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European Commission - Comenius

European Commission - Education and Culture

Project Details

MAking MAThEmatics TEAchers MObile

129543-CP-1-2006-1 -IT-COMENIUS-C21


Project span

Project Coordinator

CAFRE Centro di Ateneo di Formazione e Ricerca Educativa
Università di Pisa

Contact person


Project Partners

(AT) Universität Wien

(CZ) Univerzita Karlova v Praze

(DK) University College Lillebælt, Skårup Seminarium

(FR) Institut Universitaire de Formation des Maîtres de l'Académie de Créteil

Teaching Maths in a Foreign Language
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Italian Data Analysis of the Questionnaire for Teachers

Data Analysis of the Questionnaire
for Language Teachers

About you
  1. Thirty-two language teachers have answered: fifteen teach in lower secondary school, seventeen in upper secondary school.
  2. Out of this sample, twenty-three teach English, six French, three German, and two Spanish. Some teachers teach two languages: English and another one.
  3. Thirty-five teachers speak English; twenty French, fifteen German, thirteen Spanish, three Russian, two Romanian, one Danish, one Flemish, and two Italian as a foreign language. Many of them speak two foreign languages, and some of them three foreign languages.
  4. Two teachers have a C2 level competence in English, twenty-eight a C1 level, three a B2, one an A2. Six teachers score in French a C1 level, five B2, four B1, three A2, one A1. Three teachers have a C2 level competence in German, five C1, four B2, one B1+, two A1. In Spanish: one teacher has a C2 competence, six C1, three B2, and two A2. In Russian: one is at C1, two at B2, two at B1 level. In Danish one is at C1, in Italian as a foreign language one is at C2, and one at C1 level. In Flemish one is at C2, in Romanian one is at C1 and one at A2 level.
Prior experiences
  1. to  7. (only for Math teachers)
  2. Eight language teachers have cooperated with a Math teacher, twenty six did not.
  3. Eighteen teachers have heard of bilingual education models or schools, fifteen did not have any information about that.
Present opinions
  1. (only for Math teachers)
  2. Among the angles mentioned in the introduction, the most important aspects are teachers’ mobility (the most frequently mentioned), and communicative and intercultural advantages (very frequent). Some teachers also indicate: good practice and standardisation in Math teaching, and mathematics as a universal language.
  3. The Communicative difficulties caused by linguistic contrastive structures are the most striking.

  1. Twenty-eight teachers think it would be possible to teach mathematics in a foreign language, and two of them refer to personal CLIL experiences. Six teachers think it would be impossible, and not useful anyway.
  2. Opinions are contrasting: eighteen are not in favour because they think it is an additional difficulty for pupils; eleven are in favour but some of them only if that is given as a free option.
  3. Twenty-three favourable opinions, particularly for the opportunity to learn a special language. Seven opinions are not in favour.
  4. only for Math teachers).
Professional development
  1. Eleven teachers have experienced teaching in cooperation with another subject’s teacher (five with Art, two with History, two with foreign Literatures, one with Philosophy, one with Geography, one with Natural Sciences, one with Law).
  2. Only six teachers do not think that mathematics teachers can profit in their practices from being able to teach in a foreign language. Many (twenty-seven) are very favourable (most mentioned the multilingual dimension in teaching).
  3. Only six teachers do not think that language teachers can profit from cooperation with maths teachers. Most of them (twenty seven) think it would be an advantage for language teachers in order to develop higher analytic skills.
  4. to 21. (only for Math teachers)
  5. The prerequisites teachers needs are: B2 or C1linguistic competence, Math teaching methodology competence, and last but not least flexibility and open-mindedness.
  6. Contrasting opinions emerged: nineteen are positive because of the interdisciplinary teaching/learning opportunity, fourteen negative for the risk related to mixing very different subjects.
  7. Some ways proposed for providing the above mentioned skills are:
    • Full immersion for language skills (special language courses or/and language training abroad).
    • Formative under/postgraduate courses on interdisciplinary teaching.
    • Specific formative stages in foreign countries’ Math/Lang classrooms.

