techiaith/bydtermcymru-tm-en-cy huggingface dataset:
English: In the development of solutions, learners identify potential approaches and develop arguments, justifying their decisions.
Welsh: Wrth ddatblygu datrysiadau mae dysgwyr yn nodi dulliau posib ac yn datblygu dadleuon gan gyfiawnau eu penderfyniadau.
English: Studying mathematics develops personal effectiveness.
Welsh: Mae astudio mathemateg yn datblygu effeithiolrwydd personol.
English: When studying mathematics everyone encounters challenges at some point, and overcoming these challenges requires and develops resourcefulness and resilience.
Welsh: Wrth astudio mathemateg mae pawb yn wynebu heriau ar ryw adeg, ac mae goresgyn yr heriau hyn yn datblygu ac yn gofyn am ddyfeisgarwch a gwydnwch.
English: Communicating about mathematical thinking and solving problems is a core aspect of mathematics.
Welsh: Mae cyfathrebu am feddylfryd fathemategol a datrys problemau yn agwedd greiddiol o fathemateg.
English: Mathematical communication is precise and logical and will be useful in life generally.
Welsh: Mae cyfathrebu mathemategol yn fanwl gywir a rhesymegol, a bydd yn ddefnyddiol mewn bywyd yn gyffredinol.
English: Mathematical thinking requires learners to be organised and, as they progress through school, their organisational skills will develop, particularly as they plan and implement the
Welsh: Mae meddylfryd fathemategol yn gofyn i ddysgwyr fod yn drefnus, ac wrth iddyn nhw fynd trwy'r ysgol bydd eu sgiliau trefniadol yn datblygu, yn arbennig wrth iddyn nhw gynllunio a gweithredu'r
English: In their mathematical problem-solving, learners should be encouraged to predict and estimate solutions and then to check their answers, reflect on their results and evaluate their approaches.
Welsh: Wrth ddatrys problemau mathemategol, dylai dysgwyr gael eu hannog i ragfynegi ac amcangyfrif datrysiadau, ac yna wirio eu hatebion, myfyrio ar eu canlyniadau a gwerthuso eu dulliau.
English: Increasing confidence in decision-making for mathematical problem-solving supports learners to be more aspirational in setting goals and challenges for themselves including planning how to achieve these.
Welsh: Mae hyder cynyddol mewn datrys problemau mathemategol yn cefnogi dysgwyr i fod yn fwy uchelgeisiol wrth osod targedau a heriau i'w hunain gan gynnwys cynllunio sut i gyflawni'r rhain.
English: The different areas of mathematics are highly interconnected and dependent on one another and concepts are built up over time, drawing on prior knowledge and learning, often from more than one area of mathematics.
Welsh: Mae gwahanol feysydd mathemateg yn hynod o ryng-gysylltiedig a dibynnol ar ei gilydd, ac mae cysyniadau yn cael eu ffurfio dros gyfnod o amser, gan dynnu ar wybodaeth a dysgu cynharach, yn aml o fwy nag un maes mathemategol.
English: What is important when planning to teach any specific topic is to be aware of the prior knowledge the learners need in order to access and understand the new topic.
Welsh: Wrth gynllunio ar gyfer dysgu unrhyw bwnc penodol mae'n bwysig bod yn ymwybodol o'r wybodaeth flaenorol y mae dysgwyr eu hangen er mwyn cael mynediad i'r pwnc newydd a'i ddeall.
English: Algebra, geometry and statistics cannot be understood without a prior understanding of number and consistent reference to numbers, calculations and the number system.
Welsh: Nid oes modd deall algebra, geometreg nac ystadegaeth heb ddealltwriaeth flaenorol o rif a chyfeiriadau cyson at rifau, cyfrifiadau a'r system rifau.
English: As learners progress, they learn to see numerical expressions as relational rather than
Welsh: Wrth i ddysgwyr wneud cynnydd, maen nhw'n dysgu gweld mynegiannau rhifiadol yn berthynol yn hytrach nag yn
English: 8 + 2 = 10, 8 = 10 - 2, and so on.
Welsh: 8 + 2 = 10, 8 = 10 - 2, ac yn y blaen.
English: This lays the foundations for using
Welsh: Mae hyn yn gosod sail ar gyfer defnyddio
English: Making connections between arithmetic and algebra helps to develop tools and skills for
Welsh: Mae gwneud cysylltiadau rhwng rhifyddeg ac algebra o gymorth i ddatblygu offer a sgiliau ar gyfer rhesymu
English: Measure is an aspect of geometrical thinking which is closely connected to number, and much of the development of understanding of number can emerge through increasingly sophisticated measuring.
