Caroline Poisard
email: caroline.poisard@espe-bretagne.fr

Maire Ni Riordain

Erwan Le Pipec

Mathematics education in bilingual contexts: Irish-English, Breton-French

Keywords: bilingual contexts, Irish-English, Breton-French, linguistic differences

Irish and Breton are both Celtic languages but unity has vanished resulting in deep linguistic differences. But the common heritage is still at hand when one considers the lexicon, grammatical peculiarities and number. The concept of the structure of a language impacting on thought processes is referred to as the linguistic-relativity hypothesis, which proposes that the vocabulary and phraseology of a particular language influences the thinking and perception of speakers of this language, and that each language will have a different cognitive system. This paper examines the Irish and Breton languages in their bilingual context, their linguistic characteristics and impact on mathematics learning in comparison to English and French, while identifying future research requirements.

INTRODUCTION

Irish and Breton are both Celtic languages, spoken in the western ends of Europe, namely in Ireland and in the western half of Brittany (France). The Celtic languages are divided into two branches: the gaelic one (the native languages of Ireland, Scotland and the Isle of Man) and the brythonic one (comprising Welsh, Cornish and Breton). Accordingly, these languages might have once been the same language or at least two dialects of the same language. Nevertheless, centuries have passed by and unity has vanished, resulting in deep linguistic differences. However, the common heritage is still at hand when one considers the lexicon (roughly 5 000 shared words, those expressing very old notions such as a house: teach/ti; weather: aimsir/amzer; good: maith/mat, etc.) and grammatical peculiarities (mutations of initial consonants to distinguish word gender; mutations in syntactical context; 'declined' prepositions; word order, etc.). Numbers are also a domain where a very old continuity can be traced, as will be shown in this paper. These two languages are spoken in a bilingual context, involving either a Germanic language: English, or a Romance one: French. This is the first investigation of its nature into the Irish and Breton languages and given the rise in Irish-and Breton-medium education it is timely and can contribute to the development of policy in this area. This paper presents a preliminary study and is building on two previous research studies in these contexts [START_REF] Ni Riordain | A comparison of Irish and English language features and the potential impact on mathematical processing[END_REF][START_REF] Poisard | Enseignement et apprentissage des mathématiques à l'école primaire dans un contexte bilingue breton-francais[END_REF], with the aim of identifying future comparative studies. We focus here on languages features and the potential of language as a resource for teaching [START_REF] Adler | Teaching mathematics in multilingual classrooms[END_REF], while examining fundamental questions about relationships between mathematics and language [START_REF] Barton | The language of mathematics. Telling mathematical tales[END_REF]. Taking into account that language reflects the way we see the world and that mathematics is a modelisation of the world, our questions are: What are the features of languages that may be of importance for mathematics teaching and learning? How can language be a potential resource for teaching? How to identify mathematical particularities in linguistic expression?

LANGUAGE CONTEXTS

The history of Irish and Breton is marred by stories of decline and persecution. However, both languages have experienced parallel revivals at various times. Since the 90's on, there is more and more concern in both populations to revitalize their languages and avoid complete extinction [START_REF] Pipec | Le breton, langue-totem?[END_REF]. Strategies have been and are being designed at state or near-state level to revitalize them, primarily by supporting them as medium of education. Table 1 provides a summary of the number of students learning through the medium of Breton and Irish.

Type of schools

Number of primary and secondary students

Total of students

Bretonmedium education

Bilingual public schools 6 662 15 338 Bilingual catholic schools 4 971

Diwan schools 3 705

Irish-medium education

Maintenance heritage language 15 546 56 974

Immersion 41 428 Breton schools are part of the centralised educational system of France and the teaching of Breton is optional. There are over 15,000 pupils learning through the medium of Breton (with an average growth of 4 to 5% per year), ranging from preschool to secondary level (OPLB, 2014). There are three types of Breton-medium schools that pupils can attend, distinguishable by two ways of utilising the languages. The 'bilingual schools' (Public or Catholic) devote the same amount of time to each language. On the other hand, Diwan schools claim to be 'immersive' schools since Breton is only in use during the first four years of schooling. French is then introduced by the age of 7 to 8 and takes up to half of school time by age 11. Irishmedium education is the norm for those growing up in the Gaeltacht regions in Ireland (maintenance heritage language education). The rise in popularity of primary (Gaelscoileanna) and second level (Gaelcholaisti) immersion education (Irishmedium education outside of Gaeltacht regions) is significant and has seen an increase in excess of 60% over the past decade. Currently, approximately 8% of the primary level population and 4% of the second level population are learning through the medium of Irish (Gaelscoileanna Teo., 2014). In Ireland, there is an adequate supply of suitably qualified teachers at the primary level due to incentives and a strong history of native speakers pursuing a career in primary teaching. However, at second level education there is a shortage of suitably qualified teachers to deliver the specific subject areas of mathematics, science and foreign languages through the medium of Irish [START_REF] Gradaigh | Teacher supply and demand in second level Irish-medium school[END_REF]. Similar problems arise in Brittany. However, at primary level a shortage of skilled speakers willing to become teachers can be observed. Moreover, no specific qualification is required for teaching through the medium of Irish/Breton at primary or second level education, although some specific teacher education programmes exist. Accordingly, teachers in Irish-and Bretonmedium schools may not have high standard of Irish/Breton themselves, nor have an understanding of the complexities of teaching and learning mathematics in a bilingual context. Therefore, it is not surprising that teachers report difficulty in supporting the language development element of mathematics teaching and learning and a lack of suitable resources and textbooks to support their work [START_REF] Poisard | Enseignement et apprentissage des mathématiques à l'école primaire dans un contexte bilingue breton-francais[END_REF].

