Behnam Molaee-Ardekani

Delta waves

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

he electroencephalogram (EEG) is a sum of different sinusoids with a fairly wide frequency spectrum. The frequency range lies between 0.3 and 70 Hz and it is classically divided to different frequency bands such as delta, theta, alpha, beta and gamma bands. When an anesthetic agent is inducted and anesthesia deepens, the EEG becomes more regular before disappearing into an isoelectric activity (burst-suppression) in very deep anesthesia. In moderate to deep anesthesia the EEG is dominated by globally coherent slow wave activity in the delta frequency range (0-4 Hz) [START_REF] Constant | Sevoflurane and epileptiform EEG changes[END_REF].

According to Steriade and coworkers [START_REF] Steriade | Synchronization of fast (30-40 Hz) spontaneous cortical rhythms during brain activation[END_REF], the slow delta oscillations have the ability to trigger and group cortical B. Molaee Ardekani is with INSERM, U642, Rennes, F-35000, France; Université de Rennes 1, LTSI, Rennes, F-35000, France and with Sharif University of Technology, Tehran, Iran. (emails: behnam.molaeeardekani@univ-rennes1.fr , b_molaee@mehr.sharif.edu) L. Senhadji is with INSERM, U642, Rennes, F-35000, France and with Université de Rennes 1, LTSI, Rennes, F-35000, France. (email: lotfi.senhadji@univ-rennes1.fr) M.B. Shamsollahi and B. Vosoughi Vahdat are with BiSIPL, School of Electrical Engineering at Sharif University of technology, Tehran, Iran. (emails: mbshams@sharif.edu , vahdat@sharif.edu) E. Wodey is with INSERM, U642, Rennes, F-35000, France; Université de Rennes 1, LTSI, Rennes, F-35000, France and with CHU, Department of anesthesia Rennes, F-35000, France. (email: eric.wodey@chu-rennes.fr) network firing that correspond to faster activities of EEG. They observed that the hyperpolarizing phase of the depth recorded slow oscillation is associated with a global dysfacilitation in corticothalamic networks resulting in reduced neural firing. The depolarizing phase, on the other hand, was found to be accompanied by a corticothalamic facilitation of neural firing.

In this context, it has been speculated that in light anesthesia fast EEG oscillations are modulated by slow waves [START_REF] Burkitt | Study of neuronal gain in a conductance-based leaky integrate-and-fire neuron model with balanced excitatory and inhibitory synaptic input[END_REF]. Fast EEG oscillations reach their maximum value when slow EEG waves are in their minimum values. This yields a negative correlation between fast oscillations and slow waves. It remained unclear, however, whether the modulation of high-frequency EEG activities by slow oscillations is independent with anesthetic drug concentration or not. In the present study, we thus examine the phase of the modulation of high frequent activities (8-20 Hz) by delta waves during different depth of anesthesia in children.

Since it has been shown that in waking periods slow (0-2 Hz) and fast (2-4 Hz) components of delta waves are differently correlated to theta, alpha and beta frequency bands [START_REF] Benoit | Slow (0.7-2 Hz) and fast (2-4 Hz) delta components are differently correlated to theta, alpha and beta frequency bands during NREM sleep[END_REF], we divide the delta band into slow and fast components, and separately investigate the modulation of high frequency EEG activities by slow and fast delta waves.

In this study, we have used Desflurane and Propofol anesthetics to show that phase and strength of the modulation of high frequency EEG activities by delta waves vary with anesthetic concentration. Characteristics of modulation between two different brain activities may directly indicate the status of information processing in the brain; therefore they can be used as monitoring tools to indicate the status of the patient during anesthesia. Since such method of determining depth of anesthesia is established based on information processing of the brain, it may be employed beside many other ad hoc methods of determining depth of anesthesia such as Bispectral Index, Spectral Edge Frequency and Median Frequency [START_REF] Senhadji | Monitoring approaches in general anesthesia: a survey[END_REF] to improve their efficiencies.

II. METHODOLOGY

A. Procedure of data recording

We recorded EEG signals on 10 children 20 minutes before beginning surgical operation. Anesthesia was performed by Desflurane or Propofol agents. After intubation, different anesthetic drug concentrations were administered in stepwise manner to provide 2, 1 and 0.5

Delta waves differently modulate high frequency components of EEG oscillations in various unconsciousness levels

Behnam Molaee-Ardekani, Student Member, IEEE, Lotfi Senhadji, Senior Member, IEEE,Mohammad-Bagher Shamsollahi, Member, IEEE, Eric Wodey, Bijan Vosoughi-Vahdat, Member, IEEE T MAC (Minimum Alveolar Concentration) respectively. In order to stabilize EEG signal for each desired MAC, we resumed drug administration for each given drug concentration for about 10 minutes. Figure 1 depicts the diagram of the input desired concentration.

