Singapore Maths. in Key Stage 1 JULIE HARRISON Mathematics LEAD TEACHER. Introduction

Transcription

1 143 Singapore Maths in Key Stage 1 JULIE HARRISON Mathematics LEAD TEACHER Introduction Mathematics underpins our daiy ives. It s a subject of vita importance, and this has never been more true than today. The speed and scae of technoogica change makes mathematics increasingy essentia. As the Secretary of State said in a 2010 speech: mathematica understanding is critica to our chidren s future. Our economic future depends on stimuating innovation, deveoping technoogica breakthroughs, making connections between scientific discipines. And none of that is possibe without ensuring more and more of our young peope are mathematicay iterate and mathematicay confident. As information technoogy, computer science, modeing and simuation become integra to an ever-increasing group of industries, the importance of maths grows and grows. 1 Currenty, primary maths teaching in the UK is not meeting the chaenge the Education Secretary sets out. Internationa comparisons repeatedy show that primary schoo chidren are capabe of mastering high eves of mathematics, over and above the highest standards currenty achieved in Engand. Added to that, Engand has one of the highest gaps between high and ow performing pupis, and a strong reationship between socia background and performance. As primary teachers are not required to be quaified in mathematics beyond GCSE grade C, improving standards in KS1&2 is about subject knowedge as we as pedagogy. Teachers need to deveop their mathematica understanding, their knowedge about different maths specific pedagogies and ways of representing topics, and their knowedge about the way chidren earn. They then need to appy this to their cassroom practice. There is much interest in high-performing systems ike Singapore the country is mentioned in the recent Schoos white paper 2 and the current review of the nationa curricuum 3. Singapore 1 Michae Gove MP Advisory Committee on Mathematics Education Annua Conference (2010) 2 The Importance of Teaching The Schoos White Paper (2010) 3 Coud do better: using internationa comparisons to refine the Nationa Curricuum in Engand Cambridge Assessment (2010)

2 144 ARK ACADEMY CASE STUDY raised standards in maths by both improving the quaity of instruction and enhancing the curricuum students were foowing. In Singapore a primary teachers are required to foow research-based esson pans and use evidence-based resources. Over a period of more than 30 years these materias have been continuay evauated and improved. This focus on estabishing the right curricuum, which teaches from a young age the key mathematica principes and concepts students need, was of great interest to us at Ark Academy. This case study describes a piot initiative to teach Key Stage 1 mathematics using methods from Singapore. The aim of the Singapore Maths piot is to raise standards of attainment and progress, and ensure every chid achieves above nationa expectations. The approach has ed to word-eading resuts in Singapore. It uses a rigorous, coherent syabus, which integrates concepts and skis in a concrete to pictoria to abstract way (more on this ater). It aso emphasises probem soving at every turn. The Ark piot used an American version of the Singaporean materias, Math in Focus, for a mathematics essons. The programme begins with a curricuum that incudes fewer topics, but reaches greater depth at each eve. Aims of Singapore Maths at Ark Academy Our piot had two cear aims: 1. To ensure students deveop their conceptua, procedura and higher-order thinking in every esson through: (a) Emphasising visuaisation and mode drawing. (b) Introducing a structured approach to probem soving. 2. To improve the quaity and consistency of maths teaching by: (a) Using research-based teaching materias and esson pans. (b) Deveoping a new esson structure to meet the needs of every chid and impementing it across the schoo. (c) Improving Assessment for Learning. (d) Deveoping questioning, speaking and istening, and inks with iteracy. (e) Providing coaching and staff training.

