English grammar games in primary education

The purpose of this study was to analyse pupils’ English grammar acquisition from competitive and cooperative approaches. After searching a wide range of authors’ contribution to English language learning, grammar acquisition, classroom environment and language games. A hundred and twenty pupils from three schools; two from Ripoll and one from Campdevànol were enrolled in a specific grammar games intervention. This was imparted in three different phases: first of all, I interviewed the three teachers from the three schools, then I put into practice my competitive and cooperative games which I designed especially for this study (all the sessions were carried, assessed and registered by myself); finally, all pupils answered a questionnaire related to their experiences in my grammar games intervention. Analysis of teaching interventions showed that, in terms of English language acquisition, pupils used different strategies to show up understanding and achieve the objective of the game such as: recalling their background knowledge, expressing sentences influenced by their internal language and their mother tongue. Data collected revealed that most difficulties were founded in team work, even more in competitive games. The results also showed that team work is something which has to be developed step by step in order to achieve language learning and all pupils’ active participation successfully.

Construcció d'un SIG i sincronització de les etiquetes amb els objectes representats a GEOMEDIA PROFESSIONAL 5.2

En aquest treball de fi de carrera s'estudia en què consisteix en SIG i les seves característiques, en concret es realitza l'estudi d'un SIG comercial, GEOMEDIA PROFESSIONAL 5.2 D'aquest producte es presenta el problema de sincronització de les etiquetes amb les entitats que etiqueten, i es planteja una solució a aquest problema, mitjançant el desenvolupament d'una aplicació implementada amb MICROSOFT VISUAL BASIC 6.0

Lengua familiar y conocimiento de la lengua escolar en Cataluña al finalizar la Educación Infantil = Home Language and Knowledge of the School Language in Catalonia at the end of Nursery School

La infancia extranjera se escolariza en Cataluña en un programa de cambio de lengua del hogar a la escuela. Las investigaciones afirman que este alumnado tarda un mínimo de seis años en equiparar sus habilidades lingüístico-cognitivas con sus pares autóctonos, no así las habilidades conversacionales, las cuales se adquieren antes de los dos años de residencia. Sin embargo, no existen estudios sobre los efectos de la escolarización en el parvulario del alumnado alófono, así como de su lengua familiar, en relación con la adquisición de la lengua escolar. El artículo es un estudio comparativo de la adquisición del catalán de 567 autóctonos y 434 alófonos, al final del parvulario, en 50 escuelas de Cataluña que escolarizan a alumnado de origen extranjero. Las lenguas del alumnado autóctono son el catalán, el castellano y el bilingüismo catalán-castellano y las lenguas del alumnado alófono son el árabe, el soninké y el castellano. Los factores utilizados más relevantes han sido el nivel socioprofesional y educativo de las familias, el tiempo de residencia y el momento de escolarización del alumnado, el porcentaje de alumnado catalanohablante y de alumnado alófono en el aula y el contexto sociolingüístico del centro escolar. Los resultados muestran que el alumnado autóctono sabe más catalán que el alumnado alófono, pero las diferencias desaparecen respecto a algunos factores, de los cuales los más relevantes son los relacionados con las características del alumnado de las aulas. La lengua familiar del alumnado alófono no incide en sus resultados

En torno a los efectos de la edad en el aprendizaje escolar de una lengua extrangera

