PRIMARY. Mathematics. Guidelines for Teachers of Students with MILD. General Learning Disabilities

Transcription

1 PRIMARY Mathematics Guidelies for Teachers of Studets with MILD Geeral Learig Disabilities

2 Cotets Ratioale ad itroductio 3 School plaig 6 Classroom plaig 8 Approaches ad methodologies 12 Exemplars 52 Appedix 64

3 Ratioale ad itroductio Mathematics gives studets the laguage through which they ca iterpret, aalyse, describe, make predictios, ad solve problems i everyday life. It allows them to participate i a wide rage of mathematical experieces ad relatioships both i school ad i daily livig. Ratioale The aims ad objectives of the Primary School Curriculum, Mathematics are valid for all studets. However, ot all studets lear mathematics i a eve ad predictable maer. The abstract ad coceptual ature of mathematics poses particular challeges to studets with mild geeral learig disabilities. The teacher has a pivotal role i mediatig the objectives of the Primary School Curriculum, Mathematics for studets with mild geeral learig disabilities. To meet the eeds of studets with mild geeral learig disabilities, greater emphasis is placed o the social, rather tha the creative ad aesthetic value of mathematics without excludig those importat aspects. There will be particular emphasis o maagig moey, uderstadig timetables ad usig measures i everyday life situatios. The acquisitio of these skills must be prioritised i order to equip the studet to participate fully ad idepedetly i society. Itroductio A level of proficiecy i basic mathematics is eeded to cope idepedetly ad effectively with everyday livig icludig tellig the time, shoppig, readig timetables, cookig, measurig, ad so forth. These guidelies aim to provide teachers with a uderstadig of the particular barriers to learig mathematics that studets with mild geeral learig disabilities may ecouter, ad to provide some strategies that they ca employ i plaig mathematical experieces for their studets, whether they are i maistream classes or i special schools. As studets with mild geeral learig disabilities may be learig their mathematics i may differet settigs it is importat that the teacher iitially idetifies the poit at which the idividual studets are operatig. The sectio Before you start offers a quick checklist for teachers to idetify a startig poit withi the Primary School Curriculum, Mathematics for idividual studets, may of whom will be able to access this material. Additioal advice for teachig

4 mathematics to studets with mild geeral learig disabilities is provided here with the caveat that the age ad stage of developmet of the studet provides the basis for mathematics learig for these studets. The aims of the Primary School Curriculum, Mathematics are: to develop a positive attitude towards mathematics ad a appreciatio of both its practical ad its aesthetic aspects to develop problem-solvig abilities ad a facility for the applicatio of mathematics to everyday life to eable the child to use mathematical laguage effectively ad accurately to eable the child to acquire a uderstadig of mathematical cocepts ad processes to his/her appropriate level of developmet ad ability to eable the child to acquire proficiecy i fudametal mathematical skills ad i recallig basic umber facts. The abstract ad coceptual ature of mathematics poses particular challeges to studets with mild geeral learig disabilities. The Primary School Curriculum, Mathematics stresses the importace of active learig, thus providig opportuities for studets to maipulate, touch, ad see objects as they develop their uderstadig of mathematical cocepts. Learig withi a group i which studets are ecouraged to talk about ad explai how or why they did somethig will also support developmet of their ow thikig about mathematics. A itegrated approach to mathematics will help studets to uderstad the relevace of mathematics i their daily lives. It is importat that the teacher is fully aware of the difficulties, both persoal ad academic, ecoutered by studets with mild geeral learig disabilities. Persoal difficulties are very ofte uderpied by a poor self-image brought about by a log-term sese of failure. Failure may be oe outcome of low itellectual ability, ad ca lead to slow progress. Slow progress is further aggravated by poor memory. Laguage ad readig difficulties ca cofoud studets difficulties with mathematics. Poor academic progress cotributes to the poor self-image ad lack of motivatio, which i tur may lead to withdrawal or maladjustmet of studets. Low expectatios ca ihibit the studet s effort ad performace cotributig to a cycle of failure. Teachers of studets with mild geeral learig disabilities must strive to break that cycle by providig opportuities for studets to experiece success with mathematics. Particular issues i mathematics for studets with mild geeral learig disabilities May studets with mild geeral learig disabilities require a structured approach to mathematics. Opportuities to practice mathematics skills ad cocepts eable studets to cosolidate their learig. Direct teachig, usig explicit strategies, is essetial as some studets may acquire iappropriate or icorrect strategies from icidetal learig. While may studets lear by workig thigs out for themselves or observig how others work, whe kowledge or skills are beig used i a ew cotext it is importat to support studets by makig their learig explicit, sice trasfer of learig does ot always take place automatically. Studets with a mild geeral learig disability are ot always proficiet at usig the skills ad kowledge they have already acquired if the features of the ew task are sigificatly differet. They may have difficulty extractig the key features of a task ad igorig the less importat oes. For example, they may focus o the umbers i a problem but ot cosider what they are beig asked to do; hece they ofte just add all the umerals without cosiderig the purpose. They may also focus o icidetal iformatio ad fail to otice the saliet feature of the topic. For example, they may be able to cout by rote but fail to uderstad the use of umbers as labels for quatities (I am 7, I live i umber 7, she has 7 sweets).