3 MATHEMATICS MASTERY 145 Emphasising visuaisation and mode drawing Singapore Maths prescriptive approach to teaching ensures that a concepts and skis are taught foowing the same format. Lessons foow the concrete pictoria abstract pedagogy. Cear and engaging visuas are used to present concepts, and to mode soutions that aow a students, regardess of anguage skis, to focus on the mathematics. The concrete pictoria abstract sequence heps students buid understanding of mathematica processes. Take a simpe mutipication probem for exampe 3 x 4. Concrete: Students count out with bocks or rods three ots of four. This stage is concrete and tangibe. Pictoria: In this stage, rather than hod objects in their hands, they draw them in an exercise book, or on their show-me boards. Abstract: Finay, the support is removed, and students start to perform the cacuation in the abstract. This is when probem soving comes into pay students need to manipuate information quicky. If the probem is too difficut they can fa back on the pictoria; if that is aso too hard they go right back to the concrete. Linked to this is the bar mode technique, which is fundamenta to Singapore Maths. It teaches chidren to draw a visua representation of a word probem. Teachers were heped to see how various types of bar modes can be used to sove mathematica word probems and earn the techniques of deriving, drawing and manipuating bar modes. For exampe, teachers were taken through how to approach the foowing probem: Aan puts some brown sugar on a dish. The tota mass of the brown sugar and dish is 110g. Bea puts three times the amount of brown sugar that Aen puts on the same dish, and the tota mass of the brown sugar and dish is 290g. Find the mass of the brown sugar that Bea puts on the dish. Aan s mode: Sugar Dish 110g Aan and Bea s mode: 290g Sugar Sugar Sugar Sugar Dish 110g 290g 110g = 180g Bea puts 180g of sugar on the dish.

4 146 ARK ACADEMY CASE STUDY Being taken through the approach ourseves heped us to picture the probem mentay and hep our students to visuaise things that are not obvious at first. Questions ike the one beow are typica of the work we did with students. The bar mode heps them to be systematic in their approach to probem soving and become secure in number and cacuations. Introducing a structured approach to probem soving By foowing Math in Focus, we ensure that a pupis, regardess of teacher or key stage, foow the same, structured approach to probem soving. Pupis are taught the skis needed through the concrete pictoria abstract approach and are then expected to use and appy these skis for probem soving during essons. Pupis sove word probems during whoe cass teaching and then repeat the process either independenty or through coaborative earning in groups of two or three. Mode drawing and the bar method hep chidren to visuaise and sove probems through mathematica reasoning and critica thinking. There are, in addition, opportunities for pupis to carry out investigative activities and to discuss aternative soutions to open-ended questions through Let s Expore! pages. Each chapter aso incudes a Put On Your Thinking Cap! activity which chaenges pupis to sove non-routine questions. These probems ask chidren to draw on prior knowedge as we as recenty acquired concepts, combining probem soving strategies with critica thinking skis. The chidren deveop skis in cassifying, comparing, sequencing, anaysing, identifying patterns and reationships, inductions, deduction and spatia visuaisation.

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6 148 ARK ACADEMY CASE STUDY A Year 2 exampe probem at the end of Chapter 2, Addition up to 1000, foows: Make two 3-digit numbers from the numbers beow. Use each number ony once. What are the two 3-digit numbers that give the greatest answer when you add them? Probem soving has aways been a priority at our schoo, to hep chidren deveop their conceptua, procedura and higher order thinking skis. By foowing this approach, we have ensured that a chidren have equa access to such deveopment opportunities, and that probem soving isn t imited to Gifted and Taented students. Using research-based teaching materias and esson pans Initiay, we attempted to impement Singapore Maths aongside an existing mathematics curricuum and our existing approaches to teaching and earning. However we soon reaised that in order to be used effectivey, Singapore Maths had to be used as a standaone curricuum. We have cosey foowed the research-based teaching materias and esson pans, athough, as time has passed, we have made our own adaptations and resources to suppement the programme. The materias and workbooks that we are currenty using incude re-teach and extra practice materias which we ve inserted, as we as home-schoo connections etters written for our parents and assessment materias to hep them. These materias ensure that acquired skis are revisited and buit upon during the foowing year. To use addition as an exampe, teachers introduce tens and ones, at first without, then with, regrouping in the ones. The next year, chidren earn to add with three digit numbers, first without, then with, regrouping in the ones and tens. And then in Year 3, chidren use numbers to 10,000 and to two decima paces. Throughout, pupis experience a hands-on approach and gain experience and practice through soving a wide range of probems, incuding handing data and work with units of measure and money.

