techiaith/bydtermcymru-tm-en-cy huggingface dataset:
English: Reasoning about the sizes and properties of shapes and their surrounding spaces helps us to make sense of the physical world and the world of mathematical
Welsh: Mae rhesymu ynghylch meintiau a phriodweddau siapiau a'r gofod o'u hamgylch
English: Geometry and measurement have applications in many ﬁelds, including art,
Welsh: Gellir cymhwyso geometreg a mesur mewn sawl maes, gan gynnwys celf, adeiladu, gwyddoniaeth a thechnoleg, peirianneg, a seryddiaeth.
English: Statistics is the practice of collecting, manipulating and analysing data, allowing representation and generalisation of information.
Welsh: Ystadegau yw'r arfer o gasglu, trin a dadansoddi data er mwyn gallu cynrychioli a chyffredinoli gwybodaeth.
English: Statistics and probability rely on the application and manipulation of number and algebra.
Welsh: Mae ystadegau a thebygolrwydd yn dibynnu ar gymhwyso a thrin rhifau ac algebra.
English: Managing data and representing information effectively provides the means to test hypotheses, draw conclusions and make predictions.
Welsh: Mae rheoli data a chynrychioli gwybodaeth yn effeithiol yn cynnig ffordd o broﬁ
English: Reasoning with statistics and probability, and evaluating their reliability, develops critical thinking and analytical skills that are fundamental to making ethical and informed decisions.
Welsh: Mae rhesymu gan ddefnyddio ystadegau a thebygolrwydd, a gwerthuso eu dibynadwyedd, yn meithrin y sgiliau dadansoddi a meddwl beirniadol sy'n hollbwysig wrth wneud penderfyniadau egwyddorol a gwybodus.
English: Relationships between what matters statements in Mathematics and Numeracy
Welsh: Y berthynas rhwng y datganiadau o'r hyn sy'n bwysig mewn Mathemateg a Rhifedd
English: The different areas of mathematics are highly interconnected and dependent on one another, and, as any teacher of mathematics knows, concepts are built up over time, drawing on prior knowledge and learning, often from more than one area of mathematics.
Welsh: Mae cysylltiadau agos rhwng y meysydd mathemategol gwahanol ac maent yn ddibynnol iawn
English: What is important when planning to teach any speciﬁc topic is to work out the prior
Welsh: Yr hyn sy'n bwysig wrth gynllunio ar gyfer addysgu unrhyw bwnc penodol yw
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: Ni ellir deall algebra, geometreg nac ystadegau heb ddealltwriaeth ﬂaenorol o rif a chyfeiriadau cyson at rifau, cyfriﬁadau a'r system rhifau.
English: As learners progress they learn to see numerical expressions as relational rather than computational, e.g. a computation such as 2 + 8 = 10, and that this is the basis for deriving other facts, e.g. 8 + 2 = 10, 8 = 10 - 2, and so on.
Welsh: Wrth i'r dysgwyr ddangos cynnydd, byddant yn dysgu i ystyried mynegiadau rhifyddol fel mynegiadau perthynol yn hytrach na mynegiadau cyfriﬁannol, e.e. maent yn gweld bod cyfriﬁant fel 2 + 8 = 10, ac mae hynny yn sail i ddod o hyd i ffeithiau eraill fel 8 + 2 = 10, 8 = 10 - 2, ac yn y blaen.
English: This lays the foundations for using algebraic symbolisation successfully.
Welsh: Mae hyn yn gosod y sylfeini ar gyfer defnyddio dulliau
English: Making connections between arithmetic and algebra helps to develop tools and skills for abstract reasoning from an early age.
Welsh: Mae gwneud y cysylltiadau rhwng rhifyddeg ac algebra yn fodd i ddatblygu'r adnoddau a sgiliau ar gyfer rhesymu haniaethol o oedran cynnar.
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 feddwl geometregol sydd â chysylltiad agos iawn â rhif, a gall cryn dipyn
English: Geometric thinking involves reasoning with proportion, which connects with development in number work;
Welsh: Mae meddwl geometrig yn cynnwys rhesymu â chyfrannedd, sy'n gysylltiedig â datblygiad mewn
English: it also involves transforming shapes, which relates to the use of functions and mapping in algebra.