5 Features of the Primary School Curriculum, Mathematics The followig features of the Primary School Curriculum are relevat to studets with mild geeral learig disabilities. Early mathematical activities are aimed at ecouragig more work i pre-mathematical activities to develop cocepts before commecig formal umber work. These activities are particularly beeficial for studets with mild geeral learig disabilities. Teachers ca frequetly revisit these activities i age-appropriate settigs. The itroductio of umber limits ecourages the cosolidatio of umber facts ad the developmet of the cocept of place value. This is reflected i the reductio i the use of complex calculatios ad i the presetatio of the same cocept i differet ways. The emphasis o accurate use of mathematical laguage ad uderstadig of symbols will cotribute to a greater uderstadig of mathematics for all studets. Studets with mild geeral learig disabilities will eed frequet opportuities to cosolidate their uderstadig of both symbols ad mathematical laguage. Calculators have bee itroduced at fourth class, but it is essetial that studets develop good estimatio skills from the earliest stages if they are to use them efficietly. This is particularly true of studets with mild geeral learig disabilities, who may cofuse the meaig of arithmetical sigs or have coceptual weakesses i some areas. The icreased emphasis o the use of maipulatives (cocrete materials) throughout the school, icludig the seior classes, meas that studets who may still eed the support of materials will ot be perceived as beig differet from their peers. The Primary School Curriculum also emphasises real-life problem-solvig, usig checkable aswers ad activities based i the studet s eviromet. Ecouragig studets to egage with ope-eded problems such as makig scarves for teddy, buildig a house usig a limited umber of bricks, or workig out how to sped a sum of moey o food for a party will help them to realise that there are may ways to solve a problem, ad that sometimes there is more tha oe right aswer. The itroductio of fu areas such as chace ad mathematical trails allows for differetiated approaches, which ca iclude all learers i excitig mathematical activities. O a trail some studets may be lookig for oe digit umbers, while others may be seekig up to three digit umbers or addig umbers together. For further ideas see Primary School Curriculum: Mathematics, Teacher Guidelies (Mathematical trails). The use of a broad rage of assessmet tools is essetial i the accurate idetificatio of studets stregths ad eeds. This is particularly true i mathematics where studets may eed to acquire certai skills or cocepts before proceedig to more complex learig. The emphasis o usig a variety of methods of recordig studets progress ecourages differetiatio of respose, which recogises differet learig styles. Some studets may be able to give a aswer verbally while others would beefit from producig a diagram or drawig. All studets should have the opportuity to preset their work i a variety of ways. I the measures strad aswers should be verifiable where possible to ecourage uderstadig ad the developmet of persoal bechmarks. This ca provide support to studets with mild geeral learig disabilities. Hadweighig ad pourig activities usig a variety of shapes of cotaier will assist i this area. If studets measure ad label objects such as bookshelves, desks, etc i the classroom, they ca build up visual bechmarks. For example, a studet ca stad beside the bookshelf ad see that he/she is taller tha a metre, or that the teacher is shorter tha the door, which is more tha two metres. Icreased emphasis o itegratio ad o likage i strads of the Primary School Curriculum, Mathematics meas that studets ca come to see mathematics as relevat ad coected to their ow lives. Frequet referece by the teacher to mathematical elemets i the course of learig is essetial, for example measurig the distace from the classroom to the office usig a trudle wheel i geography, usig time words i history (before, log ago, a year), measurig jumps or distaces ru i PE.