THEORETICAL FRAMEWORK

Bilingual education research shows that using two or more languages to learn and teach is not a simple addition of languages that enable someone to use one language or another [START_REF] Cummins | Bilingualism and special education[END_REF]. Indeed, linguistic competencies and learning strategies are involved simultaneously and bi-/multilingualism is seen as a "language-sensitive approach of content" [START_REF] Bernaus | ConBaT+ Plurilingualism and pluriculturalism in content based teaching[END_REF]. Bilingualism is a particular form of multilingualism. The concept of the structure of a language impacting on thought processes is referred to as the linguistic-relativity hypothesis [START_REF] Sapir | Culture, language and personality[END_REF][START_REF] Whorf | Language, thought and reality[END_REF]. The basic premise of this hypothesis is that the vocabulary and phraseology of a particular language influences the thinking and perception of speakers of this language, and that conceptions not encoded in their language will not be available to them. Hence, they are proposing that each language will have a different cognitive system and that this cognitive system will influence the speaker's perception of concepts [START_REF] Whorf | Language, thought and reality[END_REF]. Whorf emphasises also that we act according to how we describe things, and accordingly different languages may classify experience in different ways. Therefore, in theory, an Irish speaker/learner should have a different cognitive system to that of an English speaker/learner, influence our actions and accordingly may influence mathematical understanding. For example, Miura et al. (1994, p.410) contend that 'numerical language characteristics (East-Asian languages) may have a significant effect on cognitive representation of number'. However, other researchers have questioned argued for the difficulty in applying the linguistic-relativity hypothesis and the difficulty in testing such claims in relation to mathematical thinking [START_REF] Towse | Linguistic influences on children's number concepts: Methodological and theoretical considerations[END_REF]. We acknowledge that this may be too strong of a way of viewing the influence of language on the mathematical thinking and less severe forms of this hypothesis have been proposed. We support the premise that language may not shape and determine our entire mathematical thinking, but that it may influence it to a certain degree and facilitates our thinking and perception [START_REF] Sternberg | Cognitive psychology[END_REF]. Moreover, we are acutely aware of the importance of other factors such as exposure to mathematics, teaching strategies employed and culture as influencing attainment in mathematics, not just language [START_REF] Towse | Linguistic influences on children's number concepts: Methodological and theoretical considerations[END_REF]. For example, some research shows the positive effect of teaching and learning mathematics in bilingual and multilingual classrooms. In particular, [START_REF] Adler | Teaching mathematics in multilingual classrooms[END_REF] considers linguistic plurality as a possible resource for mathematics teaching. Three types of resources are distinguished: material, cultural (including language) and human resources. Adler's work is set in the post-apartheid context in South Africa where multilingual classrooms and lack of material resources are common. She shows how linguistic diversity can gradually constitute a resource for mathematics teachers. At primary level, [START_REF] Setati | Teaching mathematics in a primary multilingual classroom[END_REF] explored the language practices in primary multilingual mathematics classroom in South Africa where the complex relationships between English language and home language and mathematics education is confirmed. In Australia, Edmonds-Wathen (2015) studied the grammar and conceptualisation of motion in Iwaidja, an indigenous language. She discusses how understanding grammatical features to express spatial concepts in Iwaidja can help teachers of Indigenous students. [START_REF] Moschkovich | A situated and sociocultural perspective on bilingual mathematics learners[END_REF] research demonstrates that language can be a resource if a teacher's focus is not only on acquiring mathematical vocabulary, but also on constructing multiple meanings across registers and on developing participation in mathematical practices. This is possible only if teachers are aware of cultural and mathematical needs to teach mathematics [START_REF] Adler | Teaching mathematics in multilingual classrooms[END_REF].

The example of New Zealand is also of interest to us [START_REF] Barton | Tikanga Reo Tatai: Issues in the Development of a Maori Mathematics Register[END_REF]. In the 1980's mathematical vocabulary was developed in Maori. Several general principles were adopted in making vocabulary decisions and "metaphors were a common method of vocabulary development in both formal and informal settings. […] An example was the development of rere and arawhata as early translations of continuous and discrete as applied to statistical data, the methaphor being that of a flowing stream or one proceeding in a sequence of waterfalls." (Barton, Fairhall & Trinick, 1998, p.5). In the Welsh context, [START_REF] Jones | Words with a similar meaning[END_REF] concluded that there are benefits to studying mathematics in a minority language due to it being developed relatively recently as a language of learning and accordingly the terminology established tends to avoid linguistic complexity and employs a more self-explanatory mode. Furthermore, [START_REF] Dowker | Linguistic influences on numeracy[END_REF] found an advantage for students learning through the medium of Welsh, in comparison to English, in terms of how numbers and arithmetical relationships are expressed in Welsh. Our work in the Breton context [START_REF] Poisard | Enseignement et apprentissage des mathématiques à l'école primaire dans un contexte bilingue breton-francais[END_REF] shows that the particularities of the Breton language can be a resource for the teaching of mathematics, for example in the teaching of geometrical concepts and oral numeration. Teachers in this study also identified a lack of suitable resources as a significant issue. In particular, many of the material resources used in class are a direct translation from French to Breton, with no consideration of linguistic and cultural specificities. Mathematical and linguistic competencies are interrelated and these competencies need to be jointly developed by students and teachers. Research in the Irish context demonstrates that students with high ability in both languages (Irish and English) perform better mathematically [START_REF] Ni Riordain | The relationship between performance on mathematical word problems and language proficiency for students learning through the medium of Irish[END_REF] and that a significant relationship exists between their performance on English mathematical word problems and their Irish language proficiency at the primary to second level education transition [START_REF] Ni Riordain | Mathematics and Gaeilge: A report on the influence of bilingualism[END_REF]. A comparison of the English and Irish languages demonstrates that there are differences between the two languages in relation syntax, semantics and access to meaning.

However, what is difficult to conclude, without further investigation, is whether differences between the languages have a differential impact upon cognitive processing [START_REF] Ni Riordain | A comparison of Irish and English language features and the potential impact on mathematical processing[END_REF]. In this paper we discuss such questions in Irish and Breton mathematical vocabulary and the structure of the languages, while demonstrating how bilingual students' languages can be a resource for them in mathematics learning. As in [START_REF] Barton | The language of mathematics. Telling mathematical tales[END_REF], we examine fundamental questions about relationships between mathematics and language.

LANGUAGES: A RESOURCE TO TEACH MATHEMATICS

Some linguistic peculiarities of Breton and Irish may influence the teaching of mathematics. The facilitating aspects and combinations of key features of Breton and Irish are presented here, and where appropriate comparisons are made with English and French. The findings presented here are hypothesis and further investigation (class observations, interviews, questionnaires, etc.) would be helpful to give some more precise conclusions of the influence of the use of these languages on bilingual learners of mathematics. We will not discuss dialects in this section, but Breton and Irish codification as united languages leave much space for dialect variation. In many places, it may happen that the language of books differs from oral use. General features of the languages (sentence length, topic prominence, mutations) are presented initially, followed by a focus on mathematical aspects (transparent lexicons, oral numerations and numbers). The six aspects we develop here are linked to our previous individual research [START_REF] Ni Riordain | A comparison of Irish and English language features and the potential impact on mathematical processing[END_REF][START_REF] Poisard | Enseignement et apprentissage des mathématiques à l'école primaire dans un contexte bilingue breton-francais[END_REF] and demonstrate commonalities between both languages.