  Data Analysis of the Questionnaire
for Mathematics Teachers

About you
  1. 83 lower secondary school teachers (loss) and 26 upper secondary school teachers (upss) have answered.
  2. The loss teachers teach “Maths and Science”; 12 upss teachers teach “Maths” and 14 upss teachers teach both Maths and Physics.
  3. Most of the teachers (85) speak English, 25 speak French, 11 speak Spanish, 3 speak German, 1 Greek, 1 Portuguese, 1 Japanese.
  4. Almost none of them is able to assess his/her foreign language competence.
Prior experiences
  1. Yes: 18 – No: 73 – No answer: 18
  2. Yes: 11 – No: 81 – No answer: 17
  3. 28 teachers have not answered. The large majority (69) of the teachers never taught maths using a foreign language. Six teachers did it with immigrant pupils, six more occasionally used a foreign language for various reasons, including the use of textbooks with some exercises in English.
  4. Only nine teachers co-operate with a language teacher for different reasons, such as: translation of the class-work for foreign pupils or of scientific papers. 23 teachers did not answer.
  5. Only fifteen teachers heard about models of bilingual education, in private schools and Northern Italian regions with significant linguistic minorities. 15 teachers did not answer.
Present opinions
  1. Most of the teachers (87) acknowledge the importance of knowing a foreign language for teaching, due to different reasons, among which: teaching abroad, fostering teacher and students exchanges, getting to know about more up-to-date teaching methodologies, professional development, facing the increasing presence of foreign pupils, Internet, the scientific and ICT terminology mostly available or better referable to in English, scientific notions recently introduced and defined in English and less understandable when translated into Italian, co-operation with teachers of English. Only seven teachers answered ‘No’, one of which wrote a rather ambiguous comment: ‘Maths has a universal language, but sometimes it is useful also to know just a few technical words for foreign pupils’.
  2. The teachers see several different important advantages, among which: mobility and greater opportunity to be a teacher, comparison and sharing of teaching methodologies with teachers from other countries, increasing of professional competence, better linguistic competence, better teachers selection, better understanding of the subject, possibility for student teachers to qualify both in maths and a foreign language, increasing ability to teach and explain using simple but rigorous words thanks to the particularly limited and specific mathematics vocabulary.
  3. The teachers have different thoughts about the possible difficulties arising when teacher and pupils do not share the same mother tongue. Among these difficulties the most mentioned one is communication. Other difficulties referred to are: to use natural language to explain mathematical situations, to use different examples to explain a concept, the lack of a shared ‘code’ for the discipline, to introduce the deepest concepts in a language not usually spoken, the mutual understanding, to use nuances, to make a new concept well understood, to explain the didactical aims, to explain the various theories and formulae. Besides the difficulties, some risks were outlined: the bad use and appropriation of the specific discipline language, misconceptions and misunderstanding.
  1. Seventy-seven teachers think it would be possible to teach mathematics in a foreign language. Most of them add, more or less, this comment ‘If the foreign language is very well known…’. Some other comments: if it is possible to use drawings and graphs, mathematics has a written basis understandable also without speaking and simple and universal rules, it is easier to teach than other subjects due to the universal nature of maths language, it could help to think in the foreign language. Most of the twenty one teachers who answered ‘No’ referred to the possible difficult communication and to the lack of the necessary language basic competence.
  2. As for the help that teaching in a foreign language could represent for mathematical learning, forty teachers say it helps, fifty-one say it doesn’t. Why yes: knowledge of the terminology, challenging for pupils, useful to be able to read texts in foreign language at higher education level, greater care in the use of the language, more rigorous and synthetic use of the mathematical grammar, proof of the universality of maths, greater pupils’ open-mindedness, greater concentration that requires more reflection on the concepts, more concern about the difficulty of maths and then about its teaching, more activities in the math laboratory. Why not: it only helps pupils who speak that language, it would be confusing, difficult communication, the language would represent a barrier despite the universal symbolism of maths, learning requires concentration and part of the concentration would be necessary to understand the language. But the large majority of the negative answers were motivated by the refrain ‘it is already difficult to teach maths in Italian...’.
  3. Sixty-one ‘yes’ and eighteen ‘no’, with thirty teachers not answering or saying ‘Don’t know’! Most of the ‘Yes’ answers refer to the opportunity to learn and use the foreign language in a meaningful, concrete and specific context. Some others refer to the positive impact that the nature of mathematical language, precise and essential, can have on the construction of sentences, in a foreign language, with a simple structure. As it is the case for the two previous questions, most of the ‘No’ answers show the trainers’ worry to add difficulty to difficulty.
  4. As to the topics to be taught in a foreign language, many teachers (32) answer ‘Any’. Geometry is explicitly mentioned by eight teachers. Quite surprisingly, fifty-five teachers do not answer.
Professional development