Welsh: Mae mesur yn agwedd ar feddylfryd geometraidd sy'n cysylltu'n agos â rhif, ac mae llawer o ddatblygiad dealltwriaeth o rif yn gallu ymddangos trwy fesur sy'n gynyddol soffistigedig.
English: Geometric thinking involves
Welsh: Mae meddylfryd geometraidd yn cynnwys
English: Probability is expressed through number in various ways, using percentages, fractions and decimals, and an understanding of the different representations; the connections between them are necessary for effective expression of probability.
Welsh: Mae tebygolrwydd yn cael ei fynegi trwy rif mewn amrywiol ffyrdd, gan ddefnyddio canrannau, ffracsiynau a degolion ynghyd â dealltwriaeth o'r gwahanol gynrychioliadau; mae'r cysylltiadau rhyngddyn nhw yn angenrheidiol ar gyfer mynegi tebygolrwydd yn effeithiol.
English: Statistics involves manipulation, representation and interpretation of data, which in turn require numerical and geometric thinking.
Welsh: Mae ystadegau yn ymwneud â thrin, cynrychioli a dehongli data, sydd yn ei dro yn gofyn am feddylfryd rhifiadol a geometraidd.
English: The aspiration is to deliver this Area so that there is a shift in culture towards learners fostering a positive and resilient attitude towards it.
Welsh: Y nod yw cyflwyno'r Maes fel bod newid mewn diwylliant gyda dysgwyr yn meithrin agwedd gadarnhaol a gwydn tuag ato.
English: Considerations for curriculum development
Welsh: Ystyriaethau ar gyfer datblygu cwricwlwm
English: Learners should be given opportunities to explore mathematically rich environments both indoors and outdoors.
Welsh: Dylai dysgwyr gael cyfleoedd i archwilio amgylcheddau mathemategol cyfoethog dan do a thu allan.
English: The environment will be developmentally appropriate and facilitate first-hand experiences with mathematical concepts and a range of resources.
Welsh: Bydd yr amgylchedd yn briodol ar gyfer datblygiad a bydd yn hwyluso profiadau uniongyrchol gyda chysyniadau mathemategol ac amrywiaeth o adnoddau.
English: The structure and sequence of mathematics and numeracy topics should be informed by the hierarchical and connected nature of mathematical concepts, in order to ensure foundations are built upon and experiences are connected.
Welsh: Dylid llywio strwythur a dilyniant pynciau o fewn mathemateg a rhifedd gan natur hierarchaethol a chysylltiadol cysyniadau mathemategol, er mwyn sicrhau adeiladu ar seiliau a chysylltu profiadau.
English: Learners need to become increasingly fluent in their use of number, through a broad range of experiences, in order to describe, interpret and communicate size, scale and comparisons, both within and beyond mathematics.
Welsh: Mae angen i ddysgwyr ddod yn gynyddol rugl yn eu defnydd o rif, trwy amrywiaeth eang o brofiadau er mwyn disgrifio, dehongli a chyfathrebu maint, graddfa a chymariaethau, o fewn yn ogystal â thu hwnt i fathemateg.
English: They should also become increasingly fluent in their calculations, both with and without the use of calculators.
Welsh: Dylen nhw ddod yn gynyddol rugl yn eu cyfrifo, gyda yn ogystal â heb gyfrifiannell.
English: By introducing a reasoning and problem-solving approach to all mathematics and numeracy experiences, the development of the four purposes and positive dispositions will be supported.
Welsh: Trwy gyflwyno dull rhesymu a datrys problemau ar gyfer holl brofiadau mathemateg a rhifedd, cefnogir datblygu'r pedwar diben ac ymagweddau cadarnhaol.
English: By using real-life examples to introduce, explore and consolidate mathematical concepts, learners of all ages make connections between the
Welsh: Trwy ddefnyddio enghreifftiau o fywyd go iawn i gyflwyno, archwilio a chadarnhau cysyniadau mathemategol, mae dysgwyr o bob oed yn gwneud cysylltiadau rhwng y
English: Through a broad range of experiences, learners appreciate the power of mathematics to express relationships concisely, in forms that are universally understood.