Sentence length: Short sentences are generally more common in Breton and Irish than in French and English, which demands less concentration for pupils and shorttime memory is devoted to side-information. Shorter sentences lend to an easier understanding of mathematical text and are a desirable feature [START_REF] Austin | Language and mathematical education[END_REF]. English and French readers may have a greater cognitive processing load, and this suggests a difference in mathematical processing.

Topic prominence: Breton and Irish are strongly oriented topic-prominence languages, in comparison to French and English. In Irish, the first word is usually the verb, while in Breton, it may be any word (rarely the verb). Indeed, in Breton, words expressing new information should come first in a sentence, no matter of their grammatical status or function. In problem solving, this gives pupils clues about relevant mathematic information, emphasised by their position in texts [START_REF] Galligan | Possible effects of English-Chinese language differences on the processing of mathematical text: A review[END_REF]) in comparison to English and French. Topic prominence may alter the complexity of semantic structures and have an effect on mathematical processing.

Mutations:

They are an important feature of Celtic languages, either to indicate word gender or in syntactical constructions. As an example, in Breton after the word tri (three), any p-standing at the beginning of a word goes to f-. When combined with poent (point), three points is thus expressed as tri foent. The permanence of words through surface changes may help to understand the permanence of mathematical relations. Although mutations would cause difficulties for pupils with good language skills, recognising mutated words (especially when there are many of them) may be problematic for those insufficiently familiar with the language. Such mutations are not evident in English and French.

Transparent lexicon: A large part of the mathematical vocabulary is coined out of autochthonous word-roots. The meanings of many words have become easier to understand. For example, to say parallel in Breton is kenstur (same direction) and in Irish is comhthreomhar (equal directionality). Many of the Breton/Irish words describe concepts/objects as opposed to just labelling them. Given that the more easily and quickly the meaning of words is activated, the simpler it is to process mathematical text. It may help to retrieve all the words associated with the concept thus enhancing the total cognitive structure [START_REF] Galligan | Possible effects of English-Chinese language differences on the processing of mathematical text: A review[END_REF]. However, Celtic-made vocabulary has been criticised for various reasons: some words might have been coined too quickly by amateur linguists; often these words are not encountered outside of the classroom; in some cases, they were promoted not in an effort to facilitate understanding, but to wash brains of a foreign language; concern lies with if pupils must leave and should adapt to a dominant-language school. This is why an international mathematical lexicon has also been developed in Breton [START_REF] Kergoat | Terminologie bretonne: rétrospective, débats et enjeux[END_REF]. Instead of kenstur, the teaching authority now recommends to express parallel a s parallelenn. Further investigation is needed in terms of student learning and accessing meaning in more common languages/lexicon of English/French.

Oral numerations and counting:

In this area [START_REF] Guitel | Histoire comparee des numerations ecrites[END_REF] gives an historical view of written numeration. One of the particularities of Celtic languages is the use of vigesimal system (base 20) to say numbers. Some groupings by 20 are evident in French also. In old Irish, we find traces of 20 groupings in all tens: 30, 40, 50, 60, 70, 80, and 90. For example 90 is ceithre fhichead a deich (four-twenty and ten, 4×20+10). We find traces in French for 80 (quatre-vingts four-twenty, 4×20+10) and 90 (quatre-vingt-dix, four-twenty-and-ten, 4×20+10) where it is literally the same expression as old Irish. Breton refers also to 20 for 40, 60, 70, 80, and 90. Indeed 40 is daou-ugent (two-twenty, 220), 60 is tri-ugent (three-twenty, 320)… 90 is dek ha pevar-ugent (ten-and-four-twenty, 10+420), etc. In Breton the word order is not the same: +10 is mentioned before and not after as in French and English. We have the equality (the model) 90=4×20+10= 10+4×20 that is shown in a comparison of languages. If we make a link with topic prominence (above), we could argue that old Irish emphasises the grouping by 20 (coming first) and Breton the addition on this grouping (+10 coming first). These characteristics are clearly different from the numerations/counting systems of English and French (base 10). We think that the comparison of number names could be a rich resource for teaching oral numeration, written numeration and the associated mathematical meaning. Oral numerations have been studied concerning other contexts. For example, number words in "other" languages is explored by [START_REF] Chronaki | Number words on 'other' languages: the case of little Marram[END_REF] in the Greek context to experiment a mathematical learning activity with young children, and shows that the creation of a culturally responsive context.

Word order to say numbers: In Breton, 32 pupils is said daou skoliad ha tregont (two pupil and thirty, 2 pupil and 30). The common name expressed by the number is in-between tens and units. One can notice that the name is here in singular form (skoliad) and not plural (skolidi). Indeed plurality is not attached to nouns but it is expressed by the adjunction of a number. For large numbers, the word order refers also to this rule. For example, 32 000 pupils (daou vil skoliad ha tregont, 2 thousand pupil and 30 (thousands not mentioned), coming from 2 000+30 000) and 3 020 pupils is (tri mil ugent skoliad, 3 thousand 20 pupil, 3 000+20). Irish is similar to Breton when using ordinal numbers in that the common name is positioned inbetween tens and units. For example, 53 pens is trí pheann is caoga (three pens and fifty, 3 pens and 50). Large numbers generally preserve this order also. This can be seen as a difficulty for students, but we also argue that this is a good opportunity to work on number sense and the place of each digit in a number. In Irish, different words are used for counting people: two, three, four etc. is expressed by beirt, triúr, ceathrar, to signify that the numbers relates specifically to counting people. The comparison between the languages is a good resource to understand the grouping by three of large numbers.

DISCUSSION AND CONCLUSION

This paper explored specific aspects of language concerned with mathematics teaching and learning in relation to the bilingual contexts of Irish-English and Breton-French. But why does this matter? The importance of language for the teaching, learning, understanding and communication of mathematics cannot be ignored. Features of the Irish and Breton languages presented in this paper demonstrate the importance of investigating languages and their potential impact on mathematical learning. For example, some Breton and Irish words assist in conveying meaning and/or permit the concept to be formed more readily. Similarly the sentence structure allows access to key information. Some promising insights are emerging, suggesting that students who learn through the medium of Irish or Breton may experience advantages in terms of mathematical learning. Further investigation is needed into how a particular language and its syntactical structure may impact on mathematical activity and reasoning [START_REF] Morgan | Grammatical structure and mathematical activity: Comparing examination questions[END_REF].

