Rhifedd yng nghyfnodau allweddol 2 a 3: adroddiad interim Numeracy in key stages 2 and 3: an interim report

Rhifedd yng nghyfnodau allweddol 2 a 3: adroddiad interim

Numeracy in key stages 2 and 3: an interim report

Cefndir Background • Yr adroddiad hwn yw’r ail mewn

cyfres o dri a gyhoeddwyd mewn ymateb i gais am gyngor yn llythyr cylch gorchwyl y Gweinidog i Estyn ar gyfer 2012-2013.

• Mae’n edrych ar safonau mewn rhifedd yng nghyfnodau allweddol 2 a 3, a sut mae sampl o ysgolion cynradd ac uwchradd yn datblygu medrau rhifedd disgyblion ar draws y cwricwlwm dros gyfnod o dair blynedd.

• Ar gyfer yr adroddiad hwn, bu’r arolygwyr yn ailymweld â’r ysgolion a gyfranogodd yn astudiaeth waelodlin rhifedd 2013 i arfarnu cynnydd dros y 12 mis diwethaf.

• This report is the second in a series of three published in response to a request for advice in the Minister’s annual remit letter to Estyn for 2012-2013.

• It looks at standards in numeracy at key stages 2 and 3 and how a sample of primary and secondary schools is developing pupils’ numeracy skills across the curriculum over a three-year period.

• For this report, inspectors re-visited the schools that participated in the 2013 numeracy baseline study to evaluate progress over the last 12 months.

Prif ganfyddiadauMain findings

• Mewn ychydig o dan hanner yr ysgolion cynradd ac uwchradd a arolygwyd yn 2013-2014, mae disgyblion yn datblygu medrau rhifedd da neu well. Yn yr ysgolion eraill, cymedrol ar y gorau yw medrau rhifiadol disgyblion. Y rheswm am hyn yw mai dim ond rhyw hanner yr ysgolion sydd wedi datblygu darpariaeth addas ar gyfer rhifedd.

• Mae’r ysgolion yn yr arolwg wedi gwneud cynnydd o ran datblygu’u darpariaeth rhifedd ers yr arolwg gwaelodlin. Mae hyn yn dechrau cael effaith ar safonau disgyblion mewn ysgolion cynradd ac uwchradd.

• In just under half of primary and secondary schools inspected in 2013-2014, pupils develop good or better numeracy skills. In the remaining schools, pupils’ numerical skills are at best average. This is because only around half of schools have developed suitable provision for numeracy.

• The schools in the survey have made progress in developing their numeracy provision since the baseline survey. This is beginning to have an impact on pupil standards in both primary and secondary schools.


• Ar y cyfan, mae disgyblion yn yr ysgolion hyn yn dangos gafael cadarn ar fedrau mathemategol sylfaenol. Mae hyn yn welliant o’r arolwg gwaelodlin.

• Yn benodol, mae cyflwyno’r Fframwaith Llythrennedd a Rhifedd Cenedlaethol wedi helpu ysgolion i gynllunio’n fwy effeithiol, ac mae athrawon yn dechrau cynllunio gweithgareddau o ansawdd gwell i gefnogi ac ehangu medrau llythrennedd disgyblion.

• In the main, pupils in these schools show a secure grasp of basic mathematical skills. This is an improvement from the baseline survey.

• In particular, the introduction of the National Literacy and Numeracy Framework has helped the schools to plan more effectively, and teachers are beginning to plan better quality activities to support and extend pupils’ numeracy skills.


• Mae safonau ac ansawdd yr addysgu yn uwch, ac mae arweinyddiaeth ar draws yr ysgolion a fu’n rhan o’r arolwg wedi gwella hefyd, er o ychydig.

• Mae athrawon wedi cael hyfforddiant o ansawdd gwell, ac mae hynny wedi datblygu’u medrau rhifiadol ac wedi arwain at gynllunio gwell a methodoleg rifiadol gyson ar draws yr ysgolion hyn.

• Standards and the quality of teaching are higher and leadership across the surveyed schools has also improved, albeit marginally.

• Teachers have received better quality training which has developed their numerical skills and led to improved planning and consistent numerical methodology across these schools.


• Er eu bod wedi gwneud cynnydd ers yr arolwg gwaelodlin, mae llawer i’r ysgol hyn i’w wneud eto, cyn bod llawer o’r strategaethau yn cael effaith gyson ar safonau. Yn benodol, mae ysgolion wedi gwneud cynnydd cyfyngedig o ran:– asesu ac olrhain medrau rhifedd

disgyblion;

– gwella parhad a dilyniant y profiad i ddisgyblion rhwng ysgolion cynradd a rhwng ysgolion cynradd ac uwchradd; a

– monitro ac arfarnu ansawdd safonau rhifedd a darpariaeth mewn ysgolion.