The purpose of this article is to treat a currently much debated issue, the effects of age on second language learning. To do so, we contrast data collected by our research team from over one thousand seven hundred young and adult learners with four popular beliefs or generalizations, which, while deeply rooted in this society, are not always corroborated by our data.Two of these generalizations about Second Language Acquisition (languages spoken in the social context) seem to be widely accepted: a) older children, adolescents and adults are quicker and more efficient at the first stages of learning than are younger learners; b) in a natural context children with an early start are more liable to attain higher levels of proficiency. However, in the context of Foreign Language Acquisition, the context in which we collect the data, this second generalization is difficult to verify due to the low number of instructional hours (a maximum of some 800 hours) and the lower levels of language exposure time provided. The design of our research project has allowed us to study differences observed with respect to the age of onset (ranging from 2 to 18+), but in this article we focus on students who began English instruction at the age of 8 (LOGSE Educational System) and those who began at the age of 11 (EGB). We have collected data from both groups after a period of 200 (Time 1) and 416 instructional hours (Time 2), and we are currently collecting data after a period of 726 instructional hours (Time 3). We have designed and administered a variety of tests: tests on English production and reception, both oral and written, and within both academic and communicative oriented approaches, on the learners' L1 (Spanish and Catalan), as well as a questionnaire eliciting personal and sociolinguistic information. The questions we address and the relevant empirical evidence are as follows: 1. "For young children, learning languages is a game. They enjoy it more than adults."Our data demonstrate that the situation is not quite so. Firstly, both at the levels of Primary and Secondary education (ranging from 70.5% in 11-year-olds to 89% in 14-year-olds) students have a positive attitude towards learning English. Secondly, there is a difference between the two groups with respect to the factors they cite as responsible for their motivation to learn English: the younger students cite intrinsic factors, such as the games they play, the methodology used and the teacher, whereas the older students cite extrinsic factors, such as the role of their knowledge of English in the achievement of their future professional goals. 2 ."Young children have more resources to learn languages." Here our data suggest just the opposite. The ability to employ learning strategies (actions or steps used) increases with age. Older learners' strategies are more varied and cognitively more complex. In contrast, younger learners depend more on their interlocutor and external resources and therefore have a lower level of autonomy in their learning. 3. "Young children don't talk much but understand a lot"This third generalization does seem to be confirmed, at least to a certain extent, by our data in relation to the analysis of differences due to the age factor and productive use of the target language. As seen above, the comparably slower progress of the younger learners is confirmed. Our analysis of interpersonal receptive abilities demonstrates as well the advantage of the older learners. Nevertheless, with respect to passive receptive activities (for example, simple recognition of words or sentences) no great differences are observed. Statistical analyses suggest that in this test, in contrast to the others analyzed, the dominance of the subjects' L1s (reflecting a cognitive capacity that grows with age) has no significant influence on the learning process. 4. "The sooner they begin, the better their results will be in written language"This is not either completely confirmed in our research. First of all, we perceive that certain compensatory strategies disappear only with age, but not with the number of instructional hours. Secondly, given an identical number of instructional hours, the older subjects obtain better results. With respect to our analysis of data from subjects of the same age (12 years old) but with a different number of instructional hours (200 and 416 respectively, as they began at the ages of 11 and 8), we observe that those who began earlier excel only in the area of lexical fluency. In conclusion, the superior rate of older learners appears to be due to their higher level of cognitive development, a factor which allows them to benefit more from formal or explicit instruction in the school context. Younger learners, however, do not benefit from the quantity and quality of linguistic exposure typical of a natural acquisition context in which they would be allowed to make use of implicit learning abilities. It seems clear, then, that the initiative in this country to begin foreign language instruction earlier will have positive effects only if it occurs in combination with either higher levels of exposure time to the foreign language, or, alternatively, with its use as the language of instruction in other areas of the curriculum.

En torno a los efectos de la edad en el aprendizaje escolar de una lengua extrangera