Welsh: Trwy amrywiaeth o brofiadau, mae dysgwyr yn gwerthfawrogi grym mathemateg i fynegi perthnasoedd yn gryno, mewn ffurfiau sy'n gyffredinol ddealladwy.
English: Learners should engage in meaningful and substantial tasks such as:
Welsh: Dylai dysgwyr ymwneud â thasgau ystyrlon a sylweddol megis:
English: modelling real-life numerical problems, financial calculations such as creating and evaluating budgets for events and analysing risks, developing mathematical sequences through patterns in nature and using the
Welsh: modelu problemau rhifiadol bywyd go iawn, cyfrifo ariannol megis creu a gwerthuso cyllidebau ar gyfer digwyddiadau a dadansoddi risgiau, datblygu dilyniannau mathemategol trwy batrymau ym myd natur a defnyddio'r
English: Practitioners should consider the appropriate use of a range of digital technologies,
Welsh: Dylai ymarferwyr ystyried y defnydd priodol o amrywiaeth o dechnolegau digidol,
English: It is important that learners are able to interpret answers and check that they make sense in context, including by estimation, and are able to use appropriate methods to answer questions by collecting, analysing and summarising data and interpreting results.
Welsh: Mae'n bwysig bod dysgwyr yn gallu dehongli atebion a gwirio eu bod yn gwneud synnwyr mewn cyd-destun, gan gynnwys trwy amcangyfrif, a'u bod yn gallu defnyddio dulliau priodol i ateb cwestiynau drwy gasglu, dadansoddi a chrynhoi data a dehongli canlyniadau.
English: They are able to evaluate their methods and suggest different or better ways to approach investigations in the future.
Welsh: Maen nhw'n gallu gwerthuso eu dulliau ac awgrymu ffyrdd gwahanol neu well o ymchwilio yn y dyfodol.
English: Deep understanding in mathematics and numeracy should develop through planning for all five of the mathematical proficiencies, and the connection and application of these in a range of contexts.
Welsh: Dylid datblygu dealltwriaeth ddofn mewn mathemateg a rhifedd trwy gynllunio ar gyfer y pum hyfedredd mathemategol, a sut mae'r rhain yn cysylltu a chymhwyso mewn amrywiaeth o gyd-destunau.
English: The proficiencies are interconnected and interdependent; they cannot be seen as hierarchical and they can be developed alongside each other.
Welsh: Mae'r hyfedreddau yn rhyng-gysylltiedig a rhyngddibynnol; ni ddylen nhw gael eu gweld yn hierarchaidd a gallan nhw ddatblygu ochr yn ochr â'i gilydd.
English: For example, as a child becomes more fluent in adding two-digit numbers, they will be developing their conceptual understanding of place value.
Welsh: Er enghraifft, wrth i blentyn ddod yn fwy rhugl yn adio rhifau dau ddigid, byddan nhw'n datblygu eu dealltwriaeth gysyniadol o werth lle.
English: It is not expected that all five proficiencies will be developed in a single session, but all five need to be developed during a particular mathematical concept.
Welsh: Nid oes disgwyl i'r pum hyfedredd i gyd ddatblygu o fewn sesiwn unigol, ond mae angen i'r pump gael eu datblygu yn ystod cysyniad mathemategol penodol.
English: There are certain processes and applications, for example the sequential data-handling cycle, which should be introduced from the outset, as they are essential to conceptual understanding.
Welsh: Mae rhai prosesau a chymwysiadau, er enghraifft y cylch trin data dilyniannol, a ddylai gael eu cyflwyno o'r cychwyn gan eu bod yn hanfodol i ddealltwriaeth gysyniadol.
English: Using the proficiencies, a contextual example:
Welsh: Defnyddio'r hyfedreddau, enghraifft gyd-destunol:
English: Learning about fractions - the case of ½
Welsh: Dysgu am ffracsiynau - achos ½
English: Understanding that a half is a result of dividing something into two equal parts.
Welsh: Deall bod hanner yn deillio o rannu rhywbeth yn ddwy ran hafal.
English: This could be through connecting concrete and/or real-life experiences of partitioning objects and numbers into equal parts with images (e.g. pictures and images on the number line) and the abstract representation of a ½ using the symbolic notation.
Welsh: Gallai hyn fod trwy gysylltu profiadau diriaethol a/neu brofiadau bywyd go iawn o ddosrannu gwrthrychau a rhifau yn rhannau hafal gyda delweddau (e.e. lluniau a delweddau ar y llinell rif) a'r cynrychioliad haniaethol o ½ gan ddefnyddio'r nodiant symbolaidd.