B. Signal analysis

EEG recordings were pre-processed by a high-pass finite impulse response (FIR) filter. The passband and stopband of this filter were 0.2 and 0.02 Hz respectively. Slow delta wave were extracted from the pre-processed EEG (see figure 2 and3) with a low-pass FIR filter with 2 Hz passband and 2.3 Hz stopband. To extract the fast delta wave and fast EEG oscillations, we used a band-pass FIR filter. The passbands and stopbands of the first filter were equal to 1.8, 3.6, 2.1 and 4 Hz. These parameters were 7, 20, 8 and 25 Hz for the second filter.

The modulation between delta waves and fast EEG oscillations was quantified as follows:

1) Slow or fast EEG delta waves were segmented to 30 seconds 50 percent overlapped epochs, and their energies were normalized to one. The analytic signal of each epoch, which is a complex signal, was calculated. The real part of the analytic signal is equal to the EEG epoch and the imaginary part is the Hilbert transform of the EEG epoch. The modulus and angle of the thereby obtained complex signal represent the amplitude and phase of slow or fast delta waves.

2) Amplitude of fast EEG oscillations were also calculated as the above described method for slow and fast delta waves

3) Amplitudes of fast EEG oscillations were sorted to 70 bins according to their corresponding values of slow or fast delta phases (See figure 2E). Such procedure could also be done for amplitude values of slow or fast delta waves.

4) The average of amplitude values of fast EEG oscillations (or delta amplitudes) was calculated in each bin. Then the mean value of all 70 bins was subtracted from the result to have a zero mean 70-points signal (see figure 4). From then, this signal is referred to as modulation signal.

III. RESULTS AND DISCUSSIONS

A. Anesthesia shifts the phase of modulation signal

In different depth of anesthesia, a modulation exists between delta waves and fast EEG oscillations (We selected 8 to 20 Hz interval as the frequency band of fast EEG oscillations because higher frequencies are not significant in children). In another word, modulation signals (MS) are not flat lines in different depth of anesthesia. Surprisingly, not only MS are not flat, but also their extremum positions change by anesthetic concentration. It means that the maximum amplitude of fast EEG oscillations happens in different phases of delta waves. This phase is referred to as phase of modulation signal. It can be said that delta waves and fast EEG oscillations are two phased-locked activities in which their phase differences are changed by anesthetic concentrations. Increasing the drug concentration to 1 MAC causes appearance of two peaks around +2 radians and -1 radian. Typically the amplitude of the peak which is around +2 radians is higher than the other one. In order to properly fit a sinusoid function to these graphs, we have to increase the frequency of the sinusoid function to 2 Hz (dashed line curve in the figure). In deep anesthesia, a single peak is observed between -2 to +1 radian. Comparison of these SMS shows that the phase of SMS moves to a lower values by increasing of drug concentration. Similar results are obtained for phase of fast modulation signals (FMS). Such SMS and FMS were obtained for all EEG epochs of the 10 patients who participate in our 20 minutes EEG recordings. Figure 5 and 6 (top) illustrate SMS and FMS graphs of a same patient in gray-level format during the 20 minutes of the EEG recording respectively.

B. Phase locking can be tracked by fitting a 2D function to SMS or FMS

In order to track the delta phase in which the maximum amplitude of fast EEG activity occurs, a 2D function is first fitted (figure 5 and 6 bottom) to 2D data points of SMS or FMS (figure 5 and 6 top). Such 2D data fitting smoothes 2D SMS and FMS in phase and time domains and also enables us to be able to better track the slow or fast delta phases because they do not change vary fast in time domain.

The following 2D functions were selected to be fitted with 2D data points of SMS or FMS to find the best function for this purpose. The shapes of one-dimensional SMS (and FMS) in figure 4 were the main motivation factors in selecting the following functions:

1 ( , ) ( )cos(2 ( )) F t At t ϕ πϕ φ = - ( ) ( ) 2 2 2 ( , ) ( ) 1 ( ( )) exp ( ( )) / 2 F t A t t t ϕ ϕ φ ϕ φ = -- -- ( ) ( ) (
) ( )

2 2 3 1 1 1 2 2 2 2 2 ( , ) ( ) 1 ( ( )) exp ( ( )) / 2 ( ) 1 ( ( )) exp ( ( )) / 2 F t A t t t A t t t ϕ ϕ φ ϕ φ ϕ φ ϕ φ = -- -- + -- --
where ( ) A t and ( ) t φ are polynomial functions:

2 3 2 3 0 1 2 3 0 1 2 3 ( ) , ( ) A t a at a t a t t b bt b t bt φ = + + + = + + + Analyses show 3 ( , )
F t ϕ has the most capability to be fitted with 2D graphs because it is consisted of two Mexican hats that their amplitudes 1,2 ( ) A t and centers 1,2 ( ) t φ are tuned separately in time domain. Since 3 ( , )

F t ϕ consists of two independent Mexican hats, it is also convenient to be fitted with the graphs that have two separate peaks (e.g. see the SMS graphs corresponding to 1 MAC in figure 4).