• Despite making progress since the baseline survey, there is still a lot for these schools to do before many of the strategies have a consistent impact on standards. In particular, schools have made limited progress with:– assessing and tracking of pupils’

numeracy skills;

– improving the continuity and progression of experience by pupils between primary schools and between primary and secondary schools ; and

– monitoring and evaluating the quality of numeracy standards and provision in schools.


• Mae gormod o ddisgyblion o hyd nad yw’r hyder ganddynt mewn medrau mathemategol pwysig fel rhannu a chanrannau. Mae’r diffygion hyn yn rhwystro gallu disgyblion i ddehongli canlyniadau a datrys problemau.

• Nid yw medrau rhesymu rhifiadol disgyblion yn ddigon cadarn o hyd. Mae gormod o ddisgyblion yn anghyfarwydd â gweithdrefnau datrys problemau, fel nodi, casglu, trefnu, cyfrifo, dehongli a gwerthuso.

• There are still too many pupils who lack confidence in important mathematical skills such as division and percentages. These deficiencies impede pupils’ ability to interpret results and solve problems.

• Pupils’ numerical reasoning skills are still not strong enough. Too many pupils are unfamiliar with problem-solving procedures such as identifying, collecting, organising, calculating, interpreting and evaluating.


• Yn rhyw hanner yr ysgolion, mae’r cynllunio yn parhau’n arwynebol, a dim ond ychydig o ysgolion sy’n gwneud digon i herio disgyblion mwy abl.

• Mae ansawdd yr addysgu i ddatblygu rhifedd yn dda mewn ychydig dros hanner y gwersi.

• Yn y gwersi lle mae’r addysgu yn llai llwyddianus, mae hyn yn aml oherwydd nad yw’r wybodaeth bynciol fathemategol gan yr athrawon i fynd i’r afael â chamsyniadau disgyblion.

• Yn gyffredinol, nid yw ansawdd marcio gwaith rhifedd disgyblion ar draws y cwricwlwm yn ddigon da.

• In around half of schools, planning is still superficial, and only a few schools do enough to challenge more able pupils.

• The quality of teaching to develop numeracy is good in just over half of the lessons.

• In the lessons where teaching is less successful, this is often because teachers lack the mathematical subject knowledge to address pupils’ misconceptions.

• In general, the quality of marking pupils’ numeracy work across the curriculum is not good enough.


• Dim ond mewn lleiafrif o ysgolion y mae’r arweinyddiaeth ar gyfer rhifedd yn dda.

• Yn y rhan fwyaf o ysgolion cynradd ac uwchradd, mae’r cynllunio a’r ddarpariaeth ar gyfer rhifedd yn wannach nag ar gyfer llythrennedd.

• Yn yr ysgolion lle mae’r arweinyddiaeth ar gyfer rhifedd gryfaf, mae strategaethau i ddatblygu rhifedd yn nodwedd gadarn o gynlluniau datblygu’r ysgol ac mae’r arweinwyr yn yr ysgolion hyn yn dyrannu amser, hyfforddiant ac adnoddau buddiol i gefnogi datblygiad rhifedd.

• Leadership for numeracy is good in only a minority of schools.

• In most primary and secondary schools, planning and provision for numeracy are weaker than that for literacy.

• In the schools where leadership for numeracy is strongest, strategies to develop numeracy feature strongly in school development plans and leaders in these schools allocate worthwhile time, training and resources to support the development of numeracy.


• Mae’r gwaith o fonitro medrau rhifedd disgyblion drwy arsylwi gwersi a chraffu ar waith yn dal heb ei ddatblygu’n ddigonol. Mae bron pob ysgol yn methu defnyddio’r technegau hyn yn systematig i arfarnu darpariaeth.

• Mae gan fwyafrif yr ysgolion ddulliau cytûn ar gyfer gwneud cyfrifiadau syml. Fodd bynnag, mae’r staff yn anghyson o ran y modd y maent yn rhoi’r dulliau cytûn hyn ar waith yn rhyw hanner yr ysgolion.

• The monitoring of pupils numeracy skills through lesson observation and work scrutiny remains underdeveloped. Nearly all schools fail to use of these techniques systematically to evaluate provision.

• The majority of schools have agreed approaches for performing simple calculations. However, staff are inconsistent in how they implement of these agreed approaches in around half of schools.


• Mewn ychydig o’r ysgolion cynradd a fu’n rhan o’r arolwg ac yn y rhan fwyaf o’r ysgolion uwchradd, mae uwch arweinwyr yn adrodd fod gwella medrau rhifiadol staff yn parhau’n flaenoriaeth er mwyn galluogi i ddarpariaeth rhifedd fod yn effeithiol ar draws yr ysgol.