English: A learner who understands what a half is might be able to give real-life or visual examples, and would also be able to explain why something might not be a half (e.g. a pizza cut into two parts which are not equal).
Welsh: Efallai y gallai dysgwr sy'n deall beth yw hanner roi enghreifftiau o fywyd go iawn neu enghreifftiau delweddol, yn ogystal â gallu esbonio pam y gallai rhywbeth beidio â bod yn hanner (e.e. pitsa wedi'i dorri'n ddwy ran nad ydyn nhw'n hafal).
English: Communicating using symbols
Welsh: Cyfathrebu gan ddefnyddio symbolau
English: Understanding the convention of how a half is written and what the symbols mean.
Welsh: Deall yr arferiad o sut mae hanner yn cael ei ysgrifennu, a beth mae'r symbolau yn ei olygu.
English: This could also involve linking division and fractions (i.e. ½ = 1 ÷ 2) and using terms such as numerator and denominator.
Welsh: Gallai hyn hefyd gynnwys cysylltu rhannu a ffracsiynau (mewn geiriau eraill ½ = 1 ÷ 2) a defnyddio termau megis rhifiadur ac enwadur.
English: Strategic competence
Welsh: Cymhwysedd strategol
English: Being able to recognise real-life situations which involve a half and being able to represent these mathematically; being able to model situations involving halving mathematically; using pictures/images and language and symbols to illustrate a half.
Welsh: Gallu adnabod sefyllfaoedd bywyd go iawn sy'n ymwneud â hanner, a gallu cynrychioli'r rhain yn fathemategol; gallu modelu sefyllfaoedd yn ymwneud â haneru yn fathemategol; defnyddio lluniau/delweddau ac iaith a symbolau i ddangos hanner.
English: Being able to understand the relationship between a half and a whole; being able to justify why
Welsh: Gallu deall y gwahaniaeth rhwng hanner a chyfan; gallu cyfiawnhau pam mae
English: Being able to reason that ½ + ½ = 1, ½ x 2 = 1 and 1 ÷ 2 = ½.
Welsh: Gallu rhesymu bod ½ + ½ = 1, ½ x 2 = 1 a 1 ÷ 2 = ½.
English: Being able to justify why there may be many ways of splitting a shape in half.
Welsh: Gallu cyfiawnhau pam mae llawer ffordd o hollti siâp yn ei hanner.
English: Through connecting these proficiencies within a learner's experience of ½, learners should develop a deep understanding of a half as an example of a fraction.
Welsh: Trwy gysylltu'r hyfedreddau hyn o fewn profiad dysgwr o ½, dylai dysgwyr ddatblygu dealltwriaeth ddofn o hanner fel enghraifft o ffracsiwn.
English: The way in which these foci are introduced could vary, but ultimately, having opportunities to explore and connect these proficiencies should ensure learner progression within this concept.
Welsh: Gellir amrywio dulliau o gyflwyno'r elfennau hyn, ond yn y pen draw, dylai cael cyfleoedd i archwilio a chysylltu'r hyfedreddau hyn sicrhau cynnydd y dysgwr o fewn y cysyniad hwn.
English: Considerations for pedagogy
Welsh: Ystyriaethau o ran addysgeg
English: There is no research that says one way of teaching mathematics is better than any other.
Welsh: Nid oes ymchwil sy'n dangos bod un ffordd o addysgu mathemateg yn well nag unrhyw ffordd arall.
English: Nevertheless pedagogy should ensure the overall development of these proficiencies and also be relevant for the mathematics being taught.
Welsh: Er hyn, dylai addysgeg sicrhau datblygiad cyffredinol yr hyfedreddau hyn a hefyd fod yn berthnasol i'r fathemateg sy'n cael ei haddysgu.
English: Mathematics teaching needs to be conceptually connected and coherent.
Welsh: Mae angen i addysgu mathemateg fod yn gysyniadol gysylltiedig a chydlynol.
English: This requires mastery and memory of earlier concepts; comprehensible starting points; consistent use of language, symbols, images and other representations; illuminating choice of examples; relevant use of digital tools.
Welsh: Mae hyn yn gofyn am feistrolaeth a chofio cysyniadau blaenorol; mannau cychwyn dealladwy; defnydd cyson o iaith, symbolau, delweddau a chynrychioliadau eraill; dewis goleuedig o enghreifftiau; defnydd perthnasol o offer digidol.