C. SMS and FMS: A comparison

In order to respond to this question that "is there any difference between the phase locking of slow and fast delta waves and fast EEG oscillations", we obtained 2D SMS and FMS of the patients and tracked their phases. Both methods show that the phase diagram of SMS and FMS varies by changing the anesthetic concentration. However there are some points that should be mentioned here.

Figure 5 depicts a 2D SMS and its fitted surface (i.e. tuned 3 ( , ) F t ϕ ) in gray-level. Since EEG epochs are overlapped 50%, the time resolution of the 2D SMS is 15 seconds. The maximum amplitude of each row of the fitted surface and its corresponding slow delta phase (i.e. phase of SMS) are plotted in figure 7. Figures 6 and8 are duals of figures 5 and 7 considering that slow delta wave has been replaced by fast delta wave.

In general, SMS are noisier than FMS so phase tracking of FMS provide more robust and clearer results. The difference between maximum and minimum values of SMS is low and their positions vary a lot in consecutive EEG epochs. This can be better understood by obtaining the histograms of 2D SMS and FMS of the patients. Figure 9 (left side) illustrates the histogram of FMS values. This histogram is wider than the SMS histogram in the right side and indicates that extermums of FMS are more distinguishable from rest of signal.

When a drug concentration is changed rapidly (e.g. from 2 MAC to 1 MAC) a biphasic response is observed on EEG signals [START_REF] Kuizenga | Quantitative electroencephalographic analysis of the biphasic concentrationeffect relationship of propofol in surgical patients during extradural analgesia[END_REF][START_REF] Kuizenga | Biphasic EEG changes in relation to loss of consciousness during induction with thiopental, propofol, etomidate, midazolam or sevoflurane[END_REF]. Transition the depth of anesthesia from one level to another level is basically accompanied by a delayed transient increase of high frequency EEG amplitudes that are disappeared after a few minutes. Basically, classical measuring methods predict a lower depth of anesthesia during biphasic response. During biphasic response, phase diagrams of FMS show slightly decrease in depth of anesthesia, but phase diagrams of SMS do not influenced by biphasic response. A comparison between top graphs in figures 7 and 8 shows that decrement of the depth of anesthesia (according to the illustrated protocol in figure 1) is accompanied by monotonic increase of the phase diagram of SMS in figure 7, but there are two local maximums on the phase diagram of FMS around 4 and 16.5 minutes that are related to biphasic response.

  Manuscript received March 20, 2007. This work was partly financed by the French Ministry of Research and Technology (Grant: DT 03 B 107-108-109; CITH Rennes).

Figure 1 :

 1 Figure 1: After intubation concentrations of anesthetic agents are changed in stepwise manner from 2 to 0.5 MAC.

Figure 2 :

 2 Figure 2: A pre-processed 30 s EEG epoch (A). Slow component of EEG delta band (0-2 Hz) (B). Phase of the delta wave which is calculated from the analytic signal. Dashed line does not participate in further signal analyses because there are more than 3 extrema between π and π + radians (C). High frequency oscillations of the EEG signal (8-20 Hz) (D). Amplitudes of the high frequency oscillations of the EEG signal (E).

Figure 3 :

 3 Figure 3: Enraged shape of depicted EEG delta wave, delta phase and fast oscillations in figure 2 between 26.5 s and 28.5 s.

Figure 4

 4 Figure 4 depicts amplitude values (in 70 bins) of fast EEG oscillations versus phase of slow delta wave for three EEG epochs in 0.5, 1 and 2 MAC. We refer to these MS's as slow modulation signals (SMS) (blue dotted lines). For comparison we have also shown amplitude values of slow delta wave versus phase of slow delta wave (red x marks). In low anesthetic drug concentration (i.e. 0.5 MAC), the

Figure 4 :

 4 Figure4: Amplitudes of fast EEG oscillations versus phase of slow delta wave for three EEG epochs in 0.5, 1 and 2 MAC (blue dotted lines) and amplitudes of slow delta wave versus phase of slow delta wave (scaled 20%, red x marks). In each case, a sinusoid function has been fitted to fast EEG oscillations. In C = 1 MAC, a 2 Hz sinusoid function provide a better matching.

Figure 5 :Figure 6 :

 56 Figure 5: Two-dimensional SMS (top) and its fitted surface by 3 ( , ) F t ϕ (bottom) in gray-level. SMS graphs are related to a patient during the 20 minutes of EEG recordings before surgical operation.