The purpose of this article is to treat a currently much debated issue, the effects of age on second language learning. To do so, we contrast data collected by our research team from over one thousand seven hundred young and adult learners with four popular beliefs or generalizations, which, while deeply rooted in this society, are not always corroborated by our data.Two of these generalizations about Second Language Acquisition (languages spoken in the social context) seem to be widely accepted: a) older children, adolescents and adults are quicker and more efficient at the first stages of learning than are younger learners; b) in a natural context children with an early start are more liable to attain higher levels of proficiency. However, in the context of Foreign Language Acquisition, the context in which we collect the data, this second generalization is difficult to verify due to the low number of instructional hours (a maximum of some 800 hours) and the lower levels of language exposure time provided. The design of our research project has allowed us to study differences observed with respect to the age of onset (ranging from 2 to 18+), but in this article we focus on students who began English instruction at the age of 8 (LOGSE Educational System) and those who began at the age of 11 (EGB). We have collected data from both groups after a period of 200 (Time 1) and 416 instructional hours (Time 2), and we are currently collecting data after a period of 726 instructional hours (Time 3). We have designed and administered a variety of tests: tests on English production and reception, both oral and written, and within both academic and communicative oriented approaches, on the learners' L1 (Spanish and Catalan), as well as a questionnaire eliciting personal and sociolinguistic information. The questions we address and the relevant empirical evidence are as follows: 1. "For young children, learning languages is a game. They enjoy it more than adults."Our data demonstrate that the situation is not quite so. Firstly, both at the levels of Primary and Secondary education (ranging from 70.5% in 11-year-olds to 89% in 14-year-olds) students have a positive attitude towards learning English. Secondly, there is a difference between the two groups with respect to the factors they cite as responsible for their motivation to learn English: the younger students cite intrinsic factors, such as the games they play, the methodology used and the teacher, whereas the older students cite extrinsic factors, such as the role of their knowledge of English in the achievement of their future professional goals. 2 ."Young children have more resources to learn languages." Here our data suggest just the opposite. The ability to employ learning strategies (actions or steps used) increases with age. Older learners' strategies are more varied and cognitively more complex. In contrast, younger learners depend more on their interlocutor and external resources and therefore have a lower level of autonomy in their learning. 3. "Young children don't talk much but understand a lot"This third generalization does seem to be confirmed, at least to a certain extent, by our data in relation to the analysis of differences due to the age factor and productive use of the target language. As seen above, the comparably slower progress of the younger learners is confirmed. Our analysis of interpersonal receptive abilities demonstrates as well the advantage of the older learners. Nevertheless, with respect to passive receptive activities (for example, simple recognition of words or sentences) no great differences are observed. Statistical analyses suggest that in this test, in contrast to the others analyzed, the dominance of the subjects' L1s (reflecting a cognitive capacity that grows with age) has no significant influence on the learning process. 4. "The sooner they begin, the better their results will be in written language"This is not either completely confirmed in our research. First of all, we perceive that certain compensatory strategies disappear only with age, but not with the number of instructional hours. Secondly, given an identical number of instructional hours, the older subjects obtain better results. With respect to our analysis of data from subjects of the same age (12 years old) but with a different number of instructional hours (200 and 416 respectively, as they began at the ages of 11 and 8), we observe that those who began earlier excel only in the area of lexical fluency. In conclusion, the superior rate of older learners appears to be due to their higher level of cognitive development, a factor which allows them to benefit more from formal or explicit instruction in the school context. Younger learners, however, do not benefit from the quantity and quality of linguistic exposure typical of a natural acquisition context in which they would be allowed to make use of implicit learning abilities. It seems clear, then, that the initiative in this country to begin foreign language instruction earlier will have positive effects only if it occurs in combination with either higher levels of exposure time to the foreign language, or, alternatively, with its use as the language of instruction in other areas of the curriculum.

En torno a los efectos de la edad en el aprendizaje escolar de una lengua extrangera

