{"id":935,"date":"2025-03-01T07:31:31","date_gmt":"2025-03-01T07:31:31","guid":{"rendered":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/?p=935"},"modified":"2025-03-01T07:31:31","modified_gmt":"2025-03-01T07:31:31","slug":"the-benefits-of-studying-mathematics-in-two-languages-cymraeg-welsh-and-english","status":"publish","type":"post","link":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/2025\/03\/01\/the-benefits-of-studying-mathematics-in-two-languages-cymraeg-welsh-and-english\/","title":{"rendered":"The benefits of studying mathematics in two languages (Cymraeg\/Welsh and English)"},"content":{"rendered":"

This post is written, in both English and Welsh, by <\/em>Dr Delyth Tomos, an OU Associate Lecturer who tutors on modules in mathematics and statistics, and engineering.<\/em><\/p>\n

Delyth has recently co-led a project looking at Welsh-medium tuition in mathematics.\u00a0 To learn more about the project, click here<\/a> \u00a0<\/em><\/p>\n

Ysgrifennwyd y neges hon, yn y Gymraeg ac yn Saesneg, gan Dr Delyth Tomos, Darlithydd Cyswllt gyda\u2019r Brifysgol Agored, sy\u2019n diwtor ar fodiwlau mewn mathemateg ac ystadegau, a pheirianneg.<\/em><\/p>\n

Yn ddiweddar mae Delyth wedi cyd-arwain prosiect yn edrych ar addysgu mathemateg drwy gyfrwng y Gymraeg.\u00a0 Er mwyn gweld mwy o wybodaeth am y prosiect, cliciwch yma<\/a>.<\/em><\/p>\n

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As someone who has lived and worked in North Wales since birth, being exposed to two languages, Cymraeg\/Welsh and English, is pretty much a way of life. Children are taught in both languages from an early age, and develop linguistic skills that allow them to participate fully in education, work, family and social activities in two languages, thus maximising the opportunities available to them.\u00a0 Discussions in formal and informal settings are frequently conducted through both languages, switching from one to the other, and most of us do this with ease, hardly realising that what we are doing is much more complicated linguistically than we possibly realise.<\/p>\n

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Welsh landscape. Image credit David Kjaer \/ Nature Picture Library \/ Universal Images Group.<\/p><\/div>\n

A bilingual education involves subjects being taught in both languages, and effective strategies have evolved over the decades, underpinned by a wealth of research in countries where living through the medium of more than one language is the norm (Spitzer, 2016 and Mukan et al, 2017). These strategies promote constructive learning where the use of two languages enhances a learner\u2019s resilience and effectiveness within specific subjects as well as their language skills in general.<\/p>\n

Learning mathematics through the medium of both Cymraeg and English encourages learners to acquire and develop flexible approaches to their studies. Understanding and learning how to solve mathematical problems requires a learner to develop a subject-specific vocabulary which needs to be incorporated within the learner\u2019s wider language skills. In mathematics, a learner needs to be able to\u00a0 describe\u00a0 and interpret a problem, analyse and select relevant pieces of information from a given situation, organise the information, consider how this information may be used to address a particular problem, select and justify suitable mathematical methods, undertake various mathematical calculations and manipulations, and finally, to interpret their solutions or results in order to address the original problem.\u00a0\u00a0 It is clear that these strategies are complex, and it can also be seen that most of these skills are deeply embedded in language.<\/p>\n

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School sign in English and Welsh languages. Image credit David Hunter \/ Robert Harding World Imagery \/ Universal Images Group<\/p><\/div>\n

When discussing mathematical concepts and terms in different languages, learners have opportunities to make connections with previous knowledge in both languages, and this, in turn helps them to construct their learning of mathematical ideas in both languages. Mathematical problems may be described and framed in a similar manner in two different languages, but the translation will not be exactly the same. Translation is not a matter of substituting one word from one language to an equal term in another language. Effective translation requires an equivalent adaptation of meaning in both languages in addition to syntactic flexibility and choosing suitable terms to delineate a problem in a manner that is accurate and helpful. Being creative and flexible as part of the translation process results in mathematical problems being conceptualized from two slightly different\u00a0 directions, resulting in a deeper understanding of how to address problems.<\/p>\n