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8 150 ARK ACADEMY CASE STUDY Deveoping a new esson structure to meet the needs of every chid, and impementing it across the schoo In 1998, the new Labour government impemented the Nationa Numeracy Strategy (NNS). This stipuated that the daiy Mathematics esson shoud be divided into three parts: 1. The Menta and Ora Starter. 2. A bock of direct interactive teaching of the whoe cass and groups, where chidren woud be grouped according to abiity. 3. A fina 10 minutes of penary review. Teachers were asked to devote a high proportion of esson time to direct teaching of whoe casses and groups. 4 An unintended consequence was that teacher tak expaining, at ength, procedura work for the chidren to do came to dominate mathematics essons, rather than the earning itsef. 5 The NNS had intended to encourage interactive whoe-cass teaching, emphasising diaogue and strategic thinking, but in practice faied to do so. 6 Moreover, the penary review became ineffective, with many teachers faiing to execute it propery, missing it out atogether or merey summarising what the chidren had aready earned. A new framework was introduced in 2006 which warned against panning in such a rigid way. It proposed a range of approaches to structuring earning within essons. 7 However, whist the onger term bock panning is ceary shown and made easy to understand, there is itte guidance given to how teachers might structure their essons differenty. As a resut, there is scant evidence to suggest that teachers have moved away from panning three-part essons. Our own experience, and our engagement with the Singapore Maths programme, ed us to concude that the three-part esson significanty hinders teachers abiities to incorporate AFL successfuy in the daiy mathematics esson. In three part essons chidren tend to spend ong periods of time on the carpet, reducing concentration and opportunities for assessment. A further 25 minutes if teacher tak did not overrun is spent competing independent tasks which aso require young chidren to concentrate for extended periods. Regardess of how engaging and inspiring the tasks, at some point chidren of a very young age are ikey to go off task. The very nature of whoe cass teaching on the carpet aso meant that for 25 minutes (incuding the ora menta starter) teachers were unabe to assess the eve of understanding of a the chidren. The structure of the esson did not provide enough opportunity for teachers to systematicay check pupis understanding, reducing the frequency of interventions. In short, there were inadequate opportunities for effective AFL. 4 Department for Education and Empoyment (1999) 5 Askew (2004) 6 Kyriacou and Gouding (2004) 7 Primary Framework for Literacy and Mathematics (2006)

9 MATHEMATICS MASTERY 151 There were further probems as we: the ora-menta starter had a standaone objective which often bore no reevance to the overa objective of the esson; opportunities for chidren to review their own earning rarey featured before the very end of the esson; and it was difficut to pan occasions for quaity tak about mathematics into the traditiona structure. Discussion in maths is vita for chidren to demonstrate conceptua understanding, verbaise methods using subject specific vocabuary, and expain mathematica ideas in their own words. So we needed a new esson structure: one that woud aow more time for tak, improve AFL, and, cruciay, provide opportunities for the chidren to grasp underpinning concepts, make connections with earier earning, and to make sense of the mathematics. Learning time woud be maximised and, infuenced by Fernandez, Yoshida, and Stiger 8, I woud turn each esson into a story ; a sequence of interconnected ideas and activities with a common theme throughout. The muti-part esson The structure of our maths essons at Ark Academy is fexibe a key advantage over the threepart aternative and can incude up to 12 mini- segments inked to the overa earning outcome for the esson. Based on the cumuative mode of Singapore, where skis mastered in one esson or unit are buit upon in ater essons, we ve created a esson structure in which each segment is designed to buid upon the previous one. This means you can arrive at more compex earning by the end of the esson without osing pupis aong the way, and ensure exceent progress is made by a. Each esson incudes a cear deveopmenta sequence, and the structure aows teachers constanty to assess pupis progress using a series of mini-penaries. These are designed to address misconceptions and to maximise the opportunities for teachers to intervene swifty. They aso provide the chance for a chidren to sef-assess their earning reguary, and to tak confidenty about what they need to do to progress. In this way, teachers become more responsive to the needs of a their pupis and can adapt essons if necessary at severa points. The increased opportunity to review and check understanding and the greater fexibiity means pupis faing behind can be identified quicky by teachers, and they or their assistants can provide instant assistance. The chidren move between the carpet and tabes on severa occasions in one esson, chanting or singing as they do so. These transitions maximise earning time, as the rhymes or chants are aways mathematicay-themed, and ensure good, focused behaviour. 8 Fernandez, Yoshida, and Stiger Learning Mathematics from Cassroom Instruction (1992)