The purpose of this article is to treat a currently much debated issue, the effects of age on second language learning. To do so, we contrast data collected by our research team from over one thousand seven hundred young and adult learners with four popular beliefs or generalizations, which, while deeply rooted in this society, are not always corroborated by our data.Two of these generalizations about Second Language Acquisition (languages spoken in the social context) seem to be widely accepted: a) older children, adolescents and adults are quicker and more efficient at the first stages of learning than are younger learners; b) in a natural context children with an early start are more liable to attain higher levels of proficiency. However, in the context of Foreign Language Acquisition, the context in which we collect the data, this second generalization is difficult to verify due to the low number of instructional hours (a maximum of some 800 hours) and the lower levels of language exposure time provided. The design of our research project has allowed us to study differences observed with respect to the age of onset (ranging from 2 to 18+), but in this article we focus on students who began English instruction at the age of 8 (LOGSE Educational System) and those who began at the age of 11 (EGB). We have collected data from both groups after a period of 200 (Time 1) and 416 instructional hours (Time 2), and we are currently collecting data after a period of 726 instructional hours (Time 3). We have designed and administered a variety of tests: tests on English production and reception, both oral and written, and within both academic and communicative oriented approaches, on the learners' L1 (Spanish and Catalan), as well as a questionnaire eliciting personal and sociolinguistic information. The questions we address and the relevant empirical evidence are as follows: 1. "For young children, learning languages is a game. They enjoy it more than adults."Our data demonstrate that the situation is not quite so. Firstly, both at the levels of Primary and Secondary education (ranging from 70.5% in 11-year-olds to 89% in 14-year-olds) students have a positive attitude towards learning English. Secondly, there is a difference between the two groups with respect to the factors they cite as responsible for their motivation to learn English: the younger students cite intrinsic factors, such as the games they play, the methodology used and the teacher, whereas the older students cite extrinsic factors, such as the role of their knowledge of English in the achievement of their future professional goals. 2 ."Young children have more resources to learn languages." Here our data suggest just the opposite. The ability to employ learning strategies (actions or steps used) increases with age. Older learners' strategies are more varied and cognitively more complex. In contrast, younger learners depend more on their interlocutor and external resources and therefore have a lower level of autonomy in their learning. 3. "Young children don't talk much but understand a lot"This third generalization does seem to be confirmed, at least to a certain extent, by our data in relation to the analysis of differences due to the age factor and productive use of the target language. As seen above, the comparably slower progress of the younger learners is confirmed. Our analysis of interpersonal receptive abilities demonstrates as well the advantage of the older learners. Nevertheless, with respect to passive receptive activities (for example, simple recognition of words or sentences) no great differences are observed. Statistical analyses suggest that in this test, in contrast to the others analyzed, the dominance of the subjects' L1s (reflecting a cognitive capacity that grows with age) has no significant influence on the learning process. 4. "The sooner they begin, the better their results will be in written language"This is not either completely confirmed in our research. First of all, we perceive that certain compensatory strategies disappear only with age, but not with the number of instructional hours. Secondly, given an identical number of instructional hours, the older subjects obtain better results. With respect to our analysis of data from subjects of the same age (12 years old) but with a different number of instructional hours (200 and 416 respectively, as they began at the ages of 11 and 8), we observe that those who began earlier excel only in the area of lexical fluency. In conclusion, the superior rate of older learners appears to be due to their higher level of cognitive development, a factor which allows them to benefit more from formal or explicit instruction in the school context. Younger learners, however, do not benefit from the quantity and quality of linguistic exposure typical of a natural acquisition context in which they would be allowed to make use of implicit learning abilities. It seems clear, then, that the initiative in this country to begin foreign language instruction earlier will have positive effects only if it occurs in combination with either higher levels of exposure time to the foreign language, or, alternatively, with its use as the language of instruction in other areas of the curriculum.

En torno a los efectos de la edad en el aprendizaje escolar de una lengua extrangera

The purpose of this article is to treat a currently much debated issue, the effects of age on second language learning. To do so, we contrast data collected by our research team from over one thousand seven hundred young and adult learners with four popular beliefs or generalizations, which, while deeply rooted in this society, are not always corroborated by our data.Two of these generalizations about Second Language Acquisition (languages spoken in the social context) seem to be widely accepted: a) older children, adolescents and adults are quicker and more efficient at the first stages of learning than are younger learners; b) in a natural context children with an early start are more liable to attain higher levels of proficiency. However, in the context of Foreign Language Acquisition, the context in which we collect the data, this second generalization is difficult to verify due to the low number of instructional hours (a maximum of some 800 hours) and the lower levels of language exposure time provided. The design of our research project has allowed us to study differences observed with respect to the age of onset (ranging from 2 to 18+), but in this article we focus on students who began English instruction at the age of 8 (LOGSE Educational System) and those who began at the age of 11 (EGB). We have collected data from both groups after a period of 200 (Time 1) and 416 instructional hours (Time 2), and we are currently collecting data after a period of 726 instructional hours (Time 3). We have designed and administered a variety of tests: tests on English production and reception, both oral and written, and within both academic and communicative oriented approaches, on the learners' L1 (Spanish and Catalan), as well as a questionnaire eliciting personal and sociolinguistic information. The questions we address and the relevant empirical evidence are as follows: 1. "For young children, learning languages is a game. They enjoy it more than adults."Our data demonstrate that the situation is not quite so. Firstly, both at the levels of Primary and Secondary education (ranging from 70.5% in 11-year-olds to 89% in 14-year-olds) students have a positive attitude towards learning English. Secondly, there is a difference between the two groups with respect to the factors they cite as responsible for their motivation to learn English: the younger students cite intrinsic factors, such as the games they play, the methodology used and the teacher, whereas the older students cite extrinsic factors, such as the role of their knowledge of English in the achievement of their future professional goals. 2 ."Young children have more resources to learn languages." Here our data suggest just the opposite. The ability to employ learning strategies (actions or steps used) increases with age. Older learners' strategies are more varied and cognitively more complex. In contrast, younger learners depend more on their interlocutor and external resources and therefore have a lower level of autonomy in their learning. 3. "Young children don't talk much but understand a lot"This third generalization does seem to be confirmed, at least to a certain extent, by our data in relation to the analysis of differences due to the age factor and productive use of the target language. As seen above, the comparably slower progress of the younger learners is confirmed. Our analysis of interpersonal receptive abilities demonstrates as well the advantage of the older learners. Nevertheless, with respect to passive receptive activities (for example, simple recognition of words or sentences) no great differences are observed. Statistical analyses suggest that in this test, in contrast to the others analyzed, the dominance of the subjects' L1s (reflecting a cognitive capacity that grows with age) has no significant influence on the learning process. 4. "The sooner they begin, the better their results will be in written language"This is not either completely confirmed in our research. First of all, we perceive that certain compensatory strategies disappear only with age, but not with the number of instructional hours. Secondly, given an identical number of instructional hours, the older subjects obtain better results. With respect to our analysis of data from subjects of the same age (12 years old) but with a different number of instructional hours (200 and 416 respectively, as they began at the ages of 11 and 8), we observe that those who began earlier excel only in the area of lexical fluency. In conclusion, the superior rate of older learners appears to be due to their higher level of cognitive development, a factor which allows them to benefit more from formal or explicit instruction in the school context. Younger learners, however, do not benefit from the quantity and quality of linguistic exposure typical of a natural acquisition context in which they would be allowed to make use of implicit learning abilities. It seems clear, then, that the initiative in this country to begin foreign language instruction earlier will have positive effects only if it occurs in combination with either higher levels of exposure time to the foreign language, or, alternatively, with its use as the language of instruction in other areas of the curriculum.