6 School plaig No school pla will be complete without takig due cogisace of the eeds of studets with mild geeral learig disabilities. With proper plaig for differetiatio to meet the eeds of studets with mild geeral learig disabilities, they ca achieve success ad participate fully i the curriculum at their ow level. Curriculum plaig While studets with mild geeral learig disabilities are expected to partake fully i the curriculum they will ot be expected to do the same tasks at the same level as the more able studets. For these studets, learig will cocetrate o the areas of the curriculum that provide them with essetial life skills, for example moey, time, ad measuremet. Studets with mild geeral learig disabilities will eed more opportuities to use cocrete materials ad egage i cocrete tasks rather tha workig from a textbook where their weakess i laguage would further aggravate their arithmetical difficulties. As their cocetratio spa is short, they beefit most from tasks which are short ad varied. Usig the same mathematical laguage ad methodology throughout the school beefits all studets, especially studets with mild geeral learig disabilities. This is especially true i such difficult areas as subtractio with reamig, ad i the teachig of fractios ad decimals. For example, i doig the algorithm 9-3, if oe teacher says ie take three ad aother says three from ie, this will cause cosiderable cofusio to the weaker studet whe she/he moves from oe teacher to aother or from class teacher to resource teacher. It follows, therefore, that it is importat to also keep parets iformed at regular itervals about what ad how studets are learig ad their geeral progress. As the studet with mild geeral learig disabilities requires the carig help of both paret ad teacher i order to make satisfactory progress, it is importat that parets ad teachers have opportuities to meet ad discuss the studet s progress. Regular commuicatio with the class teacher ad support teacher are also importat as each teacher is aware of how the studet is progressig i the classroom ad i learig support.

7 Good teachig practice eeds regular assessmet. Assessmet should be iformative ad eable the teacher to pla for further learig, ad report o the studet s progress. Teacher desiged tests ca support the studet by allowig for a certai amout of success. Whe failure occurs, the studet will beefit from a discussio of where she/he wet wrog ad reassurace that makig mistakes is part of the learig process. Studets with mild geeral learig disabilities should be provided with a test suited to their abilities ad stage of developmet. As studets with mild geeral learig disabilities may be at differet stages of developmet, differet teacherdesiged tests ad idividual learig profiles may be ecessary to best support their learig. Orgaisatioal plaig Orgaisatioal plaig ivolves cosideratio of resource requiremets, home-school policy, ad a policy o homework. As already oted, plaig will esure that the class teacher, support teacher, ad the paret are workig as a cohesive uit i supportig the studet with geeral learig disabilities. For example, parets could sped time with the studet usig mathematical games that ehace the learig of basic facts. Some parets may ot be familiar with a algorithm, for example decompositio, ad try ad teach the studet usig borrow payback, thus creatig cofusio. It is advised that teachers commuicate with parets, at the begiig of the school year as to the approaches ad methodologies used, so as to eable parets to support the studet s learig i the home cotext. Studets with mild geeral learig disabilities very ofte have poor short-term/log-term memory. Homework should be used as a opportuity for reiforcig topics covered recetly ad i the past ad should be appropriate to the child s level of progress ad achievemet. These studets eed costat reiforcemet.