10 152 ARK ACADEMY CASE STUDY An exampe muti-part esson The foowing esson was taught in a Year 2 cassroom during the Autumn term in Its objective was to sove money probems. A chidren in the cass aready had a secure understanding of pace vaue and coud add two three-digit numbers using the coumn method. The chidren coud perform this cacuation not ony as a procedura ski, but with understanding of the underying mathematica principes. Part 1: Introduction The earning objective and key vocabuary were read choray by the cass. The teacher pointed out the Star words for the esson. These words woud be a focus for assessment during pupi tak sections of the esson. Part 2: Five Minute Warm Up The chidren were given a number of cacuations to practise using the coumn method for addition. A cacuations reied on the chidren s abiity to re-group in the tens and ones. Most chidren aso had time to compete the Quick Fire activity. This required the chidren to compete cacuations such as = 16, = 120. During this time the teacher and teaching assistant checked the work of a chidren in the cass. This was a revision and practice segment designed for chidren to appy aready-earned skis, and the earning was within the mastery eve of a chidren in the cass. Part 3: Guided Practice This began with the teacher revisiting a previousy-earned ski of comparing numbers. The chidren were guided through a number of exampes as a whoe cass. Chidren compared amounts of money on the board and expained their thinking and answers. For exampe, 1.45 is ess than I know this because the pounds are the same so I had to ook at the pence and 45 is ess than 48 because 45 ony has five ones and 48 has eight ones. Part 4: Independent Practice The chidren were given two minutes to compete a task. They had to write is greater than or is ess than between two amounts of money. Some chidren chose to use the symbos < and > making further inks to prior earning. The teacher and teaching assistant moved around the cass picking up on misconceptions and strugging earners. One chid was identified and was taken immediatey for 1:1 support, returning to the cass five minutes ater. Part 5: Sef Assessment Answers were shared for the first five exampes. The chidren were then asked to use their traffic ight fans to represent how they fet about their earning so far. By sharing some answers, and the five minute warm up having been marked for most, the chidren had something concrete against which to sef assess. The teacher caed on chidren hoding orange/amber to say what they fet they needed to improve upon, and chidren coud identify these steps with confidence. Part 6: Transition The chidren stood quiety behind their chairs and then began counting in threes from zero to 30 to the carpet. By the time they reached 30, they were ready to begin the next activity.