Figure 7 :

 7 Figure 7: Phase diagram of SMS (top) and its corresponding amplitude diagram (bottom) of the patient whose 2D SMS has been illustrated in figure 5.

Figure 8 :

 8 Figure 8: Phase diagram of FMS (top) and its corresponding amplitude diagram (bottom) of the patient whose 2D FMS has been illustrated in figure 6.

Figure 9 :

 9 Figure 9: Histograms of the amplitude values of fast oscillations vs. fast (left) and slow (right) delta waves. Fast delta waves provide better distinguishable extremums in the amplitude values of fast oscillations (left histogram is wider compared with the other histogram)


Rita Khanfour-Armalé

PROFESSIONAL IDENTITY OF CHEMISTRY UNIVERSITY ACADEMICS

Keywords: University teaching, University academics, Professional identity, Chemistry

Nowadays in France, more trainings regarding "university pedagogy" are intended for teacherresearchers (TR), but very few studies are concerned in how they are absorbed by the TR. In fact, TR expectations from students of the secondary level education are also rarely studied. As a first approach to these general questions, our objective is to know better the community of the teacher-researchers of chemistry. This paper is part of a group work project on four disciplines representing chemistry, geography, mathematics, and physics in our laboratory. For this purpose, we propose to give some elements of reflection around the following questions:

-How does the discipline of teacher-researchers mark their practice? -What is the imprint of the profession of researcher on the teaching profession?

. We will link them to problems related to the epistemology of the disciplines, to tensions in the profession or to didactic elements.

INTRODUCTION

In France, research on the teaching practices and the professional identity of the teachers in the higher education started to be the subject of various studies (Annoot & Fave-Bonnet, 2004[START_REF] Caroline | L'usage du cas et de l'exemple dans l'enseignement supérieur : objet de recherche[END_REF]. The question regarding the evolution of the teaching practices in the higher education is currently being debated whether it is a fall of motivation of the students or heterogeneity of the student community. More and more of training courses covering "university pedagogy" are intended to be made for the teacherresearchers (TR) but very few studies are interested in the way in the TRs are receiving them. Also, the expectations of the TR regarding students coming especially from secondary education are not studied often.

In a recent research, de [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF], showed interest in the teacher-researchers physicists of the same Unit of Formation and Research (UFR), by questioning them on their teaching profession of physics. Their research originated from an ordering of this UFR whose objective was to identify consensual proposals of change in the teaching methods and organization of the lesson of physics of license level (in particular L1). de [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF] mobilized the framework of the professional identity [START_REF] Cattonar | Les identités professionnelles enseignantes. Ébauche d'un cadre d'analyse[END_REF] in as well "as together of particular elements of professional representations, specifically activated according to the situation of interaction" [START_REF] Blin | Les représentations professionnelles : un outil d'analyse du travail[END_REF]. It was a question of considering the occupational group teacherresearcher like a "subculture" characterized by modes to perceive, think and act particularly, and to go back to the standards, the values and the clean rules to their trade of teacher related to their object of work and their occupational practice (Cattonar, 2001, p.6) and thus on their discipline. This article belongs to a bigger project in our group on higher education whose objective is to continue the work made by [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF] while extending to other universities 1 and other disciplines (chemistry, geography, mathematics and physics). The objective is to know better the community of the teacher-researchers.

In this article, we propose to give some elements of reflection around the following research questions:

-How the discipline of TR marks their practices? -What is the imprint of the profession of researcher on the teaching profession?

FRAMEWORK

Our questioning structure around the concept of professional identity whose dimensions enable us to take into account what constitutes the heart of the profession of TR of a discipline. [START_REF] Cattonar | Les identités professionnelles enseignantes. Ébauche d'un cadre d'analyse[END_REF] defines the teaching professional identity as the way in which an individual "teacher" is defined in his/her relationship with his/her professional practice of teaching [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF]: "there are those characteristics that identify the individual as a teacher and which he/she shares and has in common with other teachers because of belonging to the same occupational group" (Cattonar, 2001, p. 5). Here are the dimensions under consideration by [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF] that we consider again:

-The qualities and competences necessary to the exercise of the profession -The standards (what the teacher judges legitimate to perform well in terms of rules, behaviors, operation and what with the opposite seems to him/her illegitimate or not very suitable) -The values and rules (what the teacher develops in his/her job, the functions which he/she would like to delegate and those that he/she would never delegate) which are related to their work object and their practice professional (Cattonar, 2001, p. 6). -The didactic dimension, the report which the teacher-researchers maintain with the discipline specialty (de Hosson & al., 2015)

METHODOLOGY

We adopted the interview used by de [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF] which was envisioned in order to collect the opinion of the teacher-researchers interviewed on the following aspects: the traditional organization lectures, directed studies and practical work, innovating practices, difficulties of the students, evaluation of the students, the university teacher training, the profession of teacher-researcher, the didactic questions. The sample is composed of 14 teacher-researchers of variable seniority (9 to 26 years), belonging to two universities. The interview parts were presented by the interviewer at the beginning, then were recalled and introduced by "what did you think about…". The talks lasted between 25 and 60 minutes.