8 Classroom plaig Classroom plaig for each school settig special school, special class, ad maistream class will differ accordig to the eeds of particular studets at ay give time. These studets progress at a slower rate tha maistream studets. Sice the Primary School Curriculum, Mathematics is sequetial ad depedet o kowledge gaied, they may experiece great difficulty i keepig abreast of their fellow studets, although they may be able to partake i the majority of mathematical activities i the class. If, for example, the teacher is teachig a ew cocept or ew algorithm he/she must be careful that the calculatios are simple, thus esurig that the lack of umber facts o the part of a studet with mild geeral learig disabilities does ot iterfere with his/her acquisitio of the cocept. For example whe usig additio with reamig, is a suitable example but is ot, sice i the secod case the studet will have great difficulty calculatig 8+9 ad will ot be able to cocetrate o the cocept ivolved. The situatio is starker whe it comes to multiplicatio. For example, 25 3 is easily maaged, whereas 49 8 is likely to brig about failure i the case of the studet with mild geeral learig disabilities. Classroom plaig for these studets will ivolve close co-operatio betwee the resource teacher ad the class teacher i order to esure that there is cotiuity ad reiforcemet i each other s work. While providig special suitable work for these studets the teacher should avail of ay opportuity to allow participatio i whole class work. Project work may provide such a opportuity. If, for example, the studets are makig a model of the school, the more able studets ca do the complex calculatios relatig to scale while studets with mild geeral learig disabilities ca be gaifully employed i measuremet. Mathematical kowledge ca be reiforced i other areas of the curriculum ad such opportuities should ot be missed whe dealig with the studet with mild geeral learig disabilities. For example, umber ad measure ca be reiforced whe doig ruig, jumpig, etc. i physical educatio.

9 Some aspects of the teachig of mathematics eed particular emphasis i the case of studets with mild geeral learig disability. These iclude equivalets, ad a example ca help studets to reiforce a correct iterpretatio of the symbol. mathematical laguage symbols + plus ad add = 7 materials worksheets ad textbooks usig ICT. Mathematical laguage Mathematics must be see as a laguage with its ow vocabulary of words, symbols ad tools that are used i particular circumstaces. May studets cofuse mathematical laguage with ordiary laguage. They say He s bigger tha me whe they mea older, or My table is loger tha his whe they mea wider. It is importat to teach mathematical laguage to the studets, ad to reiforce it o a daily basis. A list of mathematical words ca be kept either by the teacher or by the studets themselves (for example, taped ito a copybook), ad they ca tick them off as they lear to use them appropriately ad accurately, either orally or i writig. As already oted, keepig parets iformed of the words beig used ad the importace of practicig them frequetly will help the studet to make use of these words i real cotexts. Symbols Some studets may have difficulty with mathematical symbols. They will ofte call the plus sig add, ad others will use ad or plus. As already oted, cosistecy of approach is vital ad this is especially true if the class cotais studets who have come from differet schools or classes where they may have developed misuderstadigs i relatio to some of the symbols. This is particularly relevat if the studet is movig to a ew class or beig itegrated with aother class for mathematics. It is importat that parets ad all staff who are i cotact with the studet are aware of the termiology beig used. I the classroom, charts with the symbol, word Plus ad equals symbols are itroduced first, followed by the mius sig ad, subsequetly, the greater tha ad less tha sigs (see symbols chart i the teacher guidelies for mathematics i the Primary School Curriculum). Materials Age-appropriateess It is very importat that the materials used are age-appropriate. Brightly coloured couters ad iterlockig cubes may be appropriate for youger studets, but they ofte come to associate these with the ifat classes. Usig football cards or cois ca make a coutig activity more age-appropriate for older studets. Pretedig to be the ma o the turstile tottig up the takigs after a match ca make coutig more real to a older studet. Jobs that ivolve coutig ca be icorporated ito the mathematics class ad are usually good motivators, for example coutig out iformatio otes for distributio to other classes, havig a class sale of work for charity, costig ad buyig foodstuff for cookery classes, or examiig the cost of popular clothes such as jeas or favourite chocolate bars. Distributig milk, books, or pecils ca be very valuable activities that support the modellig of laguage such as Are there eough pecils for all your group? How may cartos do you usually eed for your group? Is there ayoe abset today? How may do you eed today? The teacher ca maipulate this actively by ot givig eough items to the studet ad askig how may more are eeded. Durig break times iformal discussio about luch items ca iclude such questios as, Who has the most sadwiches? or Whose carto of juice cotais the most milk?