Welsh: mae hefyd yn cynnwys trawsffurﬁo siapiau, sy'n ymwneud â defnyddio ffwythiannau a
English: Probability is expressed through number in various ways, using percentages, fractions and decimals, and an understanding of the different representations, and the connections between them, is necessary for effective expression of probability.
Welsh: Caiff tebygolrwydd ei fynegi drwy rif mewn amrywiaeth o ffurﬁau, drwy ddefnyddio canrannau,
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 eu tro'n galw am feddwl mewn ffordd rifyddol a geometrig.
English: Progression in Mathematics and Numeracy involves the development of the following
Welsh: Mae cynnydd mewn Mathemateg a Rhifedd yn cynnwys datblygu hyfedreddau rhyng-gysylltiedig a rhyngddibynnol
English: • Conceptual understanding; having the knowledge to understand and explain a mathematical concept.
Welsh: • Dealltwriaeth gysyniadol; meddu ar yr wybodaeth i ddeall ac egluro cysyniad mathemategol.
English: • Communication with symbols.
Welsh: • Cyfathrebu â symbolau.
English: • Strategic competence (i.e. formulating problems mathematically in order to solve them).
Welsh: • Cymhwysedd strategol (h.y. gosod problemau allan mewn ffurf fathemategol er mwyn eu datrys).
English: A key point to note in any planning and assessment of Mathematics and Numeracy is that the
Welsh: Pwynt allweddol i'w nodi wrth ymgymryd ag unrhyw waith cynllunio ac asesu ar gyfer Mathemateg a Rhifedd yw bod y hyfedreddau yn rhyng-gysylltiedig ac yn rhyngddibynnol;
English: they cannot be seen as hierarchical (e.g. strategic competence does not come after learning facts and techniques) and they can be developed
Welsh: ni ellir eu hystyried mewn modd hierarchaidd (e.e. nid yw cymhwysedd strategol yn ail i ddysgu ffeithiau a thechnegau) a gellir eu datblygu ochr yn ochr â'i gilydd.
English: However, it may be helpful to target certain proﬁciencies at certain points, if
Welsh: Fodd bynnag, gall fod yn ddefnyddiol targedu rhai hyfedreddau penodol ar adegau penodol, os yw hynny'n briodol er mwyn sicrhau cynnydd.
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 gyfartal.
English: This could be through connecting their 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 ddigwydd drwy
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: Mae'n bosibl y gall dysgwr sy'n deall beth yw hanner roi enghreifftiau go iawn neu enghreifftiau gweledol, ac y byddai hefyd, efallai, yn gallu egluro pam nad yw rhywbeth yn hanner go iawn (e.e. pizza wedi'i dorri'n ddwy ran nad ydynt yn hafal o ran maint).
English: Communicating with symbols
Welsh: Cyfathrebu â symbolau
English: Understanding the convention of how a half is written and what the symbols mean.
Welsh: Deall y confensiwn ar gyfer ysgrifennu hanner ac ystyr y symbolau.
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 (h.y. ½ = 1 ÷ 2) a defnyddio termau megis rhiﬁadur ac enwadur.
English: Being able to recognise real-life situations which involve a half;
Welsh: Gallu adnabod sefyllfaoedd go iawn sy'n ymwneud â hanner;
English: being able to represent these
Welsh: gallu cynrychioli'r sefyllfaoedd hyn ar ffurf fathemategol;
English: being able to model situations involving halving mathematically;
Welsh: gallu modelu sefyllfaoedd sy'n ymwneud â haneru mewn ffordd fathemategol;
English: using pictures/images and language and symbols.
Welsh: defnyddio lluniau/delweddau ac iaith a symbolau.
English: and adapted to the Welsh context by Anne Watson, Emeritus Professor of Mathematics Education, University of Oxford, 2018.
Welsh: ac wedi'i addasu ar gyfer cyd-destun Cymru gan Anne Watson, Athro Emeritws mewn Mathemateg, Prifysgol Rhydychen,2018.
English: Being able to understand the relationship between a half and a whole;
Welsh: Gallu deall y gydberthynas rhwng hanner a chyfan;
English: being able to justify why ²
Welsh: gallu cyﬁawnhau pam bod
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 ac 1 ÷ 2 = ½.