The transcriptions of the talks were read in a detailed way in order to index the ideas corresponding to the principal questions of the guide of interviews. According to the research question which they answered, the principal ideas were then categorized.

As a propriety, we considered the elements which could testify to affect the researcher profession in the teaching profession.

RESULTS

We have here partial results which still need to be supplemented and specified. We could notice common results to all the disciplines:

-The teacher-researchers are in the search of coherence with what is the discipline -including in its professional dimension -which will be translated, according to cases', by variations or proximities with the discipline -The hiatus between the comprehension and the success of the students, the hiatus between what is developed and what is evaluated in the exam.

What is specific to the research presented here is what relates to the chemistry which was associated by the teacher-researchers to understand what surrounds us and the everyday life. The teacher-researchers who are interviewed describe chemistry like an applied science more practical than theoretical. But they do not manage to practice chemistry with their students because of their difficulties and it is not easy for them to evaluate them in this sense. The principal explained that the difficulties are due to the lack of work and the insufficiency in mathematical tools. Half of them showed the difficulty of students in giving meaning to the concepts and the knowledge.

The teacher-researchers state to have learned how to teach in the course of their professional experience.

Half of the questioned TR is not favorable to the university training teacher, the other half is favorable and wishes to take trainings by professionals on pedagogy and the didactic one.

The teacher-researchers are not with a view to delegate part of their activities. But if they must, then they would go for the evaluations but they do not want to delegate the courses in master. The contact with the students appeals to them the most in their profession The women (1/3 of the sample) evoke this contact on the side of teaching and the 2/3 which is men evoke this contact on the side of research (training course or direction of thesis).

The teacher-researchers evoke that they draw from the results of their research to feed their course for the students in Master. They declare that the fact of being a researcher helps them become a good teacher.

This study has enabled us to pinpoint elements of their professional identity as teachers. TR make (or would like to make) work with their students, because according to them activity "to nearly making it research": they develop work in small groups to reflect together.

CONCLUSION AND PERSPECTIVES

This preliminary analysis of the collected data allows us to identify major trends among university academics' conceptions about teaching as follows: a good teacher is above all a good researcher [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF], or teaching has to favor interactions with students. We seek in the continuation of this project to validate a result found by [START_REF] De Hosson | Approcher l'identité professionnelle d'enseignants universitaires de physique: un levier pour initier des changements de pratiques pédagogiques[END_REF] that this identity is marked by tensions sharp between "what it would be necessary to make" and "what TR makes or which TR is ready to make"; tensions which are explained on one hand given the importance of research activity in the evolution of the teacherresearcher career, and on the other hand, by the tacit standard on which the evaluation of the students rests (checking of a technical form of skill in the detriment of comprehension). We will compare thereafter the chemistry teacher-researchers of the two universities and then we move on to comparing the enquiring teachers of the various disciplines.

We have interviewed 42 teacher-researchers from the four disciplines and in 7 different universities for the project as a whole.


The " amount of substance " and its unit the " mole " Rita Khanfour-Armalé

The « amount of substance » and its unit the « mole »

Rita Khanfour-Armalé Introduction

The 'mole' unit of the amount of substance is one of the fundamental concepts in quantitative chemistry. The ''amount of substance'' is a concept that has been a frequent subject of discussion among science education researchers [START_REF] Staver | A content analysis of the presentation of the mol concept in chemistry textbooks[END_REF][START_REF] Furio´ | Difficulties in teaching the concepts of 'amount of substance'and 'mole[END_REF]. However, previous research has shown that because of its abstract nature and the anomalous evolution of the definition in scientific history, the mole is generally acknowledged to be one of the most perplexing concepts in chemistry teaching and learning [START_REF] Fang | Teaching and learning the mole concept: an investigation of science secondary classrooms in Australia and Taiwan[END_REF].