The pedagogical value of games and songs : The perceptions of teachers

Aquest estudi intenta explorar i descobrir les actituds i creences d’alguns mestres de llengua anglesa de Catalunya sobre la naturalesa dels jocs i les cançons, així com el paper que juguen en les seves aules per ensenyar l’anglès als infants. Les opinions dels mestres de llengua anglesa van ser recollides mitjançant un qüestionari que contenia preguntes sobre els jocs i les cançons i els resultats s’analitzen i s’exposen en aquest estudi.

Defining the criteria for the evaluation of self-study multimedia language learning materials: do they facilitate or inhibit learner autonomy?

Durant els darrers anys, s’han publicat un gran nombre de materials multimèdia destinats a l’aprenentatge de llengües, la major part dels quals son CD-ROM dissenyats com a cursos per l’autoaprenentatge. Amb aquests materials, els alumnes poden treballar independentment sense l’assessorament d’un professor, i per aquest motiu s’ha afirmat que promouen i faciliten l’aprenentatge autònom. Aquesta relació, però, no es certa, com Phil Benson i Peter Voller 1997:10) han manifestat encertadament:(…) Such claims are often dubious, however, because of the limited range of options and roles offered to the learner. Nevertheless, technologies of education in the broadest sense can be considered to be either more or less supportive of autonomy. The question is what kind of criteria do we apply in evaluating them? En aquest article presentem una investigació conjunta on es defineixen els criteris que poden ser utilitzats per avaluar materials multimèdia en relació a la seva facilitat per permetre l’aprenentatge autònom. Aquests criteris son la base d’un qüestionari que s’ha emprat per avaluar una selecció de CD-ROM destinats a l’autoaprenentatge de llengües. La estructura d’aquest article és la següent: - Una introducció de l’estudi - Els criteris que s’han utilitzar per la creació del qüestionari - Els resultats generals de l’avaluació - Les conclusions que s’han extret i la seva importància pel disseny instructiu multimèdia

Investigating independent language learning in classroom-based EFL Learners

La recerca efectuada sobre les estratègies d’aprenentatge de llengües ha demostrat que els aprenents que utilitzen estratègies metacognitives (planificació, revisió i avaluació) desenvolupen estratègies cognitives més eficaces (Anderson, 2002). Aquest article descriu les activitats que 43 estudiants de llengua estrangera de la Universitat de Vic van emprendre de forma independent i dedueix les estratègies metacognitives que van utilitzar sense cap formació prèvia en estratègies. Els estudiants van completar un dossier on expressaven les necessitats d’aprenentatge, la planificació i supervisió de les activitats i finalment l’avaluació de l’aprenentatge que havien portat a terme de manera independent fora de les hores lectives. La primera fase de l’anàlisi de les dades revela que, tot i que els estudiants foren capaços d’expressar les necessitats d’aprenentatge en general, la formulació d’objectius i la supervisió de les activitats fou escassa. La discussió gira entorn de la formació dels estudiants de llengües estrangeres en estratègies metacognitives i la integració de l’aprenentatge autònom dins el currículum docent.