11 MATHEMATICS MASTERY 153 Part 7: Whoe Cass Teaching The teacher had a number of priced items on the board. These were organised into Tesco and Asda products. The chidren read the foowing question choray: Mrs King wants to buy some bread and fish. Where is it cheaper for her to buy the bread and fish? The chidren were then given one minute s taking time with their partner to discuss how they might sove this probem. The teacher asked for responses and eventuay, through questioning, the cass managed to work out how to sove the probem. At a times the teacher encouraged fu sentences and when expanations were required, the teacher probed with further questions unti the answer given was 100% correct. The fina response was is ess than 3.72, therefore it is cheaper for Mrs King to buy the bread and fish from Tesco. In this part of the esson, new knowedge was introduced and skis were appied in new contexts. Part 8: Transition The chidren moved from the carpet to the tabes speaking an odd and even chant. The teacher quicky expained that she wanted the chidren to work in their teacher/pupi pairs. Part 9: Pupi/teacher paired earning Two further probems were shown on the board. One chid taught and the other wrote on a mini-whiteboard. During this section, the teacher and teaching assistant moved around the cass, istening to the chidren s expanations, picking up on errors, probing with questioning and intervening where necessary. Part 10: Independent Appication The chidren used the skis practiced and taught in the esson to sove a number of simiar probems. They made further inks to prior earning by choosing and using the most appropriate method of cacuation. For exampe, the coumn method for cacuations such as , or menta strategies for cacuations such as Towards the end of this segment, activities were introduced to encourage chaenge and refection. The chidren were given receipts with totas, but missing the constituent amounts. They were required to reason and generaise about number and to use and appy mathematics to gain understanding. Throughout this section the teacher stopped the chidren to address misconceptions and errors. Part 11: Refection The teacher took the opportunity to address any further errors, for a imited time ony as she had previousy stopped the esson on a number of occasions throughout to do the same. The chidren were given time to refect on their earning and use their sef assessment fans. Most coud say what they needed to do to improve, with many expressing the desire to get better at using and appying their mathematics to sove chaenges more efficienty, such as the receipts provided in the previous segment. This wide-ranging, muti-part esson incuded extended periods of pupi tak. Precise mathematica vocabuary usage by both teacher and pupis is essentia for this to work hence the Star words. The transitions work together with the segments to create a seamess earning journey.

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13 MATHEMATICS MASTERY 155 Improving Assessment for Learning As a schoo we re committed to continuay improving the quaity of our teaching, so refining our AfL practice is aways at the forefront of our minds. The inear nature of the curricuum over a year, and the teaching of essons in smaer parts, ent itsef to effective AfL. We found new, efficient ways of assessing our pupis, incuding a succession of mini-penaries and reguar sefassessment using traffic ight cooured fans throughout the esson. We became quicker at recognising where pupis encountered difficuties and at intervening immediatey. This ensured that misconceptions did not impede the next steps in earning. Teachers aso began to be more fexibe in their approaches to panning and teaching and were more wiing to adapt their pans, both within and after the esson, enabing them to pan propery for progression in earning. Deveoping questioning, speaking and istening, and inks with iteracy We have aways had a poicy of no hands up in our schoo. This aows teachers to cod ca as many chidren as possibe throughout a esson and increases eves of concentration and engagement. This cod caing technique ensures chidren are aways ready to respond to any question. We wanted to deveop this area further sti, to encompass cod caing, better questioning and more sophisticated use of mathematica vocabuary by chidren in their expanations and reasoning about number. We created a whoe-schoo focus on deveoping chidren s answers through further and higher eve questioning, as we as through ony accepting mathematicay precise answers, using specific vocabuary in fu sentences. Finay, we deveoped the pupi as teacher mode you can see in the exampe esson above. Here, we encouraged chidren to use mini-whiteboards to teach each other a method or how to sove a probem. Teachers now use this as an opportunity to assess chidren s use of mathematica anguage and how good their understanding is. It aso heps to deveop the chidren s confidence. Through better panning for questioning, and monitoring and feedback by eaders, peers and through sef-refection, our schoo was abe to deveop this area with great success.