The concept of amount of substance and mole present difficulties to students because they are abstract [START_REF] Dierks | Teaching the Mole[END_REF] and there is a lack of understanding of the microscopic and macroscopic scales [START_REF] Claesgens | What are students' initial ideas about 'Amount of Substance[END_REF]. Common misconceptions include defining the mole as Avogadro's number [START_REF] Claesgens | What are students' initial ideas about 'Amount of Substance[END_REF], as a mass or as a property of a molecule. Students have no context for the mole (Gorin 1994) and there is a diversity of language used to establish the concept of amount of substance1 and this causes problems for many students. The teachers have the notion that the 'mole' unit is introduced as a unit of 'chemical mass' that serves to count the elementary entities of different substances. [START_REF] Furio´ | Difficulties in teaching the concepts of 'amount of substance'and 'mole[END_REF] found that teachers themselves were confused about the meaning of "amount of substance". They have an operational form of teaching resulted from a nonproblematic vision of science which gives students a decontextualized meaning. [START_REF] Pekdag | Semantic mistakes and didactic difficulties in teaching the "amount of substance" concept: a useful model[END_REF] found that there are semantic mistakes in the presentation of the amount of substance and the mole concept in chemistry textbooks.

To understand these difficulties, it would be useful to provide a brief review of the historical development of the amount of substance and mole concepts. From the 20th century, the worldwide acceptance of the atomic-molecular theory of matter to interpret chemical changes eventually led the scientific community to adopt amount of substance as a fundamental quantity and to define the mole as its unit [START_REF] Fang | Teaching and learning the mole concept: an investigation of science secondary classrooms in Australia and Taiwan[END_REF]. At first glance, the SI definition of a mole2 accords with the atomistic paradigm because it refers to a certain number of elementary particles. However this number is actually defined by a specific mass of a specific substance (12 g of 12C), an idea originally attached to the equivalentist paradigm. The attempt to make two apparently incompatible paradigms, the equivalentist and the atomistic paradigm, converge helped the scientific community to reach agreement on what the word "mole" actually means. However, the consequences of the convergence were that multiple meanings and conceptual contradictions resulting from the historical evolution of the mole have become sedimented in the SI definition of the mole.

The amount of substance connects the macro-world with the micro-world. Learning the amount of substance concept meaningfully and in-depth is closely dependent on how well teachers are able to present the concept in a manner that creates meaningful relationships between the macroscopic, the microscopic and the symbolic level [START_REF] Pekdag | Semantic mistakes and didactic difficulties in teaching the "amount of substance" concept: a useful model[END_REF]. Rare French study about these two concepts has been encountered in chemical education; however Laugier and Dumon (2004) have attempted to elucidate the nature of the difficulties faced by high school students and undergraduate degree courses for understanding and mobilization of the concepts of mole and amount of substance in stoichiometry problems. I'm interested about the way the mole concept is presented in classrooms.

Method

I used for this pilot study two videos 3 of 2 teachers presenting and teaching the amount of substance and the mole in their classes. Videos helped us to transcribe the interactions between teachers and students. The two teachers had been teaching for 4 and 19 years. They use the same teaching sequence designed and improved during meetings between these teachers and SESAMES group. In the postlab, the teachers take back the responsibility of organizing the knowledge after having let his/her students be autonomous during the labwork. They give to students a document with a summary of the knowledge to be learned designed and improved by the same group.

The semantic mistakes [START_REF] Pekdag | Semantic mistakes and didactic difficulties in teaching the "amount of substance" concept: a useful model[END_REF] are classified under three different sub-groups: "missing concept" was defined as ''a concept that is absent at the macroscopic, microscopic or symbolic level. The mismatching concept was defined as ''using the amount of substance concept as equivalent to the concepts of mass, molar mass, number of particles or molar volume''. And Inappropriate expression was defined as ''the observed incorrect usage of a microscopic level concept in place of a macroscopic level concept or vice versa''. [START_REF] Fang | Unpacking the Meaning of the Mole Concept for Secondary School Teachers and Students[END_REF] use the expression "the mole concept" and proposed a concept map (Figure 1). They point out explicitly that the key to making meaning of the mole is to relate the mole concept to the atomic-molecular concept from both the number and the mass aspect. The number aspect (linking idea 1) provides a theoretical (atomic) view of chemical reactions to be the right amounts of chemicals involved in a chemical reaction. The mass aspect in terms of the connection between molar mass and relative atomic mass (linking idea 2) explains why the molar mass of a substance has the same numerical value as its relative atomic or molecular mass, and which rationalizes practical laboratory work.

In one hand, the analysis of the summary document is based on the semantic mistakes. In the other hand, based on the concept map linking idea were searched in the postlab session.

Results

The analysis shows that the summary document (4 pages) use the correct expression. I found just 1 inappropriate expression and 1 mismatching concept. The analysis of the videos shows that the mole concept was defined and conceptualized with emphasis on the mole as a number. Neither the SI definition in terms of 12 grams of 12C (the mass aspect of linking idea 1) nor the connection between molar mass and relative atomic mass (linking idea 2) was explicitly explained. The two teachers adopted same strategies in the lessons and the presentation was very similar.