When investigating the Irish and Breton languages we are cognisant of the fact that that we are investigating bilingual learners (Irish-English, Breton-French). Clearly the intricate relationship between mathematics learning and a student's language is highly complex. This is further complicated when working with bilingual learners. Moreover, we need to consider mathematics as a discourse and that this is not a singular or homogenous discourse [START_REF] Adler | Teaching mathematics in multilingual classrooms[END_REF]. Accordingly, mathematical learners use multiple resources and languages from their experiences (both in and outside of the learning context) and we need to be cognisant of multiple registers co-existing in the learning environment. Bilingual learners should not be viewed in a deficit mode, but rather view their language(s) as a resource for learning mathematics. However, as demonstrated in this research paper, this area is under-researched and undertheorised. Research practices/findings generated from participants from a dominant group (e.g. monolingual speakers) assumes these to be the norm for all learners. We endorse a call for more research in relation to the specific role of bilingual learners' different languages when engaged in mathematical learning [START_REF] Barwell | Multilingual issues in mathematics education: introduction[END_REF]. There has been a focus more on the social, rather than cognitive functions of code switching [START_REF] Ni Riordain | A comparison of Irish and English language features and the potential impact on mathematical processing[END_REF]. The authors of this paper purpose that there is a need for a coherent and integrated framework to investigate whether differences in languages, and their use, by bilingual mathematical learners, have a differential impact upon cognitive mathematical processing. The authors also stress the importance of recognising and integrating the social aspect of learning into the framework and seeing language as a resource for the teaching and learning of mathematics.

Table 1 : A comparison between Irish and Breton educational contexts

 1


Julie Paxion
email: julie.paxion@gmail.com

Edith Galy

Catherine Berthelon
email: catherine.berthelon@ifsttar.fr

Overload depending on driving experience and situation complexity: which strategies faced with a pedestrian crossing?

Keywords: Subjective workload, Driving experience, Situation complexity

The purpose of this study was to identify the influence of situation complexity and driving experience on subjective workload and driving performance, and the less costly and the most effective strategies faced with a hazard pedestrian crossing. Four groups of young drivers (15 traditionally trained novices, 12 early-trained novices, 15 with three years of experience and 15 with a minimum of five years of experience) were randomly assigned to three situations (simple, moderately complex and very complex) including unexpected pedestrian crossings, in a driving simulator. The subjective workload was collected by the NASA-TLX questionnaire after each situation. The main results confirmed that the situation complexity and the lack of experience increased the subjective workload. Moreover, the subjective workload, the avoidance strategies and the reaction times influenced the number of collisions depending on situation complexity and driving experience. These results must be taken into account to target the prevention actions.

Introduction

Epidemiological studies covering 37 countries show that young drivers are the most involved in road accidents (Organisation for Economic Co-operation and Development (OECD) / International Transport Forum (ITF), 2014). The age is thus an important factor and more precisely the experience inherent in the age, as the accident rate decreases with experience [START_REF] Mayhew | Changes in collision rates among novice drivers during the first months of driving[END_REF] with a high risk the first months and the first kilometres after getting the driving license [START_REF] Mcknight | Content of driver education. Driver education: The path ahead[END_REF][START_REF] Preusser | The novice driver problem. Driver education: The path ahead[END_REF]. During the first eight months, the number of accidents involving novice drivers decreases by approximately 50% (Sagberg, 2000, cited by OECD, 2006), confirming that these road accidents are more linked to their driving experience than to their age.

Situation complexity and hazard events also constitute a major determinant of driving performance. Generally, most fatalities occur on rural roads compared to urban roads and motorways, with 65% of the fatalities in France, 62% in Austria, almost 60% in the United Kingdom, 49% in United States and 48% in Belgium in 2012 (OECD/ITF, 2014). These types of roads define the situation complexity, according to a taxonomy that classifies the elements of a situation as more or less complex [START_REF] Fastenmeier | Die Verkehrssituation als Analyseeinheit im Verkehrssystem [The road traffic situation as analysis unit in the road traffic system[END_REF]. The complexity can thus vary with road geometry (rectilinear vs. curvilinear, flat vs. hilly), roadside environment (quantity and variability of traffic signs, variability of the scenery) and traffic density (low vs. high).

Finally, hazard events are broadly observed with pedestrians crossing the road, making them the largest group of vulnerable road users in most countries. The number of fatalities amongst pedestrians slightly increases since 2009 and represents 19% of all fatalities in the 37 countries recorded by the International Traffic Safety Data and Analysis Group (IRTAD) in 2014 (OECDE/ITF, 2014). Data from the Detailed Accident Study collected by the Mechanisms of Accidents Laboratory at IFSTTAR (French Institute of Science and Technology for Transport, Development, and Networks) also precise that unexpected events, such as a pedestrian crossing in front of a driver, correspond to prototypical accident scenarios [START_REF] Damm | The evaluation of traditional and early driving learning with simulated accident scenarios[END_REF]. Among several configurations of accidents between a vehicle and a pedestrian, many occur when a pedestrian moves more or less perpendicular to the vehicle path covers [START_REF] Wisch | Scenarios and weighting factors for pre-crash assessment of integrated pedestrian safety systems[END_REF].