English: Being able to justify why
Welsh: Gallu cyﬁawnhau pam y gall fod sawl ffordd
English: Through connecting these proﬁciencies within a learner's experience of ½, learners should develop
Welsh: Drwy gysylltu'r hyfedreddau hyn o fewn proﬁad dysgwr o ½, dylai dysgwyr feithrin dealltwriaeth ddofn o hanner fel enghraifft o ffracsiwn.
English: The way in which these foci are
Welsh: Gallai'r dulliau ar gyfer cyﬂwyno'r ffocysau hyn amrywio ond, yn y pen draw, dylai'r ffaith bod cyﬂeoedd yn cael eu cynnig i archwilio a chysylltu'r
English: Being able to count in steps of a half and being able to begin to recall halves of numbers.
Welsh: Gallu cyfrif fesul hanner a gallu dechrau galw haneri rhifau i gof.
English: Literacy can be developed through engaging and accessible experiences where learners are given regular opportunities to describe, explain and justify their understanding of various mathematical concepts, using appropriate mathematical vocabulary.
Welsh: Gellir datblygu llythrennedd drwy broﬁadau diddorol a hygyrch, lle y cynigir cyﬂeoedd rheolaidd i ddysgwyr ddisgriﬁo, egluro a chyﬁawnhau eu dealltwriaeth o amrywiol gysyniadau mathemategol,
English: The development of these skills can be seen in rhymes and songs through to discussions around abstract concepts.
Welsh: Caiff y sgiliau hyn eu datblygu mewn rhigymau a
English: Learners will also use and develop their literacy skills in a written form in order to describe mathematical processes, such as reasoning.
Welsh: Bydd dysgwyr hefyd yn defnyddio ac yn meithrin eu sgiliau llythrennedd ar ffurf ysgrifenedig er mwyn disgriﬁo prosesau mathemategol,
English: Learners will increasingly use literacy skills in order to understand a range of calculation strategies, describing visualisation of shapes, studying and interpreting information in statistics and comparing alternative methods before arriving at a solution to a mathematical problem.
Welsh: Bydd dysgwyr yn defnyddio sgiliau llythrennedd yn gynyddol er mwyn deall amrywiaeth o strategaethau cyfrifo, gan ddisgriﬁo'r broses o ddelweddu siapiau, astudio a dehongli gwybodaeth
English: They should use these literacy skills as they encounter practical, real-world problems.
Welsh: Dylent ddefnyddio'r sgiliau llythrennedd hyn wrth iddynt ddod ar draws problemau ymarferol go iawn.
English: Mathematics and Numeracy, by deﬁnition, has numeracy at its heart.
Welsh: Yn ôl ei ddifﬁniad, mae rhifedd wrth wraidd Mathemateg a Rhifedd.
English: Numeracy involves applying and connecting the ﬁve mathematical proﬁciencies
Welsh: Mae rhifedd yn cynnwys cymhwyso a chysylltu'r pum hyfedredd mathemategol
English: Real-life contexts can be used to introduce and explore mathematical concepts, as well as to consolidate them.
Welsh: Gellir defnyddio cyd-destunau go iawn i gyﬂwyno ac ystyried cysyniadau mathemategol, yn ogystal
English: For example, the use of percentages can be applied to annual percentage rates
Welsh: Er enghraifft, gellir cymhwyso'r defnydd o ganrannau at gyfraddau canrannol blynyddol (APR) er mwyn dangos bod y defnydd hwnnw yn berthnasol i lythrennedd ariannol.
English: Digital approaches will enhance learners' mathematical and numeracy skills across a range of situations that will naturally occur within the area of learning and experience.
Welsh: Bydd dulliau gweithredu digidol yn gwella sgiliau mathemategol a sgiliau rhifedd dysgwyr mewn amrywiaeth o sefyllfaoedd a fydd yn digwydd yn naturiol yn y maes dysgu a phroﬁad.
English: Digital competence is more than the interaction with technology.
Welsh: Mae cymhwysedd digidol yn fwy na dim ond ymwneud â thechnoleg.
English: For example, collaborating to solve a problem and the development of algorithms to support the understanding of patterns will provide the opportunity to support the development of learner's digital skills.