Discussion and conclusion

Despite the use of the sequence and the summary text designed by the group, teachers fail to take full advantage. As suggested by [START_REF] Fang | Teaching and learning the mole concept: an investigation of science secondary classrooms in Australia and Taiwan[END_REF] because of the differences in how the mole concept has been conceptualized between the scientific and the educational domains, through their training, chemists and teachers learn to use the mole concept as a 'tool'. Their associated conceptual understanding becomes so ingrained that its importance goes unrecognized. As a consequence, it seems that the teachers' lack of explicit awareness of the underlying concepts resulted in some ambiguities in their classroom instruction. Pekdag and Azizoglu (2014) proposed three models for the correct scientific representation of the mole. With the model 1 it is not semantically correct to have knowledge at the macroscopic level (element, compound, etc.) immediately follow the term mole that defines the number of particles. Model 2, can be applied to expressions where physical quantities such as mass and volume are being used. Model 3 can be used in representations in which the amount of substance concept is associated with the number of particles. This paper reports the findings from a content analysis relating to the concept of the mole. This content analysis formed a part of a project that will investigate the process of teaching and learning the mole concept in secondary classrooms.

In Latin, the word moles means ''big mass''; adding the suffix -cula converts the word to the term molecula, meaning ''small and tiny''. The term molar, mean large or macroscopic mass, the opposite of the term ''molecular mass''.

A mole is the amount of substance of a system which contains as many elementary entities as there are carbon atoms in 0.012 Kg of 12C. its symbol is ''mol''. The elementary entity must be specified. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. The mole is a base unit of the International System of Units(BIPM, 2006, p. 115).


Rita Khanfour-Armalé

Jean François Le Maréchal

Teacher activities for structuring student knowledge after chemistry laboratory work

Introduction

Laboratory activities have the potential to enhance constructive social relationships as well as positive attitudes and cognitive growth [START_REF] Hofstein | The Role of the Laboratory in Science Teaching: Neglected Aspects of Research[END_REF], but they can not govern the overall learning process. One of the reasons is that students do not have clear ideas about the general or specific purposes for their work in science laboratory activities [START_REF] Chang | The Effect of Levels of Cooperation with Physical Science Laboratory Groups on Physical Science Achievement[END_REF]. As a result, during laboratory activities, students involve the knowledge that is to be learned, but also incorrect knowledge (within observations and interpretations) without being aware of it. Teacher intervention is therefore necessary in order to point out the correct and the incorrect knowledge, to formulate and to structure it. As only a few teacher interventions occur during the laboratory sessions, a moment where the teacher can come back to the knowledge to be learned must be planned during the teaching sequence. A way to enter more deeply into the learning process is therefore to analyse a class discussion during this "come back". It might involve linguistic tools for structuring the discussion as well as didactic tools to specifically understand and compare the knowledge imbedded into the teacher-class interaction. The aim of our research has been to provide a new insight into these moments occurring after profitable experimental activities. We have given the name of "debriefings" to these moments. During a debriefing, the teacher takes back the responsibility of organizing the knowledge after having let his/her students be autonomous during the laboratory work. We consider that these moments are debriefings only if the teacher comes back to the concepts imbedded in the activity within the same context as the experimental situations. We consider that knowledge in class can be reconstructed from examining the teacher-class interaction. This interaction has been analysed from two perspectives: a linguistic analysis based on ternary exchange [START_REF] Lemke | Talking science: Language, learning and values[END_REF]Manzoni-de-Almeida, and al.2014) and a didactical one based on a division of knowledge into facets [START_REF] Minstrell | Facets of students' knowledge and relevant instruction[END_REF]. In the linguistic analysis, whether it is a dialog between a teacher and his/her class. The basic structure of the conversation can be viewed as a ternary exchange where a first speaker initiates the discussion, the second one answers, and the first one evaluates the answer. This sequence currently noted I-A-E has been observed in class discussions [START_REF] Mortimer | Multivoicedness and univocality in classroom discourse: An example from theory of matter[END_REF]. Deviations from this basic ternary exchange are interesting to understand, as are the characteristic of the interactionswe have, for example, compared their lengths. The division of knowledge from a facet perspective allows it to compare the knowledge involved in the interactions of different situations. Facets are units of knowledge that are reconstructed from utterances. For comparisons between different situations to be possible, this reconstruction has to respect the idea carried along by the utterance, and include a generalization of contextual words. What are the possible class organisations to debrief laboratory activities and how is it possible to characterize them in terms of their linguistic structure and scientific content?