Considering that 90% of road accidents are due to human errors [START_REF] Amditis | Towards the Automotive HMI of the Future: Overview of the AIDE-Integrated Project Results[END_REF], the research question concerns the processes involved and particularly the subjective workload, i.e. cost perceived depending on the interaction between required tasks and drivers' internal state (Hockey, 2003). Situation complexity and low driving skills can particularly enhance the drivers' level of subjective workload, leading to performance impairments. Based on the taxonomy of situation complexity [START_REF] Fastenmeier | Die Verkehrssituation als Analyseeinheit im Verkehrssystem [The road traffic situation as analysis unit in the road traffic system[END_REF], a recent study revealed performance degradations in "urban" sections and "oncoming traffic" sections (complex situations) compared to "rectilinear roads" sections (simple situation), characterized by higher Standard Deviations of the Lateral Position (SDLP) and higher Standard Deviations (SD) of speed [START_REF] Baldauf | Time perception as a workload measure in simulated car driving[END_REF]. Meister's model (1976) explains these results by a link between the situation complexity, the level of subjective workload and the performance. When the situation is low demanding (e.g., in long and monotonous roads with a low traffic density), or conversely high demanding (e.g., in rural roads with a high traffic density), the level of subjective workload is high and the performance is impaired, revealing an overload. Indeed, when the level of demand is low, the driver has to provide a high effort to overcome the vigilance decrement and when the level of demand is high, the driver needs to provide a high effort to process the vast amount of information. In these types of situations, the level of workload thus increases with the provided effort, until the driver doesn't have sufficiently available resources to maintain a good performance. However, when the situation is moderately complex (e.g., in rural roads with a moderate traffic density), the level of subjective workload is relatively low. Even if it slightly increases, drivers can adopt the compensatory strategy of reducing their speed in order to correctly perform the task. Accident reports on rural roads provide few details about road characteristics at the time of the accidents. However, it is necessary to identify the potential complex elements of the situation in the aim of better discern the origin of rural roads' accidents.

Workload varies differently depending on driving experience. The Skill, Rule, Knowledge (SRK) model of [START_REF] Rasmussen | Information processing and human-machine interaction[END_REF] shows that driving skills are acquired in three steps with experience. The Knowledge-based behavior, mainly adopted by novice drivers, is a controlled action (slow and effortful) referring to the knowledge about the Highway Code and previous experiences. The Ruled-based behavior is an intermediate step which can be adopted either by novice or experienced drivers. It is a controlled action which follows prescribed rules (e.g., stopping at a red traffic light). The Skill-based behavior is an automatic action (fast and effortless) rather adopted by experienced drivers (e.g., changing gear without attention). This model confirms that novice drivers predominantly have a lack of routine automation [START_REF] De Craen | The development of a method to measure speed adaptation to traffic complexity: Identifying novice, unsafe, and overconfident drivers[END_REF]. Performing the task thus implies producing a higher effort for novices than for experienced drivers (Patten, Kircher, Östlund, Nilson, & Svenson, 2006), this effort reflecting a high level of subjective workload.

Consequently, novice drivers are more likely to have accidents when they are overloaded, with a level of workload too high to maintain a good performance.

Three profiles of young French drivers can especially qualify the different levels of experience. Traditional trained drivers have 20 hours of driving lessons with an instructor.

Early-trained drivers have an additional driving practice with an adult during 3000 km and can start the learning at the age of 16. These two profiles of novice drivers can both get their driving license from the age of 18. They subsequently have a restricted license including a speed limitation and a restriction to 6 points instead of 12 points on their license. This probationary period, preceding the obtaining of a full license, lasts three years for traditionally trained drivers and two years for early trained drivers. It also appears that drivers with more than five years of experience are three times less likely to have an accident compared to drivers who have just had their driving license [START_REF] Maycock | The accident liability of car drivers[END_REF].

Therefore, the overload probably appears earlier with the lack of experience, in the following order for: novice drivers who are traditionally trained, novice drivers who are early-trained, drivers arriving at the end of the three year probationary period, and drivers having more than five years of experience.

Faced with a hazard event with a high temporal pressure as a pedestrian crossing, reacting in time to avoid the vulnerable user becomes difficult. Several strategies can be adopted to avoid the accident, i.e. braking, swerving, making a combination of both of them, or anticipating the hazard appearance by braking, swerving or releasing the accelerator pedal in advance. According to a literature review about possible avoidance maneuvers in emergency situations [START_REF] Adams | Review of the literature on obstacle avoidance maneuvers: braking versus steering[END_REF], drivers brake more than they swerve, although braking alone is less effective to avoid any collision than swerving or both braking and swerving.

Age and experience are often combined in driving studies. The present objective is to particularly focus on driving experience by comparing, among young drivers, groups having different levels of experience. The main hypothesis is that combined effects of high temporal pressure inducted by pedestrian apparition, situation complexity (simple or very complex situations) and lack of experience should enhance the level of subjective workload and impair driving performance when drivers are faced with an unexpected pedestrian crossing the road.

Performance decrement could be longer reaction times and a higher number of collisions with the pedestrians due to costly and inappropriate avoidance maneuvers as braking alone [START_REF] Adams | Review of the literature on obstacle avoidance maneuvers: braking versus steering[END_REF].

Methods

Participants

Fifty-seven young drivers (33 males and 24 females) were divided up into four groups depending on their driving experience. Two groups were composed of novice drivers who obtained their driving license within the last two months. Fifteen novices aged 18-20 (mean = 19, SD = 0.84) were Traditionally Trained Drivers (TTD), with a minimum of 20 hr of driving lessons. Twelve novices aged 18 (mean = 18, SD = 0) were Early-Trained Drivers (ETD), with a minimum of supplementary driving practice of 3 000 km under the monitoring of an adult having a full driving license. The two other groups included more experienced drivers, with 15 drivers aged 21 (mean = 21, SD = 0) arriving at the End of the three-year (more or less 3 months) Probationary Period (EPP), and 15 Experienced Drivers (ED) aged between 23-30 (mean = 26.87, SD = 2.97) with a minimum experience of five years. The participants' recruitment was realized by soliciting driving schools, secondary schools, universities, and university institutes of technologies (UTI). Only participants corresponding to the inclusion criteria were selected, i.e. in good health, with a normal or corrected view, and without any sensitivity to motion sickness. All have signed a written informed consent form and the experimental setup has been approved by the IFSTTAR ethic committee for biomedical research.

Apparatus

The experiment was carried out on the fixed-base driving simulator of the Laboratory of Accident Mechanisms Analysis (LMA), equipped with a multi-actor parallel architecture for traffic simulation (ArchiSim) and an object database SIM²-IFSTTAR (simulation software) [START_REF] Espié | Driving simulators validation: The issue of transferability of results acquired on simulator[END_REF]. The "ArchiSim" architecture was built on the DR2 traffic simulation model (management of "autonomous" and "enslaved" vehicle with a behavior defined by the scripts for each scenario, simulation generated by captors of punctual and space traffic) and on the 3D SIM2 loop of visualization. The interactive driving station comprised one quarter of a vehicle including a seat, a dashboard, and controls equipped with captors, i.e. pedals and steering wheel (see Fig. 1).