10 Accessibility Aother importat feature of usig materials i the classroom is that they must be stored i ways that make them easily accessible to studets. Clearly labelled ad colour-coded boxes, a routie tidy-up sessio, ad procedures to maitai clea ad eat materials will ecourage studets to use the materials appropriately ad resposibly. Havig a mathematics table where the materials eeded for the lesso are easily accessible is importat ad ca be a role of resposibility for differet studets. It ca be chaged as topics chage, for example Our measures table, Sets of four, etc. Worksheets ad textbooks It is importat that worksheets ad textbooks are used carefully with studets who have a mild geeral learig disability. Some maistream textbooks move too quickly through the cotet areas ad therefore should be see as a complemet to other meas of istructio rather tha the oly source. With these studets it is particularly importat to maitai a balace betwee computatioal ad problem-solvig tasks ad betwee the use of cocrete ad symbolic represetatio. I usig worksheets ad textbooks, the followig questios should be cosidered: Is there too much text i the worksheet/textbook? (This could ihibit the ability of poor readers to egage with the mathematical cotet.) Is there a lot of clutter o the page? (Studets are ofte distracted by busy pages cotaiig too much uimportat iformatio or illustratio.) Are the spaces give for the aswer large eough for studets who may have poor motor cotrol or write their umbers very large? Are worksheets that are iteded for homework clear i their istructios so that parets kow what the studet is supposed to be doig? Do worksheets/textbooks offer a variety of task types, for example practical tasks, ope-eded ivestigatios, puzzles, games, project-based work, ad word problems? Do they preset material i differet ways for differet purposes ad learig styles, for example pictorially, diagrammatically, ad usig miimal laguage as appropriate? Is the prit size appropriate to the developmetal stage of the studet? Over time, do worksheets/textbooks offer a appropriate balace betwee the strads? Do they offer opportuities for collaborative or group work, for example active ivestigatio ad talk-about sectios, ad itegratio opportuities that focus o other areas of the curriculum? Do they reflect the iterests ad eviromet of the studet? Do they cosider the social aspects of mathematics, for example shoppig, measurig for a purpose, life-skills? Are computatioal activities carefully graded, offerig appropriate opportuities to cosolidate learig at each level? Makig sure that worksheets ad textbooks are ageappropriate is extremely importat, sice studets are usually very aware that a particular book is beig used by a youger brother/sister or by a more juior class withi the school, ad this ca seriously impact o their self-esteem. Usig ICT May software programmes ca be used at differet levels withi the oe group or class. Valuable teacher time ca be take up i establishig the correct startig poit for a particular studet. Colour codes ad symbolic represetatios taped to the frot of software boxes ca help, ad a card with clear istructios ca be give to the idividual studet. Oce studets have practiced this procedure, they will be able to locate ad load the software themselves, ad a older studet ca either help or supervise. It is helpful to keep symbols costat ad, where possible, iclude the studets i the choice of how iformatio ca be preseted symbolically. This activity is also part of the advice provided i the Primary School Curriculum: Mathematics, Teachers Guidelies. 10

11 Assessmet for learig Studets should have opportuities to experiece differet assessmet methods from a early age, ad play a active part i their ow assessmet. Early idetificatio of difficulties i mathematics is essetial if the studets are to achieve their full potetial. Assessmet should be see as a positive rather tha egative experiece that will help them i their future learig, ad clear, costructive feedback to studets is ecessary if they are to play a active part i their ow future learig. Good commuicatio is essetial betwee the teachers ad parets, other teachers ad professioals who come ito cotact with studets regardig each studet's progress, stregths ad future learig goals. A importat issue i assessmet is the evaluatio of a plaed test with regard to its aims ad its suitability for the studets for whom it is iteded. The laguage of the test is crucial. If the laguage is too difficult or wordy for studets who have a readig difficulty the test may ot accurately reflect their mathematical ability. Teachers should use a variety of assessmet tools that take accout of differet learig styles. Whe plaig a sequece of learig outcomes for a particular studet or group it is ecessary to keep i mid how progress will be assessed. Too ofte a pe ad paper test at the ed of a uit of work is used. However, it is possible to assess progress by observig, for example, how a studet hadles moey i the class shop, how accurately a studet ca cotiue a patter, or ca make a shape with his/her body. Whe assessig studet progress i the various areas of mathematics teachers should use a variety of assessmet tools, icludig teacher observatio, teacher-desiged tasks ad tests, portfolios, projects, work samples, ad criterio referece tests. See the assessmet sectio i the Itroductio to the Primary School Curriculum for further details o assessmet techiques. 11