Welsh: Er enghraifft, bydd cydweithio er mwyn datrys problem a datblygu algorithmau er mwyn ategu dealltwriaeth o batrymau yn cynnig
English: Creating a graph by using a spreadsheet, for example, will enhance digital understanding and also strengthen learners' mathematical and numerical skills.
Welsh: Bydd creu graff gan ddefnyddio taenlen,
English: Naturally, as learners develop and progress they will increasingly use more complex digital skills and
Welsh: Yn naturiol, wrth i ddysgwyr ddatblygu a gwneud cynnydd, byddant yn defnyddio'n gynyddol sgiliau a phrosesau, technegau a systemau digidol mwy cymhleth, i greu datrysiadau er mwyn
English: Aspects of collection, representation and analysis, for example, will become more sophisticated as learners progress.
Welsh: Bydd agweddau ar gasglu, cynrychioli a dadansoddi, er enghraifft, yn dod yn fwy sofﬁstigedig wrth i ddysgwyr wneud cynnydd.
English: Welsh language
Welsh: Y Gymraeg
English: The number system in Welsh (Cymraeg) is an area that highlights the distinctive nature of mathematics in a Welsh context.
Welsh: Mae'r system rhifau yn y Gymraeg yn faes sy'n tynnu sylw at natur arbennig mathemateg mewn cyd-destun Cymreig.
English: In the early years, in particular, it would be helpful if teachers could consider teaching learners the traditional (vigesimal) way of counting in Welsh, as well as the more modern way.
Welsh: Yn ystod y blynyddoedd cynnar, yn arbennig, byddai'n ddefnyddiol pe gallai athrawon ystyried addysgu dysgwyr sut i gyfrif yn y Gymraeg gan ddefnyddio'r dull traddodiadol (fesul ugain), yn ogystal â'r ffordd fwy modern.
English: The decision as to when to introduce it, however, should be left to individual schools, to
Welsh: Fodd bynnag, dylai ysgolion unigol benderfynu
English: Children from homes/communities where Welsh is widely spoken,
Welsh: Mae'n bosibl y bydd plant sy'n dod o gartreﬁ/cymunedau lle y caiff y Gymraeg ei siarad yn helaeth, er enghraifft, eisoes yn gyfarwydd
English: The Welsh number system, as with other Celtic and some European languages, traditionally used the vigesimal system, using a base of 20 instead of the modern (and common) base of 10.
Welsh: Yn draddodiadol, roedd y system rhifau yn Gymraeg, fel gydag ieithoedd Celtaidd eraill a rhai ieithoedd Ewropeaidd, yn defnyddio'r system ugeiniol yn hytrach na'r sail fodern (a chyffredin) sy'n defnyddio sail o 10.
English: In comparatively recent times a decimal system, in common with other Indo-European languages, was set up to simplify the teaching of number.
Welsh: Yn gymharol ddiweddar, sefydlwyd system ddegol, yn gyffredin ag ieithoedd Indo-Ewropeaidd eraill, er mwyn symleiddio'r broses o addysgu rhif.
English: (For example, in the old system 11 was 'un ar ddeg' [1+10] and 14 was pedwar ar ddeg [4+10].
Welsh: (Er enghraifft, yn yr hen system,
English: In the 'new' system, 11 is 'un deg un' [10+1] and 14 is 'un deg pedwar' [10+4]).
Welsh: Yn y system 'newydd', cyfeirir at 11 fel 'un deg un' [10+1] a chyfeirir at 14 fel 'un deg pedwar' [10+4]).
English: The Welsh dimension and international perspective elements will enable learners to understand the connection between mathematics (and numeracy) and authentic real-world contexts that span across both Wales and the world.
Welsh: Bydd elfennau'r dimensiwn Cymreig a phersbectif rhyngwladol yn galluogi dysgwyr i ddeall y
English: Mathematics is a universal language, but in order for learners to make sense of this language, and to understand mathematical concepts, it helps to provide examples rooted in everyday life.
Welsh: Mae mathemateg yn iaith i bawb, ond er mwyn i ddysgwyr wneud synnwyr o'r iaith honno, a deall cysyniadau mathemategol, mae'n helpu i ddarparu enghreifftiau sy'n berthnasol i fywyd pob-dydd.