Learning mathematics (and other subjects) through the medium of two languages thus provides learners with opportunities to fully engage in learning, in both their first and second language, and to engage with concepts from two slightly different directions. This in turn encourages them to become flexible, creative and resilient learners\u00a0 and this naturally benefits mathematics learners.<\/p>\n

Manteision astudio mathemateg mewn dwy iaith (Cymraeg a Saesneg)<\/strong><\/h2>\n

Fel rhywun sydd wedi byw a gweithio yng Ngogledd Cymru ers ei geni, mae dod i gysylltiad \u00e2 dwy iaith, Cymraeg a Saesneg, yn ffordd o fyw. Caiff plant eu haddysgu yn y ddwy iaith o oedran cynnar, a byddant un datblygu sgiliau ieithyddol sy\u2019n caniat\u00e1u iddynt gymryd rhan lawn mewn addysg, gwaith, gweithgareddau teuluol a chymdeithasol mewn dwy iaith, gan wneud y mwyaf o\u2019r cyfleoedd sydd ar gael iddynt.\u00a0 Caiff trafodaethau mewn sefyllfaoedd ffurfiol ac anffurfiol eu cynnal yn aml drwy\u2019r ddwy iaith, gan newid o\u2019r naill i\u2019r llall, ac mae\u2019r rhan fwyaf ohonom yn gwneud hyn yn rhwydd, prin yn sylweddoli bod yr hyn yr ydym yn ei wneud yn llawer mwy cymhleth yn ieithyddol nag yr ydym o bosibl yn sylweddoli.<\/p>\n

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tirwedd Cymru. Credyd delwedd David Kjaer \/ Llyfrgell Lluniau Natur \/ Gr\u0175p Delweddau Cyffredinol.<\/p><\/div>\n

Mae addysg ddwyieithog yn golygu bod pynciau\u2019n cael eu haddysgu yn y ddwy iaith, ac mae strategaethau effeithiol wedi datblygu dros y degawdau, wedi\u2019u hategu gan gyfoeth o ymchwil mewn gwledydd lle mae byw trwy gyfrwng mwy nag un iaith yn norm. (Spitzer, 2016 A Mukan et al, 2017). Mae\u2019r strategaethau hyn yn hybu dysgu adeiladol lle mae\u2019r defnydd o ddwy iaith yn gwella gwydnwch ac effeithiolrwydd dysgwr o fewn pynciau penodol yn ogystal \u00e2\u2019u sgiliau iaith.<\/p>\n

Mae dysgu mathemateg trwy gyfrwng y Gymraeg a’r Saesneg yn annog dysgwyr i gaffael a datblygu ymagweddau hyblyg at eu hastudiaethau. Mae deall a dysgu sut i ddatrys problemau mathemategol angen i ddysgwr ddatblygu geirfa pwnc-benodol y mae angen ei hymgorffori o fewn sgiliau iaith ehangach y dysgwr. Mae angen i\u2019r dysgwr allu disgrifio a dehongli problem, dadansoddi a dewis darnau perthnasol o wybodaeth o sefyllfa benodol, trefnu\u2019r wybodaeth, ystyried sut y gellir defnyddio\u2019r wybodaeth hon i fynd i\u2019r afael \u00e2 phroblem benodol, dewis a chyfiawnhau dulliau mathemategol addas, gwneud cyfrifiadau a thriniadau mathemategol amrywiol, ac yn olaf, dehongli eu hatebion neu ganlyniadau er mwyn mynd i\u2019r afael \u00e2\u2019r broblem wreiddiol.\u00a0 Mae\u2019n amlwg bod y strategaethau hyn yn gymhleth, a gellir gweld hefyd bod y rhan fwyaf o\u2019r sgiliau hyn wedi\u2019u gwreiddio\u2019n ddwfn mewn iaith.<\/p>\n