• Ers yr arolwg gwaelodlin, nid oes llawer o gynnydd wedi bod o ran cydweithredu rhwng ysgolion partner cynradd ac uwchradd ar draws cyfnodau allweddol 2 a 3.

• In a few primary schools surveyed and in most secondary schools, senior leaders report that improving the numerical skills of staff remains a priority to enable numeracy provision to be effective across the school.

• Since the baseline survey, there has been little progress on collaboration between primary and secondary partner schools across key stages 2 and 3.

ArgymhellionRecommendations

Dylai ysgolion:•A1 sicrhau bod disgyblion yn meistroli medrau rhif pwysig, fel rhannu, gwaith gyda mesurau metrig, canrannau, cymarebau a chyfrannau, mewn gwersi mathemateg;•A2 datblygu medrau rhesymu rhifiadol disgyblion mewn gwersi mathemateg ac mewn pynciau eraill;•A3 ehangu’r cyfleoedd i ddisgyblion o bob gallu ddefnyddio’u medrau rhifedd mewn pynciau ar draws y cwricwlwm;

Schools should:•R1 ensure that pupils master important number skills, such as division, work with metric measures, percentages, ratio and proportion, in mathematics lessons;•R2 develop pupils’ numerical reasoning skills in mathematics lessons and in other subjects;•R3 extend the opportunities for pupils of all abilities to use their numeracy skills in subjects across the curriculum;


• A4 cynorthwyo staff i ehangu’u gwybodaeth a’u dealltwriaeth o strategaethau i ddefnyddio rhifedd ar draws y cwricwlwm;

• A5 gwella asesu ac olrhain medrau rhifedd disgyblion;

• A6 cryfhau gweithdrefnau ar gyfer arfarnu darpariaeth rhifedd; a

• A7 gweithio’n agosach gydag ysgolion clwstwr i ddatblygu mwy o gysondeb mewn addysgu ac asesu medrau rhifedd disgyblion.

• R4 support staff to widen their knowledge and understanding of strategies to use numeracy across the curriculum;

• R5 improve the assessment and tracking of pupils’ numeracy skills;

• R6 strengthen procedures for evaluating numeracy provision; and

• R7 work more closely with cluster schools to develop greater consistency in teaching and assessing pupils’ numeracy skills.


Dylai awdurdodau lleol a chonsortia rhanbarthol:•A8 gynorthwyo ysgolion i helpu staff wella’u gwybodaeth, medrau a hyder wrth ddatblygu medrau rhifedd disgyblion drwy eu pynciau; ac•A9 rhannu arfer orau rhwng ysgolion.

Dylai Llywodraeth Cymru:•A10 ystyried datblygu system genedlaethol ar gyfer olrhain medrau rhifedd disgyblion.

Local authorities and regional consortia should:•R8 support schools to help staff to improve their knowledge, skills and confidence in developing pupils’ numeracy skills through their subjects; and•R9 share best practice between schools.

Welsh Government should:•R10 consider developing a national system for tracking pupils’ numeracy skills.

Arfer orauBest practice

Ysgol Gynradd Litchard, Pen-y-bont ar OgwrMae dosbarth Blwyddyn 5 ag 20 o ddisgyblion o allu cymysg yn defnyddio medrau rhifiadol i gefnogi’u gwaith gwyddonol.

Mae’r athro yn dechrau’r wers gyda sesiwn frwdfrydig o holi ac ateb. Mae hyn yn ennyn diddordeb y disgyblion, yn profi eu gwybodaeth a’u dealltwriaeth o waith blaenorol ac yn eu paratoi’n dda ar gyfer cynnwys y wers. Gwneir cysylltiadau pwrpasol gyda chyd-destunau bywyd go iawn yn ymwneud â chyfaint gwaed mewn cyrff dynol, rhoddwyr gwaed a thrallwysiadau gwaed. Mae hyn yn cydio yn nychymyg y disgyblion yn dda ac yn rhoi cyd-destun ystyrlon i osod y gwaith ynddo. Mae’r wers yn cynnwys ystod o weithgareddau wedi’u cynllunio’n dda, gan gynnwys gwaith ymarferol, fel mesur uchder a chyfaint. Mae’r rhain yn galluogi’r disgyblion i ymarfer a chymhwyso ystod o fedrau mathemategol mewn cyd-destun gwyddonol i ddatrys problemau.