English: These should be combined into lesson sequences which might include problem-solving, exploration, direct instruction, application, exercises and extended tasks as appropriate for the specific mathematics being taught and the overall development of the five proficiencies.
Welsh: Dylai'r rhain gael eu cyfuno o fewn dilyniannau gwersi a allai gynnwys datrys problemau, archwilio, cyfarwyddyd uniongyrchol, cymhwysiad, ymarferion a thasgau estynedig fel sy'n briodol ar gyfer y fathemateg benodol a ddysgir a datblygiad cyffredinol y pum hyfedredd.
English: At any point in a sequence the mathematical focus might be a new concept, an extension of an earlier concept, a relationship, a technique, a fact, a theorem, a mathematical strategy or a way of thinking.
Welsh: Ar unrhyw bwynt yn y dilyniant gallai'r ffocws mathemategol fod yn gysyniad newydd, ymestyniad o gysyniad blaenorol, perthynas, techneg, ffaith, theorem, strategaeth fathemategol neu ffordd o feddwl.
English: Guiding questions and information about choice and sequencing of pedagogical approaches to manage this diversity will be included in the
Welsh: Bydd cwestiynau sy'n arwain, ynghyd â gwybodaeth am ddewis a dilyniannu dulliau addysgeg er mwyn rheoli'r amrywiaeth hon, yn cael eu cynnwys yn yr adnodd ar
English: Numeracy and knowledge of real-world contexts could include understanding exchange rates, mortgage calculations and taxation, including the developing system of Welsh taxes.
Welsh: Gallai rhifedd a gwybodaeth am gyd-destunau byd go iawn gynnwys deall cyfraddau cyfnewid, cyfrifiadau morgeisi a threthiant, gan gynnwys y system treth sy'n datblygu yng Nghymru.
English: Through algebraic thinking and knowledge, learners could develop capabilities that can be applied to topics including personal finance and energy production in Wales and elsewhere.
Welsh: Drwy feddwl algebraidd a gwybodaeth am algebra, gallai dysgwyr ddatblygu galluoedd y gellir eu cymhwyso i destunau gan gynnwys cyllid personol a chynhyrchu ynni yng Nghymru ac mewn mannau eraill.
English: Geometry could draw examples from, and help develop a knowledge of, urban development as it differs across Wales, medical technology and computer imaging.
Welsh: Gallai geometreg dynnu ar enghreifftiau, a helpu i ddatblygu gwybodaeth, o ddatblygu trefol, sy'n wahanol ledled Cymru, technoleg feddygol a delweddu cyfrifiadurol.
English: From a strong foundation of problem solving, logical reasoning and understanding data, Mathematics and Numeracy is critical for informed citizens who are ready to play a full part in life and work.
Welsh: O sylfaen gadarn o ddatrys problemau, rhesymu rhesymegol a deall data, mae Mathemateg a Rhifedd yn hanfodol i ddinasyddion gwybodus sy'n barod i chwarae rhan lawn mewn bywyd a gwaith.
English: When designing your curriculum, you should consider how learning links across Areas in order to achieve a holistic approach to learning.
Welsh: Wrth gynllunio eich cwricwlwm, dylech ystyried sut mae dysgu yn cysylltu ar draws Meysydd er mwyn sicrhau dull holistaidd o ddysgu.
English: Mathematics and numeracy can be used across all other Areas to enhance, stimulate and support learning.
Welsh: Gellir defnyddio mathemateg a rhifedd ar draws pob Maes arall i gyfoethogi ysgogi a chefnogi dysgu.
English: Equally, mathematics and numeracy can be developed through other Areas.
Welsh: Yn ogystal, gellir datblygu mathemateg a rhifedd trwy Feysydd eraill.
English: Some of the key links to learning in this Area are detailed below.
Welsh: Mae rhai o'r cysylltiadau allweddol i ddysgu yn y Maes hwn yn cael eu hamlinellu isod.
English: The use of numeracy and concepts from this Area are embedded in the Expressive Arts Area of Learning and Experience supporting all disciplines.
Welsh: Mae'r defnydd o rifedd a chysyniadau o'r Maes hwn wedi ymwreiddio ym Maes Dysgu a Phrofiad y Celfyddydau Mynegiannol, gan gefnogi pob disgyblaeth.
English: The use of songs and rhymes can assist with the embedding of numeracy during the early progression steps.