14 156 ARK ACADEMY CASE STUDY Providing coaching and staff training Adopting Singapore Maths, incuding the above adaptations, was not as straightforward as simpy impementing and teaching a mathematics scheme of work. It has required a staff to have a professiona diaogue about teaching and earning and we have encouraged discussion and debate. Through this diaogue teachers have taken ownership of the approach and it s become embedded. Whist it has required strong eadership and a focus on consistency, it has aso needed consutation and a wiingness to et teachers adapt it to their own stye. Our training has sought to inspire not mandate. We ve covered: panning training using the new esson structure the use of transitions in cass to maximise earning time and improve behaviour the progression of skis (for exampe addition) from Reception through to Year 3, working backwards from the desired outcome extensive watching of esson videos to iustrate outstanding practice and stimuate professiona discussion about teaching monitoring of, and feedback on, a teachers essons throughout the schoo on a reguar basis using working was to enhance earning work scrutinies At Ark we pride ourseves on our cuture of openness, and fee strongy that esson observations are an entitement of professiona deveopment. We have an open door poicy and wecome observations by eaders and peers. We aso encourage a teachers to record themseves teaching using cassroom observation rooms 9. These are invauabe in heping teachers to sefrefect and to deveop their practice in the cassroom. Evauation of impact The impementation of Singapore Maths at Ark Academy has significanty improved both teaching standards and student outcomes. Students are showing better mathematica understanding and mastery; assessment for earning is improved; teacher questioning is more varied and effective; and students have a better grasp of mathematica anguage. Key eements of our success are: Visuaisation and mode drawing are used confidenty and effectivey by students. Visuas promote probem-soving, and they aow a chidren to access the curricuum, regardess of anguage or abiity. Our chidren draw bar modes to represent the reative sizes of quantities and fractiona parts, and in doing so they can sove probems that far exceed nationa expectations for their age. 9 See Case Study 1 A Year in the Life

15 MATHEMATICS MASTERY 157 We have a consistent approach towards teaching mathematics across year groups and key stages. Since introducing Singapore Maths a year ago, we have created an identity for ourseves. Teachers approach panning and essons in the same way, chidren tacke probems and use visuaisation and mode drawing techniques consistenty, and pupis have a rich mathematica vocabuary which can ceary be seen in every cassroom throughout the schoo. It is a progressive and cumuative mode, whereby each esson, and each segment within that esson, ay the foundations for the next buiding bock. Progression is systematic and ogica; skis mastered in one esson or unit are buit upon to advance to more compex earning ater on. There is a cear deveopmenta sequence throughout each year group and throughout the schoo as a whoe, and the chidren recognise how their prior earning and earier work is reevant. For exampe, the Year 1 chidren who joined Year 2 in September 2011 had an exceent grounding in the Singaporean approach to mathematics. In the eary weeks they were abe to dea confidenty with numbers to 1,000 and add and subtract numbers to 1,000 using the coumn method for addition and subtraction. They were aready abe to speak confidenty about their earning and use mathematica anguage to express their thinking using the correct vocabuary. This has enabed the Year 2 teachers quicky to advance the chidren s earning this year.