Mae’r athro yn derbyn ymatebion y disgyblion i gyd mewn trafodaeth ac yn delio’n effeithiol â chamgymeriadau a chamsyniadau disgyblion, yn aml gan ddefnyddio disgyblion eraill i ddarparu cymorth a syniadau pellach. Mae’r athro yn defnyddio’r disgyblion i gynhyrchu data go iawn y bydd y dosbarth yn eu dehongli wedyn. Trwy gydol y wers, mae’r athro yn creu cyfleoedd i ddisgyblion drafod eu dysgu a chanolbwyntio ar fedrau datrys problemau a rhifiadol.

Mae pob un o’r disgyblion yn ymgysylltu’n eithriadol o dda â’u dysgu. Dangosant wybodaeth a dealltwriaeth sicr o waith a ddysgwyd yn flaenorol, a defnyddiant eu medrau mathemategol yn dda yn y cyd-destun gwyddonol. Mae’r rhan fwyaf yn dangos medrau mesur da ac maent yn cyfrifo’n gywir wrth weithio i un lle degol. Mae llawer o’r disgyblion yn dangos medrau rhesymu da ac maent yn nodi patrymau yn dda. Mae’r disgyblion yn arfarnu eu gwaith yn dda a gallant awgrymu mireiniadau i wella cywirdeb eu gwaith.

Litchard Primary School, Bridgend

A mixed-ability Year 5 class of 20 pupils use numerical skills to support their scientific work.

The teacher starts the lesson with an enthusiastic question and answer session. This engages pupils, tests their knowledge and understanding of previous work and prepares them well for the lesson content. Purposeful links are made with real-life contexts to do with the volume of blood in human bodies, blood donors and blood transfusions. This captures the pupils’ imagination well and provides a meaningful context in which to set the work. The lesson contains a range of well-planned activities, including practical work, such as measuring heights and volumes. These allow pupils to practise and apply a range of mathematical skills in a scientific context to solve problems.

The teacher accepts all pupils’ responses in discussion and deals effectively with pupils’ mistakes and misconceptions, often using other pupils to provide support or further ideas. The teacher uses the pupils to generate real-life data which the class then interpret. Throughout the lesson, the teacher creates opportunities for pupils to discuss their learning and focus on problem solving and numerical skills.

All pupils engage exceptionally well with their learning. They demonstrate a secure knowledge and understanding of previously learnt work and use their mathematics skills well in the scientific context. Most display good mensuration skills and calculate accurately when working to one decimal place. Many pupils display good reasoning skills and identify patterns well. The pupils evaluate their work well and are able to suggest refinements to improve the accuracy of their work.

10 cwestiwn i ddarparwyr10 questions for providers

• Pa mor dda yw medrau mathemategol disgyblion?

• Pa mor dda mae adrannau mathemateg ac adrannau eraill yn datblygu medrau rhesymu rhifiadol disgyblion?

• A ydyn ni’n herio disgyblion mwy abl yn ddigonol?

• A ydyn ni’n cynorthwyo staff yn ddigon da i gyflwyno rhifedd yn effeithiol ar draws pynciau?

• A yw athrawon yn gwybod digon am gryfderau a gwendidau rhifiadol disgyblion?

• How good are pupils’ mathematical skills?

• How well do maths departments and other departments develop pupils’ numerical reasoning skills?

• Do we challenge more able pupils sufficiently?

• Do we support staff well enough to deliver numeracy effectively across subjects?

• Do teachers know enough about pupils numerical strengths and weaknesses?

10 cwestiwn i ddarparwyr10 questions for providers

• A yw gwaith rhifiadol yn cael ei farcio’n briodol y tu allan i fathemateg?

• A yw arweinwyr yn rhoi blaenoriaeth ddigonol i rifedd ar draws y cwricwlwm?

• Wrth arfarnu darpariaeth rhifedd, a ydyn ni’n rhoi digon o ystyriaeth i safonau gwaith disgyblion mewn gwersi a llyfrau?

• A ydyn ni’n gweithio’n ddigon da gydag ysgolion partner i wella parhad a dilyniant datblygiad medrau rhifedd disgyblion?

• Is numerical work marked appropriately outside of maths?

• Do leaders prioritise numeracy across the curriculum sufficiently?

• When evaluating numeracy provision do we take enough account of the standards of pupils’ work in lessons and books?

• Do we work well enough with partner schools to improve the continuity and progression of numeracy skill development experienced by pupils?

Gwe-ddolen i’r adroddiad llawn

Web-link to full report

http://www.estyn.gov.uk/cymraeg/docViewer-w/338001.3/Rhifedd%20yng%20nghyfnodau%20allweddol%202%20a%203:%20adroddiad%20interim%20-%20Tachwedd%202014/?navmap=30,163,

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Rhifedd yng nghyfnodau allweddol 2 a 3: adroddiad interim Numeracy in key stages 2 and 3: an interim report