English: Learners, especially young learners, are often unable to think
Welsh: Yn aml, nid yw dysgwyr, yn enwedig dysgwyr ifanc, yn gallu meddwl mewn ffordd haniaethol ac maent yn ei chael hi'n haws dysgu mathemateg mewn ffordd fwy diriaethol.
English: Each school in Wales will have a unique environment in which they work, and schools should explore local sources and resources that might have a mathematics application.
Welsh: Bydd gan bob ysgol yng Nghymru amgylchedd unigryw y bydd yn gweithio ynddo, a dylai ysgolion
English: The Learned Society of Wales refers to Wales providing 'practical contexts through which procedure, theories, and/or principles are given concrete form through examples, case study, and illustrations of real-lifeapplications' (The Learned Society of Wales, 2018).
Welsh: Mae Cymdeithas Ddysgedig Cymru yn nodi bod Cymru yn darparu cyd-destunau ymarferol ar gyfer cynnig ffurf ddiriaethol i weithdrefnau, damcaniaethau a/neu egwyddorion drwy enghreifftiau,
English: Emeritus Professor Gareth Ffowc Roberts, in his submission to the Learned Society paper, stated that 'while there may be no such thing as 'Welsh mathematics/numeracy' there are very particular Welsh ways of experiencing mathematics/numeracy'.
Welsh: Yn ei gyﬂwyniad i bapur y Gymdeithas Ddysgedig, nododd yr Athro Emeritws Gareth Ffowc
English: The challenge is to teach and learn mathematics and numeracy in Wales so that children gain ownership of them, and perceive them as being a natural part of their culture rather than believing that they are copying another community's culture.
Welsh: Yr her yw addysgu a dysgu mathemateg a rhifedd yng Nghymru
English: Various local and national organisations (e.g. the National Museum of Wales and CADW) have already developed mathematics teaching resources.
Welsh: Mae amrywiol sefydliadau lleol a chenedlaethol (e.e. Amgueddfa Genedlaethol Cymru a CADW) eisoes wedi datblygu adnoddau addysgu mathemateg.
English: Since April 2019 the Welsh Government has had responsibility for deciding the rates of Income Tax paid by Welsh taxpayers.
Welsh: Ers Ebrill 2019, mae gan Llywodraeth Cymru gyfrifoldeb dros benderfynu y cyfraddau treth incwm sy'n cael eu talu gan drethdalwyr Cymru.
English: Schools are encouraged to use Welsh examples when
Welsh: Mae ysgolion yn cael eu hannog i ddefnyddio enghreifftiau Cymreig wrth addysgu materion ariannol, megis treth, gan bwysleisio y cysylltiad rhwng Mathemateg a Rhifedd, y byd go iawn a chyfrifoldeb Llywodraeth Cymru i bennu cyfraddau treth incwm yng Nghymru.
English: There are particular contributions to the ﬁeld of mathematics from Wales and internationally that
Welsh: Ceir cyfraniadau penodol at faes mathemateg o Gymru ac yn rhyngwladol y gellid eu defnyddio i ategu dealltwriaeth o gysyniadau a chonfensiynau mathemategol, yn ogystal ag ategu dealltwriaetho'r broses o ddatblygu mathemateg fel corff gwybodaeth.
English: Wales has a proud history of producing outstanding mathematicians such as Robert Recorde and William Jones.
Welsh: Mae gan Gymru hanes balch o gynhyrchu
English: Schools should consider every opportunity to highlight their achievements and, hopefully, inspire learners to become mathematicians themselves.
Welsh: Dylai ysgolion ystyried pob cyﬂe i dynnu sylw at eu cyﬂawniadau gan ysbrydoli dysgwyr, gobeithio, i ddod yn fathemategwyr eu hunain.
English: Using international examples from a range of cultures could enable learners to understand the history of mathematics and its development into an international and universally applicable language.
Welsh: Gallai defnyddio enghreifftiau rhyngwladol o amrywiaeth o ddiwylliannau alluogi dysgwyr i ddeall hanes mathemateg, a'r ffordd y mae wedi datblygu'n iaith ryngwladol y gellir ei defnyddio gan bawb.
English: This could also promote and support cross-curricular learning.