16 158 ARK ACADEMY CASE STUDY We ve taken ownership of the Singaporean approach by creating our own Ark versions of the resources. The standard Singapore curricuum uses textbooks for guided practice and whoecass teaching; we make our own materias and worksheets that work better than textbooks. We make them coourfu and chid-friendy, and the chidren are abe to manipuate and move the visuas, which reinforces the hands-on, pictoria approach to teaching maths that the Singaporean approach embodies. For exampe, the figure beow is from an interactive whiteboard side used to teach division. Chidren are encouraged to come to the board and move the oranges into groups of three to sove the foowing probem: There are 18 oranges. from an Interactive Whiteboard Side used to teach division. Chidren are encouraged to come They to are the board put into and baskets move the of 3. oranges into groups of three to sove the foowing probem: There How are many 18 oranges. baskets They are there? are put into baskets of 3. How many baskets are there? We aso We aso suppement suppement the the curricuum curricuum with with extra extra resources resources to to compement compement our our new new esson esson structure. structure. We often make warm up sheets and extra resources for the chidren. We wanted We often to deveop make our warm speaking up and and sef-assessment istening and deveop sheets the for chidren s the chidren. confidence We wanted with to deveop our speaking mathematica and istening vocabuary, and deveop so have the buit chidren s in sections confidence to our essons with mathematica which give chidren vocabuary, so have opportunities buit in sections to teach to our each essons other, which expain give methods chidren or make opportunities up mathematica to teach probems each other, or expain methods stories. make up mathematica probems or stories. Marking foowing each esson aways feeds directy into panning the next day. Our Marking teachers foowing do not each spend esson countess aways hours feeds writing directy next into step panning comments the and next modeing day. Our methods teachers do not to chidren, spend countess but are abe hours to use writing their next time step far more comments efficienty. and Errors modeing are identified methods and to chidren, pupis are provided with feedback during the esson or activity which foows. If a quick recap is but are instead use their time far more efficienty. Errors are identified and pupis are provided needed, it can be buit into the five-minute warm up. If more expicit modeing is required, it with can feedback be panned during into the a esson guided or activity. activity If the which chidren foows. need If a time quick to practise recap is and needed, expore, it can a be buit pupi-to-pupi into the five-minute teaching warm activity up. or If discussion more expicit activity modeing can be is panned. required, For it can chidren be panned who require into a guided a chaenge, activity. investigative If the chidren and need probem-soving time to practise activities and expore, can be panned a pupi-to-pupi for, whist teaching whoecass teaching continues for the remainder of the cass. activity or discussion activity can be panned. For chidren who require a chaenge, investigative and Stages probem-soving of earning activities in each can esson be panned are short for, and whist transitions whoe-cass are teaching used creativey. continues Shorter for the remainder episodes of the and cass. frequent mini-penaries avoid off-task behaviour and hep AfL. Transitions from one task to the next maximise earning time and bring in an eement of fun; they aso ensure that behaviour is exempary. Transitions can incude counting on and back in any step, or Stages movement of earning through in each song esson or chants. are short and transitions are used creativey. Shorter episodes and frequent mini-penaries avoid off-task behaviour and hep AfL. Transitions from one task Chidren to the next have maximise a secure earning grasp time of mathematica and bring in concepts an eement and of principes fun; they aso and ensure the that anguage to describe them. They are abe to speak confidenty about mathematics in a range of contexts. The chidren are encouraged to expain their methods in whoe-cass and paired activities. For exampe, chidren worked in pairs for three minutes to think of a mutipication probem to go with the image provided:

17 are provided with feedback during the esson or activity which foows. If a quick recap is needed, it can be buit into the five-minute warm up. If more expicit modeing is required, it can be panned into a guided activity. If the chidren need time to practise and expore, a MATHEMATICS pupi-to-pupi MASTERY teaching activity or discussion activity can be panned. For chidren who require 159 a chaenge, investigative and probem-soving activities can be panned for, whist whoecass teaching continues for the remainder of the cass. Stages of earning in each esson are short and transitions are used creativey. Shorter behaviour episodes exempary. and frequent Transitions mini-penaries can incude avoid off-task counting behaviour on and back and in hep any AfL. step, Transitions or movement from through one song task or to chants. the next maximise earning time and bring in an eement of fun; they aso ensure that behaviour is exempary. Transitions can incude counting on and back in any step, or movement through song or chants. Chidren have a secure grasp of mathematica concepts and principes and the anguage to describe Chidren them. have They a are secure abe grasp to speak of mathematica confidenty about concepts mathematics and principes a range and of the contexts. The chidren anguage are to encouraged describe them. to expain They their are abe methods to speak in whoe-cass confidenty about and paired mathematics activities. in a For range of contexts. The chidren are encouraged to expain their methods in whoe-cass and exampe, paired chidren activities. worked For exampe, in pairs for chidren three worked minutes in to pairs think for of three a mutipication minutes to think probem of a to go with the image mutipication provided: probem to go with the image provided: After that time, a Year 2 chid responded with the foowing: There are 5 girs. Each gir has 3 baoons. How many baoons are there in a? 5 groups of 3 = 15 5 x 3 = 15 There are 15 baoons in a. The chidren are abe to teach each other with confidence, and teaching staff are trained ony to accept entirey accurate expanations and answers, using precise anguage. A partiay accurate response or expanation wi be used as an opportunity for earning.