Welsh: Gall defnyddio caneuon a rhigymau gynorthwyo gydag ymwreiddio rhifedd yn ystod y camau cynnydd cynnar.
English: The Humanities
Welsh: Mae
English: Humanities enquiries will often include the collection of primary data using sampling methods, and the representation and analysis of data and statistics in a range of forms.
Welsh: Yn aml byddant hefyd yn cynnwys casgliad o ddata craidd gan ddefnyddio dulliau samplu, a chynrychioliad a dadansoddiad data ac ystadegau mewn amrywiaeth o ffurfiau.
English: Learners are provided with opportunities to sort and classify data, and identify patterns, trends and anomalies.
Welsh: Cynigir cyfleoedd i ddysgwyr drefnu a dosbarthu data ac adnabod tueddiadau, patrymau ac anomaleddau.
English: Supporting entrepreneurship, ratio and scale; finance; rounding; ordering will also be relevant.
Welsh: Mae cefnogi entrepreneuriaeth, cymhareb a graddfa, cyllid, talgrynnu a threfnu hefyd yn berthnasol.
English: Finding and applying patterns for problem solving is a skill required for progress in these two Areas.
Welsh: Mae dod o hyd i batrymau a'u cymhwyso ar gyfer datrys problemau yn sgil sydd ei hangen ar gyfer cynnydd yn y ddau Faes yma.
English: From the use of data and statistics in inquiry and evidence, geometry and measurement in design and development, through to data handling in technology learning in science and technology is often underpinned by progression in mathematical understanding, as expressed through the five
Welsh: O'r defnydd o ddata ac ystadegau mewn ymholiad a thystiolaeth, geometreg a mesur mewn dylunio a datblygu, hyd at drin data mewn technoleg, mae dysgu mewn gwyddoniaeth a thechnoleg yn aml yn seiliedig ar gynnydd mewn dealltwriaeth fathemategol, fel y'u mynegir trwy'r pum hyfedredd mathemategol.
English: Curriculum links between these two Areas are, therefore, multiple and often quite detailed.
Welsh: Felly mae sawl cysylltiad cwricwlaidd rhwng y ddau Faes yma ac, yn aml, maen nhw'n eithaf manwl.
English: Schools may wish to consider curriculum sequencing in particular when designing and planning their curriculum to ensure opportunities in science and technology to contextualise mathematical conceptual learning are fully optimised.
Welsh: Gall ysgolion ddymuno ystyried dilyniannu cwricwlwm yn arbennig wrth ddylunio a chynllunio eu cwricwlwm er mwyn sicrhau bod cyfleoedd mewn gwyddoniaeth a thechnoleg i gyd-destunoli dysgu mathemategol cysyniadol yn cael eu gweithredu'n llawn.
English: Mathematics is a universal language.
Welsh: Mae mathemateg yn iaith fyd-eang.
English: To make sense of this language and to understand mathematical concepts, learners need examples rooted in everyday life.
Welsh: Er mwyn gwneud synnwyr o'r iaith hon a deall cysyniadau mathemategol, mae dysgwyr angen enghreifftiau wedi'u gwreiddio mewn bywyd pob-dydd.
English: This is especially important for young learners who are often unable to think abstractly.
Welsh: Mae hyn yn arbennig o bwysig i ddysgwyr ifanc nad ydyn nhw'n aml yn gallu meddwl yn haniaethol.
English: Learning within local, national and international contexts will enable learners
Welsh: Bydd dysgu o fewn cyd-destunau lleol, cenedlaethol a rhyngwladol yn galluogi dysgwyr
English: Wales has a proud history of producing outstanding mathematicians and schools should consider every opportunity to highlight their achievements, inspiring learners to become mathematicians themselves.
Welsh: Mae gan Gymru hanes balch o gynhyrchu mathemategwyr nodedig, a dylai ysgolion ystyried pob cyfle i dynnu sylw i'w llwyddiannau, gan ysbrydoli dysgwyr i ddod yn fathemategwyr eu hunain.
English: Using international examples from a range of cultures enables learners to understand the history of mathematics and its development into an international and universally applicable language.
Welsh: Mae defnyddio enghreifftiau rhyngwladol o amrywiaeth o ddiwylliannau yn galluogi dysgwyr i ddeall hanes mathemateg a'i datblygiad i fod yn iaith ryngwladol, ac un y gellir ei chymhwyso'n fyd-eang.