Methodology

Our main source of data is a corpus of 35 class videos recorded with the camera focused on the teacher. Five teachers were observed as they were debriefing experimental activities at the upper secondary level in chemistry classes. These activities were drawn from a pool of nine; most of them had been designed during meetings between these teachers and our research group. The conversations between teachers and their class were transcribed. In one hand, the transcriptions were split into ternary exchanges. The initiative interventions of ternary exchange were compared to the questions of the text of the laboratory work. In the other hand, facets of knowledge were extracted from the teachers' and students' utterances where sensitive concepts were involved (a concept is said to be sensitive when the teacher has a learning objective regarding this concept).

Results

Our analyses led us to consider three kinds of debriefings: feedback debriefing, summary debriefing and lecture debriefing. For all of them, the teachers were back in charge of the knowledge to be taught. They used the same sensitive concepts as those the students had used during the laboratory work, and in the same context. Feedback debriefing is by far the most observed practice (30/35). During such a debriefing, the teacher has in his/her hands the text the students had worked with, and s/he reviews most of the items in the same order. The class discussion is most often (81%) structured as ternary exchanges, with the teacher's questions serving as initiators for interaction. These questions have been categorized as text questions if they belong to the text of the laboratory task (22.7%, N = 366), and non-text questions (77.3%). For the latter, 44.8% deal with the context of the experiment, 5.6% are meta-questions (reflections about the knowledge), 5.4% are based on relations between different text questions and 3.9% are given as simplifications of a text question. This categorisation left over 17.6% of uncategorised questions that are mainly continuity interventions such as: "and then?" or "what else?" to incite the student to keep on talking. Student interventions were categorised in terms of I-A-E. Most of them were A (97%), a few were I. The former category often dealt with observations or interpretations. After the teacher's initiations and the students' answers, the teacher's evaluations were categorized. The most frequent E-interventions were formulations. A formulation could be a teacher's repetition or reformulation of the student's answer (57%, N = 791, there could also be more than one category of evaluation per ternary exchange). The teacher could also deal with the knowledge imbedded in the student's answer (26%), contextualise it (11 %) or generalise it (6 %). Summary debriefings are organised around a document that the teacher gives to pupils, with a summary of the knowledge to be learned. The facets of knowledge were found to be the same in the summary and in the corresponding experimental activities. Only 3 summary debriefings were found out of 35, but when asked about their practices, teachers sent us 4 other summaries that had been used in debriefing conditions. Such a debriefing is therefore not as rare as the analysis of our corpus might suggest. In the summary, experiments may be compared (thin layer chromatography / column chromatography). Teachers may also hinge sensitive concepts introduced in different lessons (Lewis representation / Cram representation). One of these courses may be the following in the teaching sequence. In lecture debriefings, teachers develop a structured presentation of the knowledge that includes the sensitive concepts of the laboratory work and present it to the class. We observed only two lecture debriefings. In the first one, the organisation of the knowledge was the same as the one of the laboratory work, with the addition of a few extra examples and topics. In the second one, the organisation of the knowledge was different. Much more facets were used in these debriefings than in their corresponding laboratory sessions (66 vs. 8 in one case and 54 vs. 10 in the other one). The link between the laboratory work and the debriefing came from several examples of the former that were introduced in the latter.

Conclusion and discussion

In the feedback, the teachers spend little time with generalisation and contextualisation (prime importance in science teaching). Moreover, they spend little time in asking questions that could be cognitively motivating (relation, meta), or helpful (simplification). These data are in agreement with the fact that students often get bored during such debriefings; when we recorded the videos, students did not pay much attention to the teacher unless they were requested and produced a background noise. In addition, teachers feel uncomfortable with feedback debriefing. When interviewed about the reasons for doing it, they said that they felt obliged to come back to the activity they had proposed to the class and that this format is easy to work with. One of the aims of the summary is to provide the students with a written record, whereas during feedback debriefing, most, if not all, courses are oral. In the summary, the language is more formal and complex than during the oral discourse of the feedback debriefing. We found that the summary was commented in relation to the experiment done in class, or just assigned as homework. Unlike the feedback debriefings, as it happened, students took the initiative in ternary exchanges and asked questions (25 in one case and 45 in the other one). These students' attitudes show their motivation in and interests for lecture debriefings. The linguistic structure was different from the one observed for other types of debriefing. Half of the ternary exchanges were interrupted by a long comment by the teacher. This comment was neither an evaluation of the previous exchange, nor an initiative toward the following exchange. We called this comment counter-exchange. The density of facets was higher during the counter exchange than at any other moment of the debriefings (50% of the facets attributed to the teacher during the debriefing). Our research has been able to provide an understanding of the way teachers come back to an experimental activity. Such an understanding may help to improve novice teachers' practices as our feeling is that they will spontaneously adopt feedback-type debriefing. The efficiency of these three teachers' practice remains to be evaluated. We already proved that from the content measured in terms of facets, the lecture is more effective than the summary and the feedback. The lecture also provides more student motivation than the feedback.