Experimental situations

Three National roads respecting a width of 3.50 m, corresponding to the international standardization of main roads taking the lateral safety margins as a function of the speeds used into account (Vertet & Giausserand, 2006), were stretched over 22.5 km each (around 15 minutes of driving). According to the taxonomy of the elements characterizing the complexity of a driving situation [START_REF] Fastenmeier | Die Verkehrssituation als Analyseeinheit im Verkehrssystem [The road traffic situation as analysis unit in the road traffic system[END_REF], two elements have been taken into account in the experiment, i.e. road geometry (rectilinear vs. curvilinear) and traffic density (without vs. with). The simple situation consisted in a rectilinear national road with two ways, without any traffic. The center marking was a continuous white line. The moderately complex situation included 5 right and 5 left curves (length: 600 m, radius: 300 m). The very complex situation had double and sharper curves (length: 300 m, radius: 120 m), with oncoming traffic. Whatever the situation, three scenarios implying a pedestrian were included. The pedestrians, randomly hidden by a billboard, a bus stop or a tree on the right side of the way, crossed the road around 2.7 seconds before the participant arrived at their level. This time was calculated in such a way that, as soon as the pedestrian appeared in the drivers' visual field, they could brake in time to avoid the pedestrian. Each pedestrian walked at 5 km/hr (walking average speed of an adult, see Seiniger, Bartels, Pastor, & Wisch, 2013) and had a 90° crossing angle, perpendicular at the participants' trajectory.

Subjective measures

The workload was self-assessed by the NASA Task Load Index questionnaire [START_REF] Hart | Development of NASA-TLX (Task Load Index): Results of Emperical and Theoritical Research[END_REF]) comprising 6 subscales: Mental Demands, Physical Demands, Temporal Demands, Own Performance, Effort and Frustration. For each subscale, participants estimated their level of workload during the previous situation on a 20 points scale ranged from 0 = 'very low' to 20 = 'very high'. For the Own Performance subscale, the scale was ranged from 0 = 'success' to 20 = 'failure'. The questionnaire was adapted to the experimental situations.

For each subscale, the question concerned the level attributed to the pedestrian crossings.

Objective measures of driving performance

During the portions with pedestrians, the objective driving behavior was observed by the strategies to avoid the pedestrians (braking, swerving, combination of both braking and swerving, and anticipating), the Reaction Times (RT) of the first action realized after the pedestrians appearances in the driver's vision field, and the number of collisions with the pedestrians. The action of anticipation was defined as the action made just before the pedestrian appearance. This action could be either releasing the accelerator pedal, pressing the brake pedal, or swerving on the right or on the left of the pedestrian. For each situation, swerving was noted when the Lateral Position (LP) of the driver increased from more or less than the mean of the Standard Deviation of Lateral Position (SDLP) observed on all the rectilinear portions of the whole situation. The collisions with the pedestrians did not have a negative impact on the participants who passed through the image without any visual change.

Procedure

Before the experiment, the participants were trained in order to get accustomed to the simulator as a function of the different tasks which they had to perform during the three situations. They thus had to drive at 90 km/h on a straight line, to turn left, to turn right, and to brake. The training was stopped when they judged it sufficient to feel comfortable with the simulator commands. The three situations were then presented in a counterbalanced order, with the same instruction, i.e. "you will be on a National Road limited at 90 km/h. Drive by respecting the rules of the Highway Code, as in real driving". The NASA-TLX questionnaire was filled out after each situation to collect the subjective level of workload induced by the different driving situations (see Fig 2). The whole experiment lasted around 1h30.

Statistical analyses

As we observed a significant order effect of the pedestrian appearance on the number of collisions with the pedestrians with a higher number of collisions with the first pedestrian than with the second and the third ones, analyses only took into account the second and third pedestrian appearances which were more expected than the first pedestrian. Therefore, the surprise effect of the first pedestrian appearance was not analyzed.

Four statistical analyses (statistical significance set at p≤.05) were carried out. Second order polynomial regressions were realized on standardized data for all analyses except from the second one. Subsequently, post-hoc analyses were followed with independent samples t-tests for pairwise comparisons, and with simple linear regressions for the effect of a variable on another one in each condition.

The first analysis was on a 4 (driving experience: Traditionally Trained Drivers vs.

Early-Trained Drivers vs. drivers at the End of the Probationary Period vs. Experienced Drivers) × 3 (situation complexity: simple vs. moderately complex vs. very complex) × 4 (strategy: braking vs. swerving vs. combination of braking and swerving vs. anticipating) partially crossed design. Indeed, each strategy was not found in each situation. The dependent variable was the subjective workload attributed to pedestrian crossings.

The second analysis followed a 4 × 3 mixed factorial design, with driving experience as a between-participants variable, and situation complexity as a within-participants variable.

The dependent variable was the strategy. A repeated measures analysis of variance (ANOVA) was followed by Bonferroni post-hoc tests used for pairwise comparisons.

Before the third analysis, Sobel tests were realized in order to identify the mediation effects, i.e. effects of driving experience and situation complexity on the Reaction Time, mediated by subjective workload. The third analysis was based on a 4 (driving experience) × 3 (situation complexity) × 3 (subjective workload) partially crossed design. The dependent variable was the Reaction Time (RT).

Before the last analysis, Sobel tests analyzed the effects of driving experience and situation complexity on the number of collisions, mediated by subjective workload, strategy and RT. The effect of subjective workload on the number of collisions, mediated by RT was also analyzed. The last analysis thus based on a 1 (subjective workload) × 4 (strategy) × 1 (RT) partially crossed design. The dependent variable was the number of collisions with pedestrians.

Results

Subjective workload attributed to pedestrian crossings

For the mean scores of subjective workload, a 4 (driving experience) × 3 (situation complexity) × 4 (strategy) second order polynomial regression was run. In this model, all the predictors accounted for 13.04% of the variance (adjusted R-squared).

Driving experience significantly influenced the subjective workload (linear effect: β = -.27, p < .001; non linear effect: β = -.23, p < .001). ETD (M = 14.43, SD = 3.62) had higher scores than TTD (M = 12.00, SD = 4.18), EPP (M = 11.42, SD = 3.34), and ED (M = 10.08, SD = 2.91). Moreover, TTD had higher scores than ED. Situation complexity also had a significant linear effect on subjective workload (β = .15, p < .01). Post-hoc analyses did not reveal any difference between each situation, except from a marginally significance (t(160) = -1.69, p = .09) with higher scores in very complex situation (M = 12.44, SD = 3.83) than in simple situation (M = 11.01, SD = 3.94).