  1. Only twenty-nine teachers have experienced teaching in cooperation with another subject’s teacher, mostly with teachers of other scientific or technical subjects, but also with teachers of humanities, musical education, physical education, arts, environment science and … English. A few of these cooperation experiences were carried out in the form of activities in favour of disabled pupils. Fifty-seven teachers had no cooperation experiences and twenty three do not even answer.
  2. Approximately the three quarters of the teachers (seventy-six) think mathematics teachers can profit from being able to teach in a foreign language. Here are their most significant comments: it is useful for ICT, it helps in the search for a job abroad, it is necessary for exchanges and professional development, it obliges to a more rigorous and synthetic use of the mathematical grammar, it requires a greater precision in the exposition, it increases the ability to explain concepts, it is an opportunity to consider other aspects of the subject, paying more attention to something that is usually viewed as obvious, it could be helpful to understand some aspects of the subject that our language cannot point out in the right way, it represents an additional communication tool, it is helpful with foreign pupils. Only seventeen teachers answer ‘No’, but they do not give any justification.
  3. About half of the teachers (49) think language teachers can profit from co-operation with maths teachers. Here are their most interesting justifications: interdisciplinary teaching starts ways of reasoning that are different from the usual ones and positive for the teaching/learning process, everybody can profit from getting in touch with a maths teacher, faster learning, interdisciplinary approach is always positive, teachers can acquire logical methodology and greater acquaintance with calculations, they can get support in activities where logical reasoning is needed, learning and school are not watertight compartments, it increases teachers’ competences, it can increase pupils’ interest through the use of exercises, they could use language in a real context, they could profit from the use of maths language, it helps with foreign pupils, it widens and enriches the lexical language. As to the eighteen negative answers, the only explanation given is: language teachers are not much interested in maths. Significant is the number of teachers that do not answer (25) or answer ‘don’t know’ (17).
  4. Concerning professional development, teaching mathematics in a foreign language is viewed as a positive factor by the great majority (72) of the maths teachers, while only fourteen of them consider it negative (without providing a justification). Only very few explanations of the ‘Yes’ answers have been provided, among which: positive but hard, helpful with foreign pupils, useful like all new experiences, positive but not at the beginning of the career, further experience, positive but impossible in our schools at present, in a foreign country, for the communication improvement.
  5. More contrasting is the judgment about a possible consequent change of teaching methods. Whereas forty-six teachers answer ‘No’ without a single explanation, thirty nine teachers answer ‘Yes’ providing very few comments: some changes would be necessary, a radical change if in Italy but no change if abroad, enlargement and 360° view of the programmes, more language accuracy, more concise language.
  6. Regarding the prerequisites needed for teachers or student teachers to be able to teach in a foreign language, in addition to the obvious reference to the foreign language knowledge, the following ones are also mentioned: ability to use standard maths terminology, good knowledge of the to-be-taught topic, prior experience in teaching in the foreign language, motivation, interest, basic communication competences, non-formal language knowledge, ability to express oneself using terms understandable by pupils, mastery of the language at scientific level at least, language courses during maths teacher training, availability of qualified and motivated teachers for methodologies’ teaching, good teaching education.
  7. As to the possible difference in prerequisites if the language of instruction is the pupils’ mother tongue and a foreign language for the teacher, the same number (31) of teachers say ‘Yes’ and say ‘No’. Here are some comments: the teacher’s ability to communicate mathematical concepts could be lower if the language is not well known, misunderstandings could occur or the teacher should teach in a simpler way to facilitate learning, pupils could understand also some defects of pronunciation and errors of sentence construction, teachers need to know the programmes as well as pupils’ knowledge and competences, for a mathematical topic, prerequisites are not dependent on the language used, no difference but greater attention to the pupils’ reality, pupils learn more easily new things like a language, the maths teacher can profit from the fact that pupils can understand also if the language is not correctly spoken.
  8. The necessary skills could be provided to teachers, above all, through specific training courses, but also through: language courses, living for some time in the country where they plan to teach, stays abroad, mock classes and discussions, courses on the foreign schools’ programmes, introducing maths classes in English in the teacher training courses, teaching maths in a foreign language, courses showing the different ways maths is introduced in various European countries, courses on the foreign language and the teaching methodologies to be used, language classes focused on mathematical language, exchange visits with mother tongue speaking maths teachers, vocational courses with mock maths classes in foreign language, classes on scientific English, exams in a foreign language.

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