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Arwyddion ysgol yn y Gymraeg a’r Saesneg. Credyd delwedd David Hunter \/ Robert Harding World Imagery \/ Gr\u0175p Delweddau Cyffredinol.<\/p><\/div>\n

Wrth drafod cysyniadau a thermau mathemategol mewn gwahanol ieithoedd, caiff dysgwyr gyfleoedd i wneud cysylltiadau \u00e2 gwybodaeth flaenorol yn y ddwy iaith, ac mae hyn, yn ei dro, yn eu helpu i adeiladu eu dysgu o syniadau mathemategol yn y ddwy iaith. Gellir disgrifio problemau mathemategol a’u fframio mewn modd tebyg mewn dwy iaith wahanol, ond ni fydd y cyfieithiad yn union yr un fath. Nid yw cyfieithu yn fater o amnewid un gair o un iaith i derm cyfartal mewn iaith arall. Mae cyfieithu effeithiol yn gofyn am addasiad cyfatebol o ystyr yn y ddwy iaith yn ogystal \u00e2 hyblygrwydd cystrawennol a dewis termau addas i amlinellu problem mewn modd sy’n gywir ac yn ddefnyddiol. Mae bod yn greadigol a hyblyg fel rhan o’r broses gyfieithu yn arwain at gysyniadoli problemau mathemategol o ddau gyfeiriad ychydig yn wahanol, gan arwain at ddealltwriaeth ddyfnach o sut i fynd i’r afael \u00e2 phroblemau.<\/p>\n

Mae dysgu mathemateg (a phynciau eraill) trwy gyfrwng dwy iaith felly yn rhoi cyfleoedd i ddysgwyr ymgysylltu\u2019n llawn \u00e2 dysgu, yn eu hiaith gyntaf a\u2019u hail iaith, ac i ymgysylltu \u00e2 chysyniadau o ddau gyfeiriad ychydig yn wahanol. Mae hyn yn ei dro yn eu hannog i ddod yn ddysgwyr hyblyg, creadigol a gwydn, ac mae manteision amlwg i hyn ar gyfer dysgwyr mathemateg.<\/p>\n

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References\/Cyfeiriadau<\/strong><\/p>\n

Mukan, N.\u00a0 et al (2017). The Development of Bilingual Education in Canada<\/em>. Advanced Education, Issue 4(8) pp. 35 \u2013 40.<\/p>\n

Mukan, N. et al (2017). Datblygiad Addysg Ddwyieithog yng Nghanada<\/em>. Addysg Uwch, Rhifyn 4(8) tt. 35 \u2013 40.<\/p>\n

Spitzer, M (2016). Bilingual Benefits in Education and Health<\/em>. Trends in Neuroscience and Education, Volume 5, Issue 2, pp 67-76.<\/p>\n

Spitzer, M (2016). Buddion Dwyieithog mewn Addysg ac Iechyd<\/em>. Tueddiadau mewn Niwrowyddoniaeth ac Addysg, Cyfrol 5, Rhifyn 2, tt 67-76.<\/p>\n

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 <\/p>\n","protected":false},"excerpt":{"rendered":"

This post is written, in both English and Welsh, by Dr Delyth Tomos, an OU Associate Lecturer who tutors on modules in mathematics and statistics, and engineering. Delyth has recently co-led a project looking at Welsh-medium tuition in mathematics.\u00a0 To … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-935","post","type-post","status-publish","format-standard","hentry","category-uncategorised"],"_links":{"self":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/935","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/comments?post=935"}],"version-history":[{"count":12,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/935\/revisions"}],"predecessor-version":[{"id":953,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/935\/revisions\/953"}],"wp:attachment":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/media?parent=935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/categories?post=935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/tags?post=935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}