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19 MATHEMATICS MASTERY 161 Attainment and Progress Data Students who finished Year 2 in Juy 2011 had foowed the Singapore Maths curricuum for one academic year. Their resuts were we above nationa expectations: 100% finished KS1 on Leve 2 in maths 97% achieved at east 2b (in ine with nationa expectations) 83% achieved 2a+ 32% achieved eve 3 The tabe beow aso shows that there were no significant differences between groups of students in terms of their progress in sub-eves. Gender Av. Progress No. Boys Girs Tota EAL Av. Progress No. No Yes Tota SEN Av. Progress No. None Schoo Action Schoo Action Statemented Tota Ethnicity Av. Progress No. Asian or Asian British Back or Back British Mixed/Dua Background White Any Other Ethnic Group Tota Gifted & Taented Av. Progress No. No Yes Tota Free Schoo Meas Av. Progress No. No Yes Tota These resuts have been moderated internay, and via the ARK network, Brent Loca Education Authority and Ofsted. They represent outstanding progress and attainment in maths, and were directy inked to the Singapore Maths piot.

20 162 ARK ACADEMY CASE STUDY Refection Having undertaken extensive deveopment work in this area, Ark Academy is now at the forefront of teaching mathematics using the Singaporean stye in the United Kingdom. The Singapore Maths initiative has ed to significant improvements in the quaity of our mathematics teaching and in students progress and attainment. We are now seeking to extend and further embed Singapore Maths in our curricuum. Our approach wi: Ensure consistency and equaity of provision in a casses Make more efficient use of the hour for mathematics through a change in esson structure and use of transitions Incude effective AfL Encourage an open cuture of sharing best practice Aow for coaboration and sharing of best practice with other schoos in our network Continue to improve the quaity of our mathematics teaching Focus on probem soving Pace an emphasis the on deveopment of skis, concepts, underying processes and methodoogy Lead chidren to have a better conceptua understanding Deveop the chidren s use of mathematica vocabuary, meta-anguage and iteracy across the curricuum Show cear progression throughout the schoo, with the secure foundations aid for ater earning in the eary years Improve the subject knowedge and confidence of teachers Deveop effective questioning used by teachers to extend thinking, improve expanations and prove conceptua understanding Encourage independence and deveop confidence

21 MATHEMATICS MASTERY 163 In June 2011, seven months into our Singapore Maths piot, we were invited to be a part of an Ofsted review of good practice in KS1 Maths. The inspector s findings refected our own sefevauation. Teaching the Math in Focus curricuum, with our adaptations, has had a significant positive impact on the chidren s earning and attainment. Ofsted noted 10 : Pupi s achievement in number is outstanding Pupis sustain their concentration very we in essons. These are designed as a sequence of short stages of whoe-cass teaching or individua/pair work, often with bursts of song, rhyme or chanting as pupis move from one stage to the next. No time is wasted. Teachers use of assessment in essons is a particuar strength. Teachers and teaching assistants are constanty assessing pupis progress. Consequenty, they are abe to pick-up and tacke quicky any misunderstanding or difficuty, occasionay using immediate one-to-one support, so that pupis do not fa behind. Reguar mini-penaries are a common and key feature of the essons. Moreover, the teachers informa ongoing assessments feed directy into the next day s essons. Probem-soving is an integra part of a essons. The subject eader provides an exceent roe mode of cassroom practice. The Headteacher and her are aware of the need to refect upon the successes of this new curricuum, and to taior it to the academy s context and ambitions for the pupis. We take great pride in the impact our work has had, and the quaity and consistency we ve achieved in maths teaching. As the importance of maths grows and grows 11, so does our understanding of how best to teach it. 10 Letter to head from Jane Jones, Ofsted inspection team (20 June 2011) 11 Michae Gove MP, ibid

22 164 ARK ACADEMY CASE STUDY CIVITAS IN ACTION