Eliciting and fostering learners' metacognitive knowledge about language learning in self-directed learning programs: a review of data collection methods and procedures

Són molts els estudis que avui en dia incideixen en la necessitat d’oferir un suport metodològic i psicològic als aprenents que treballen de manera autònoma. L’objectiu d’aquest suport és ajudar-los a desenvolupar les destreses que necessiten per dirigir el seu aprenentatge així com una actitud positiva i una major conscienciació envers aquest aprenentatge. En definitiva, aquests dos tipus de preparació es consideren essencials per ajudar els aprenents a esdevenir més autònoms i més eficients en el seu propi aprenentatge. Malgrat això, si bé és freqüent trobar estudis que exemplifiquen aplicacions del suport metodològic dins els seus programes, principalment en la formació d’estratègies o ajudant els aprenents a desenvolupar un pla de treball, aquest no és el cas quan es tracta de la seva preparació psicològica. Amb rares excepcions, trobem estudis que documentin com s’incideix en les actituds i en les creences dels aprenents, també coneguts com a coneixement metacognitiu (CM), en programes que fomenten l’autonomia en l’aprenentatge. Els objectius d’aquest treball son dos: a) oferir una revisió d’estudis que han utilitzat diferents mitjans per incidir en el CM dels aprenents i b) descriure les febleses i avantatges dels procediments i instruments que utilitzen, tal com han estat valorats en estudis de recerca, ja que ens permetrà establir criteris objectius sobre com i quan utilitzar-los en programes que fomentin l’aprenentatge autodirigit.

The Third Language in Dubbing

Si tenim en compte que el procés de traducció és un procés complex, el procés de traducció d'un text audiovisual encara ho és més. A part dels problemes tècnics com per exemple la sincronització labial i temporal hi ha altres factors a tenir en compte com és l'ús d'estructures lingüístiques i textuals específiques d'aquest canal de comunicació. Moltes de les pel·lícules que sovint podem veure a la pantalla estan produïdes als Estats Units, i per tant estan en anglès, i hi ha una necessitat imperiosa de traduir-les al català i castellà. A part d'això, en algunes ocasions el text audiovisual original conté més d'una llengua; aquest és el cas de Raid on Rommel i Butch Cassidy and the Sundance Kid, entre d'altres. En aquests casos, ens trobem amb una nova dificultat: el traductor ha de traduir aquesta tercera llengua (o dialecte) a la corresponent cultura d'arribada. Aquest article vol presentar i exposar alguns exemples d'aquest tipus de dificultats així com també les diferents solucions que s'han aportat davant una "tercera" llengua.

The Spanish cadet in the European military context a comparative analysis of the professional socialisation

Research on the attitudes, motivations and social and political behavior of European cadets have been made throughout the last decade. Nowadays Spain also joins those surveys. Thru the analysis of polling data, we can consider the different attitudes of Spanish cadets in relation with the other European ones. The conclusion is that although the Spanish political transition to democracy has not ended already in the military teaching system, there are a lot of similarities among Spanish and European cadets.

Sequencing games without initial order

In this note we study uncertainty sequencing situations, i.e., 1-machine sequencing situations in which no initial order is specified. We associate cooperative games with these sequencing situations, study their core, and provide links with the classic sequencing games introduced by Curiel et al. (1989). Moreover, we propose and characterize two simple cost allocation rules for uncertainty sequencing situations with equal processing times.

Distribution center consolidation games

We study the location-inventory model as introduced by Teo et al. (2001) to analyze the impact of consolidation of distribution centers on facility and inventory costs. We extend their result on profitability of consolidation. We associate a cooperative game with each location-inventory situation and prove that this game has a non-empty core for identical and independent demand processes. This illustrates that consolidation does not only lower joint costs (which was shown by Teo et al. (2001)), but it allows for a stable division of the minimal costs as well.