No other significant effect was obtained for subjective workload (strategies, β = -.02, ns; driving experience × situation complexity interaction, β = .02, ns; driving experience × strategies interaction, β = -.02, ns; and situation complexity × strategies interaction, β = -.07, ns).

Strategies

Participants' strategies were submitted to a 4 (driving experience) × 3 (situation complexity) repeated measures ANOVA. In this model, the adjusted R-squared were 0.23% for the simple situation, -1.12% for the moderately complex situation, and -0.36% for the very complex situation. Driving experience (F (3,110) = 0.21, n.s), situation complexity (F (2,220) = 2.13, ns) and driving experience × situation complexity interaction (F (6,220) = 1.54, ns) did not have any effect on the type of strategies.

Reaction Times

The mean scores of RT were submitted to a 4 (driving experience) × 3 (situation complexity) × 3 (subjective workload) second order polynomial regression. In this model, all the predictors accounted for 3.20% of the variance (adjusted R-squared). Driving experience significantly shortened the RT (linear effect: β = -.16, p < .01). RTs were thus longer for ETD than for TTD, EPP and ED. Moreover, TTD and ED had longer RT than EPP (see Table 1). The increase of subjective workload significantly shortened the RT with a linear effect (β = -.13, p < .05) and lengthened the RT with a non linear effect (β = .21, p < .05). The driving experience × subjective workload interaction had a significant non linear effect (β = -.21, p < .05). For ETD and EPP, the increase of subjective workload shortened the RTs (respectively β = -.34, p < .01; β = -.22, p < .05), whereas for TTD and ED, the subjective workload did not influence the RTs (respectively β = -.21, ns; β = .07, ns).

No significant effect of situation complexity (β = .05, ns), driving experience × situation complexity interaction (β = -.10, ns), and situation complexity × subjective workload interaction (β = -.08, ns) on RTs was observed.

Sobel tests did not reveal any mediation effect.

Number of collisions with pedestrians

For the mean number of collisions with pedestrians, a 4 (strategy) × 1 (subjective workload) × 1 (RT) second order polynomial regression was run. In this model, all the predictors accounted for 16.72% of the variance (adjusted R-squared). The increase of subjective workload significantly enhanced the number of collisions (linear effect: β = .12, p < .05). The lengthening of RT increased the number of collisions with a significant linear effect (β = .27, p < .001) whereas it started to slightly increase the number of collisions and finished to decrease the collisions number with a non linear effect (β = -.26, p < .01).

The situation complexity × driving experience interaction had a significant non linear effect on the collisions number (β = -.12, p < .05). For TTD, the number of collisions was higher in very situation than in simple situation. For ED, the scores were higher in simple situation than in moderately complex situation. No other difference was observed (see Table 2). The driving experience × subjective workload interaction significantly influenced the number of collisions (linear effect: β = -.14, p < .05). Indeed, for TTD and ETD, the increase of subjective workload enhanced the number of collisions (respectively β = .22, p < .05; β = .29, p < .05), whereas for EPP and ED, the subjective workload did not influence the number of collisions (respectively β = .08, ns; β = -.08, ns). The situation complexity × strategies interaction significantly influenced the number of collisions (linear effect: β = -.12, p < .05; non linear effect: β = .17, p < .05). In simple situation, the scores were higher for the braking and the combination of braking and swerving than for the swerving. In moderately complex situation, no difference between the strategies was observed. In very complex situation, the scores were higher for the braking than for all the other strategies (see Table 3). The subjective workload × strategy interaction had a significant non linear effect on the collisions' number (β = .14, p < .05). For the braking strategy, the increase of subjective workload enhanced the number of collisions (β = .33, p < .001). When the drivers swerved, both braked and swerved, or anticipated, no effect of subjective workload was observed (respectively β = -.04, ns; β = -.15, ns; β = -.25, ns). Finally, the RT × strategy interaction had a significant non linear effect on the collisions' number (β = .14, p < .05). When drivers braked or made a combination, the lengthening of RT increased the number of collisions (respectively β = .33, p < .001; β = .25, p < .01), whereas no effect was observed when they swerved (β = -.13, ns).

The number of collisions was not influenced by strategies (β = . turn increased the number of collisions (respectively β = .17, p < .01; β = .18, p < .01).

Discussion

The main purpose of this study was to identify the subjective level of workload produced by situation complexity and driving experience but also to identify the critical level of workload (overload) which produced performance decrement faced with a pedestrian crossing the road in front of the drivers. Three levels of environment complexity and four levels of driving experience were manipulated. The strategies used by the drivers to avoid the pedestrian were analyzed in terms of cost and effectiveness, as a function of situation complexity and driving experience.

As expected, the showed an effect of situation complexity and driving experience on subjective workload and driving performance. Thus, for all the drivers, an increase of subjective workload was globally observed when the situation complexity increased, with a tendency to higher self-assessment of the workload in very complex situation than in the simple one. The absence of subjective workload difference between the moderately complex situation and the very complex one could be due to a lack of complexity variation, the curves succession probably being too repetitive to modify the perception of the difficulty between these two situations.

Moreover, the lack of experience increased the subjective workload with the highest levels of workload for novice drivers (traditionally trained and early-trained drivers). This increase of subjective workload enhanced the number of collisions with the pedestrians, probably revealing an overload. Therefore, compared to traditionally trained drivers, the additional experience acquired by early-trained drivers did not allow managing a sudden hazard event such as the pedestrian crossing. Conversely, the three-year probation period was sufficient to cope with this event and seems sufficient to acquire a certain level of driving automation, i.e. skill-based behavior [START_REF] Rasmussen | Information processing and human-machine interaction[END_REF], which requires less resources to avoid the pedestrians.

As expected and independently of the subjective workload, the number of collisions made by traditionally trained drivers was higher in very complex situation than in the simple one. However, experienced drivers made more collisions in simple situation than in the moderately complex one. This suggests that the subjective workload is not the only factor that could influence driving performance. Indeed, in simple situation (e.g., a monotonous road), low vigilance could not only lead to an increase in errors but to an increase in reaction times as well [START_REF] Lal | Reproducibility of the spectral components of the electroencephalogram during driver fatigue[END_REF]. Consequently, the difficulty to avoid the sudden pedestrian appearance was probably enhanced for experienced drivers who drove with a routine automation in a monotonous environment without being flexible. Indeed, routine automation might have produced difficulties to switch from an automatic action to a controlled one which can involve errors [START_REF] Besnard | Troubleshooting in mechanics: A heuristic matching process[END_REF].