Welsh: Gallai hyn hefyd hyrwyddo a chefnogi dysgu trawsgwricwlaidd.
English: The Mathematics and Numeracy Area of Learning and Experience has developed a set of
Welsh: Mae Maes Dysgu a Phroﬁad Mathemateg a Rhifedd wedi datblygu cyfres o hyfedreddau
English: These proﬁciencies build on the work
Welsh: Mae'r hyfedreddau hyn yn seiliedig ar waith Kilpatrick et al.
English: The Mathematics and Numeracy Area of Learning and Experience provides opportunities for learners to develop all four of the following wider skills.
Welsh: Mae'r Maes Dysgu a Phroﬁad Mathemateg a Rhifedd yn darparu cyﬂeoedd i ddysgwyr ddatblygu pob un o'r pedwar sgil ehangach canlynol.
English: Critical thinking and problem‑solving
Welsh: Meddwl yn feirniadol a datrys problemau
English: The development of logical and critical thinking underpins learning in mathematics.
Welsh: Mae datblygu sgiliau meddwl yn rhesymegol ac yn feirniadol yn sail i ddysgu mewn mathemateg.
English: Mathematics teaches us problem-solving skills, which transfer to all areas of the curriculum, to life in general and to the world of work.
Welsh: Mae mathemateg yn addysgu sgiliau datrys problemau sy'n trosglwyddo i bob maes o'r cwricwlwm, i fywyd yn gyffredinol ac i'r byd gwaith.
English: The work of mathematics involves solving problems, beginning by analysing requirements, asking questions and evaluating information.
Welsh: Mae mathemateg yn ymwneud â datrys problemau, gan ddechrau drwy ddadansoddi yr hyn sydd ei angen, gofyn cwestiynau a gwerthuso gwybodaeth.
English: In the development of solutions, learners identify potential approaches and develop arguments, justifying their decisions.
Welsh: Wrth ddatblygu datrysiadau, mae dysgwyr yn adnabod dulliau gweithredu posibl ac yn datblygu
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 data-handling cycle.
Welsh: Mae meddwl yn fathemategol yn gofyn i ddysgwyr fod yn drefnus ac, wrth iddynt wneud cynnydddrwy'r ysgol, bydd eu sgiliau trefnu yn datblygu, yn enwedig wrth iddynt gynllunio a gweithredu'r cylch trin data.
English: In their mathematical problem-solving, learners are encouraged to predict and estimate solutions
Welsh: Wrth ddatrys problemau mathemategol, anogir dysgwyr i ragfynegi ac amcangyfrif datrysiadau ac wedyn i wirio eu hatebion, myfyrio ar eu canlyniadau a gwerthuso eu dulliau gweithredu.
English: Increasingconﬁdence in decision-making for mathematical problem-solving supports learners to be more
Welsh: Mae cynyddu eu hyder wrth wneud penderfyniadau er mwyn datrys problemau mathemategol yn helpu dysgwyr i fod yn fwy uchelgeisiol wrth bennu nodau a heriau iddynt eu hunain.
English: Mathematical working requires and develops creativity and curiosity which also transfer to other aspects of life.
Welsh: Mae gweithio'n fathemategol yn gofyn am greadigrwydd a chwilfrydedd ac yn datblygu'r agweddau hynny y gellir hefyd eu trosglwyddo i agweddau eraill ar fywyd.
English: Frequently in mathematical problem-solving the learner does not immediately know how to approach the problem;
Welsh: Yn aml, wrth ddatrys problemau mathemategol, nid yw'r dysgwr yn gwybod ar unwaith sut i ymdrin â'r broblem;
English: it takes creativity and courage to explore different approaches before deciding how to proceed.
Welsh: mae angen creadigrwydd a beiddgarwch wrth ystyried gwahanol ddulliau gweithredu cyn penderfynu sut i fwrw ymlaen.
English: Planning and modelling tasks within mathematics develops learners' ability to turn ideas into action.
Welsh: Mae cynllunio a modelu tasgau ym maes mathemateg yn datblygu gallu dysgwyr i roi syniadau ar waith.
English: Everyone encounters challenges in studying mathematics at some point, and overcoming the challenges requires and develops resourcefulness and resilience.
Welsh: Mae pawb yn wynebu heriau ar ryw