of the knowledge already at disposal" (Agnese). If we refer to the functions of proof pointed out in the literature (de Villiers, 1990;[START_REF] Hanna | Some pedagogical aspects of proof[END_REF], we may note that for some PST proof convinces, ("Proofs allow me to verify a thesis, that otherwise, if not proved, I would not accept"; Betta), while, for others, proof, besides convincing, illuminates and explains ("I liked to see an ordered path of the reasons why from some hypotheses it is possible to reach some theses, besides the formal justification of what I found evident"; Anita). Personal narrations sometimes include reflections that tell the story of one's understanding. This is the case of Biagio who points out the gap existing between proof in mathematics and proof in the classroom:

In mathematics, you do each step coherently... to its system of rules. If somebody proved a theorem and the scientific community accepted this proof, the theorem is correct. But, for the student, the proof looses its main meaning and its role is "only" to help understand the theorem itself. But if the student does not understand the proof, what is the befit of proving?.

Proof as a process or proof as a product is another dimension that emerges from narrations. Most PSTs conceive proof essentially as a product that the teacher presents in its final form and the students must learn and reproduce; other PSTs view proof as a process, as a special case of problem solving. The importance of taking into account both the process and the product aspects is well expressed by Biagio: I often had difficulties with proofs, when I met sentences like "if we note that this term may be written in this way…", or "now, it is sufficient to note that…". Well, if the student "does not note", he will never finish the proof, and proving will be reduced to memorizing and reproducing that "awful step" created by the first who proved the theorem, rather than to justifying and really understanding the theorem.

Another important theme that emerged from some individual stories is the special nature of proof in mathematics, if compared with proof in the other sciences:

In the last years of secondary school […] I started to distinguish empirical sciences from mathematics: the differences rely in the different kinds of proof that are accepted: empirical-experimental proof in sciences, abstract and formalized in mathematics (Alessandro).

Proof is different in experimental physics. […] In physics, proving means planning some experiments to investigate the existence or non-existence of a phenomenon, and explaining why it "works" that way (Biagio).

Online discussion

Nine of the 16 pre-service teachers attending the course took part in the online discussion. Our PSTs had little previous experience with forums and distancelearning, and the participation in the online discussion was not part of the usual didactical contract in the teacher training school. We anyway proposed an online discussion for two reasons. Firstly for lack of time, as the course was not long enough to discuss in depth all relevant topics during class hours. Second, but not least, we wanted to grant the participants a looser time, allowing the possibility to reflect on similarities and differences before writing. The fact that part of the group never intervened in the forum was due mainly to difficulty to find time to log in, as several of the PSTs were commuters or did not have Internet connection at home. Totally, 28 comments to the individual stories were posted. Not all stories were mentioned and discussed, but only those that were making some strong point with which the others felt the need to agree or disagree.

In general, we can single out different themes emerging from the posts:

• the feeling of pleasure in relation to creating and/or understanding proof; • the differences and similarities between proving a statement and other school activities, such as translating from Latin; • previous experiences as students (and their possible influence on the future profession of teacher); • the complex work of a teacher.

Some themes are clearly linked to beliefs on proof, others are more general but anyway consistent with the aim of fostering reflectivity on teaching and learning as a crucial feature for professional development.

Particularly interesting appears the stream of discussion started with a comment on Clara's story (Usually I don't remember the proof, what I like is proving), which deepened the theme of proof-related pleasure besides raising other interesting points, such as the product/process nature of proof:

Daria: I agree with those who wrote that s/he never remembers proof, because the pleasure is building it. Actually, for me more than a pleasure the proof was a necessity, because I never remember things, and proving helped me to learn and memorize formulas and statements. Anyway, I think that reaching the end of a proof gives a real satisfaction! Anita: I'm curious about this issue of satisfaction at the end of proof. At the university, whenever I reached the end of a long and complex proof, I felt satisfied because I had understood more deeply why the theorem held. But, to be honest, I felt even more satisfied in secondary school when I was able, after squeezing my brain, to prove by myself some geometric fact. But maybe, I had a great teacher… Brigitta: When I think of proof, only geometric proofs come to my mind. And do you know why? Because geometric proofs were the most challenging and demanding for me.

[…] I did not have the opportunity to see a lot of proofs. And I was never asked to prove by myself. Therefore, over the years I conceived proof as "something that must be done"… but I never felt a strong motivation to reach the end. I'm a little lazy in this. I prefer to get proofs already done, and just understand them.

[…] I remember that when the teacher showed the proof I was very attentive, so as not to loose any step, and after, at home, I felt satisfied, when I was able to reach the end (but the proof was already done!).

We may add that the theme of proof enjoyment raised again during classroom discussion. We suppose that our PSTs felt allowed to talk of satisfaction, enjoyment and other "affective" aspects because these had already been mentioned online, hence their role had been recognized as relevant to mathematics teaching and was worth detailed attention.

DISCUSSION AND CONCLUSION

The outcomes presented in the previous section suggest that the experience was successful as concerns reaching its educational aim, in that it actually managed to make PSTs' beliefs about proofs emerge, and contributed, together with other activities on proof that were developed afterwards, to build a good level of awareness and understanding.

The PSTs produced a large variety of stories. The whole set of them included all aspects that the concise literature review presented above spots as characterizing proof, such as the difference between creating and reproducing proof the different roles it can play in mathematics understanding. No narration, however, mentioned all aspects. Hence, sharing and discussing individual narrations was very important, because it allowed our PSTs to remark, on practical accounts rather than on a scholarly essay, how complex and articulated is the concept of proof, and how useful (even though demanding) may be its use to support mathematics learning.

The reported narrations show that a few PSTs had a negative relationship with proof, and hence were like to give scarce importance to this topic in their future teaching. This, together with the lack of a complete vision of the many aspects of proof, stresses the need to address proof in mathematics teacher training, and to do it starting from detecting trainees' beliefs, so as to allow the overcoming of negative dispositions and incomplete understanding. Eliciting beliefs at the beginning of the course resulted very useful to the teacher educator as well, in that it allowed her to know her students better and hence to adjust the course development as necessary.

The experience appeared successful also from a methodological point of view. The narrative approach resulted a gentle and effective way to make beliefs emerge, while the use of the written form, for both narrations and comments, stimulated reflection and self-study.