Driving experience also had an effect on the reaction times faced with the pedestrians.

Indeed, early-trained drivers had longer reaction times than the other groups, and traditionally trained drivers and experienced drivers had longer reaction times than drivers at the end of the probationary period. The results also highlighted that for early-trained drivers and drivers at the end of the probation, the increase of subjective workload shortened their reaction times.

This could explain the shortest reaction times of drivers at the end of the probation but not the longest reaction times of early-trained drivers. Another factor might have lengthened earlytrained drivers' reaction times, such as the anxiety related to the hazard pedestrian appearance. Indeed, the high temporal pressure to avoid the pedestrian could have provoked a high level of anxiety, often responsible of long reaction times among novice drivers [START_REF] Wallis | Using fuzzy signal detection theory to determine why experienced and trained drivers respond faster than novices in a hazard perception test[END_REF].

Concerning the adopted strategies to avoid the pedestrians, the results revealed no difference between the groups and the situations, probably because none of the strategies was perceived as more costly than another strategy. The strategy adoption was thus not constrained by the felt cost. Consistent with our expectations, several adopted strategies increased the number of collisions as a function of the situation complexity. In simple situation, the number of collisions was higher when the drivers braked and made a combination than when they swerved. According to [START_REF] Adams | Review of the literature on obstacle avoidance maneuvers: braking versus steering[END_REF], this result confirms that the swerving strategy was more effective than the braking one. But, contrary to the statement of [START_REF] Adams | Review of the literature on obstacle avoidance maneuvers: braking versus steering[END_REF], the combination strategy was not more effective than the braking one, and we noted that the anticipation strategy did not lead to fewer collisions. These results could be due to the high monotony of the simple situation which could decrease the level of vigilance, leading to specific difficulties to effectively combine two actions in a short time or to prevent the drivers from rapidly conducting their avoidance maneuver despite the early setting up of an action.

In very complex situation, the number of collisions was higher when drivers braked than when they made a combination of braking and swerving, or when they swerved or anticipated. These three avoidance maneuvers were thus the most effective strategies. The high complexity probably allowed the drivers being vigilant and prepared them to adopt the most effective strategies [START_REF] Adams | Review of the literature on obstacle avoidance maneuvers: braking versus steering[END_REF].

Additionally, the increase of subjective workload only enhanced the number of collisions when the drivers braked, confirming that the braking strategy did not prevent colliding with the pedestrian. Furthermore, whatever the situation and the driving experience, braking or making a combination was not effective when the reaction times were lengthened, as the number of collisions increased. Conversely, swerving was always effective, even with the lengthening of reaction times (constant number of collisions).

To conclude about the strategies, they did not vary between the situations and the groups and had an equivalent cost. However, this study reveals that whatever the situation complexity and the driving experience, the swerving strategy was the most effective to avoid

Fig. 1 .

 1 Fig. 1. Driving simulator.The different movements and actions exerted on the vehicle were virtually reproduced.

Fig 2 .

 2 Fig 2. Experimental procedure.

  05, ns), situation complexity × subjective workload (β = -.01, ns), driving experience × strategy (β = .05, ns), driving experience × RT (β = -.11, ns), situation complexity × RT (β = -.04, ns), and subjective workload × RT (β = .03, ns). Sobel tests revealed mediation effects. The effects of situation complexity (z = 2.13, p < .05) and driving experience (z = -2.71, p < .01) on collisions number were mediated by subjective workload. The increase of situation complexity and the lack of driving experience enhanced the subjective workload (respectively β = .15, p < .01; β = -.25, p < .001) which in

Table 1 . Reaction Times of each group.

 1

	Driving experience	Reaction Times, Mean (SD)
	Traditionally Trained Drivers (TTD)	0.73 (0.26)
	Early Trained Drivers (ETD)	0.90 (0.36)
	End of Probationary Period (EPP)	0.62 (0.22)
	Experienced Drivers (ED)	0.70 (0.30)

Table 2 . Average number of collisions of each group in each situation.

 2

	Driving experience	Simple, Mean (SD)	Moderate, Mean (SD)	Very complex, Mean (SD)
	Traditionally Trained Drivers (TTD) 0.07 (0.25) 0.17 (0.38) 0.33 (0.48)
	Early Trained Drivers (ETD)	0.25 (0.44) 0.25 (0.44) 0.37 (0.49)
	End of Probationary Period (EPP)	0.07 (0.25) 0.17 (0.38) 0.23 (0.43)
	Experienced Drivers (ED)	0.03 (0.18) 0.02 (0.41) 0.13 (0.35)

Table 3 . Average number of collisions in each situation and for each strategy.

 3

	Situation complexity	Braking, Mean (SD)	Swerving, Mean (SD)	Combination, Mean (SD)	Anticipation, Mean (SD)
	Simple	0.18 (0.40)	0 (0)	0.14 (0.35)	0 (0)
	Moderately complex	0.12 (0.33)	0.27 (0.46) 0.21 (0.41)	0.14 (0.38)
	Very complex	0.54 (0.50)	0.04 (0.21) 0.15 (0.36)	0.17 (0.39)

Acknowledgements

We thank the participants for their enthusiastic participation, the simulation team at IFSTTAR (COSYS: components and systems department), notably Isabelle Aillerie for having designed the displays. We also thank Thomas Arciszewski (Aix-Marseille University, Research Center PsyCLE: Psychology of Cognition, Language and Emotion) for having facilitated the data sorting.

an accident with a sudden pedestrian crossing, even when drivers' reaction times were long.

Further research is needed to confirm a possible link between the level of vigilance due to the situation complexity and the strategy effectiveness.

Finally, all the results revealed that, in these experimental conditions, the subjective workload was depending on driving experience and situation complexity and determined reaction times for early-trained drivers and drivers at the end of the probation. Moreover, the number of collisions was depending on subjective workload, avoidance strategies and reaction times, and this link was modulated by situation complexity as a function of driving experience Therefore, only considering driving characteristics (performance) and environment characteristics (complexity) is not sufficient to explain and to understand driving situations.

Taking the individual characteristics into account seems essential and will permit to implement preventions targeted to individuals.