12 Approaches ad methodologies The Primary School Curriculum recogises that studets lear withi a social cotext ad are active participats i the learig process. They aturally ivestigate ad rely o their ow methods of workig out mathematical problems ad therefore eed to experimet ad discuss i a supportive eviromet that eables them to build o ad develop their ideas. Studets with mild geeral learig disabilities eed to build up persoal support structures which they ca use whe faced with a ew situatio or problem. They eed to lear how to lear', how to verbalise what the problem is, ad how they ited to go about solvig it. I the classroom situatio, it may be good for the more able studet ad the less able studet alike if peer teachig is itroduced. The more able studet ca be gaifully employed i helpig his/her less able peer i reiforcig algorithms, learig basic facts, ad i providig reiforcemet of the cocepts already leared. Difficulties with umbers Studets with mild geeral learig disabilities fid it very difficult to memorise basic facts. Cosequetly, umber is a area that presets multiple difficulties. This has a debilitatig effect o their success rate as very ofte they may have a algorithm doe correctly but the aswer is wrog because of lack of kowledge of basic facts. I order to overcome this difficulty, the teacher should 12 choose figures that are easy to calculate whe teachig a ew cocept or algorithm allow studets to use a calculator or a oe hudred square whe calculatig more difficult basic facts if part of a algorithm is correct, mark the part that is correct ad discuss the error i the remaider part with the studet. Cocrete materials Whe teachig ew algorithms it is importat (where possible) to use cocrete materials, for example, i difficult areas like decompositio or fractio or decimal cocepts. Studets should have opportuities to use such materials util the cocept is well grouded. Whe mistakes occur after the cocrete materials are removed, they must be reitroduced to the studet durig the remediatio process.

13 Learig basic facts Learig basic facts is very ofte a log ad tedious task for the studet with mild geeral learig disabilities due to possible short-term ad log-term memory difficulties. However, these difficulties ca be alleviated by providig the studet with strategies for learig basic facts usig some of the large variety of table games available, for example domioes usig computer games to reiforce kowledge of basic facts. It is of crucial importace to match the work give with the studet s ability to do it, i order to esure that the studet will experiece success. Potetial areas of difficulty The potetial areas of difficulty are described i order to outlie the possible implicatios for learig ad suggest possible differetiated teachig strategies. Studets with mild geeral learig disabilities are more like their peers tha ualike. They have the same rage of iterests, the same eed for affirmatio ad success, ad exhibit a wide rage of learig styles. Not all studets with mild geeral learig disabilities will exhibit all of the potetial areas of difficulty, but it may be helpful for teachers to uderstad the implicatios that these may have for their teachig ad, cosequetly, for the studet s learig. Durig his/her early years a studet with mild geeral learig disabilities may have had restricted experieces i compariso to his/her more able peer. Restricted mobility, poor motor cotrol, or poor uderstadig may have resulted i fewer opportuities to use the laguage of mathematics for example coutig stairs, judgig distaces or heights, ad learig mathematical rhymes. Teachers should be aware that they may ot have leared these thigs icidetally. Some studets with mild geeral learig disabilities will have difficulties i problem-solvig due to iheret limitatios i their ability to abstract ad geeralise. Their ability to work idepedetly is costraied by poor attetio spa ad retetio. Hece, the learig process eeds to be broke dow ito short sequetial steps ad work doe eeds to be reiforced through over-learig ad repetitio. The difficulties experieced by these studets ca lead to poor self-esteem ad a fear of failure. These combied ca lead to a sese of helplessess that results i the studet costatly seekig help or refusig to proceed with eve the simplest of tasks. Studets may get trapped i the I ca t do maths sydrome. It is importat that such studets experiece success as ofte as possible ad participate i fu mathematical activities if they are to overcome this feelig. The settig of realistic learig targets by teacher ad studet may help i the achievemet of success ad the retur of cofidece. It is also importat for studets to realise that makig mistakes is a itegral part of the learig process, ad that they should ot be discouraged by their mistakes. While difficulties i umeracy ad literacy ofte overshadow the studet s learig experiece, it is importat to provide a wide variety of learig tasks i order to allow studets to show their skills ad develop cofidece i other areas of the curriculum. The use of the calculator, for example, ca eable the studet to sometimes bypass arithmetical difficulties ad work successfully o other mathematical topics. Studets eed costat ecouragemet. They eed to be ivolved i their ow learig ad have opportuities to discuss their difficulties. Studets have valuable isights ito their ow learig eeds ad this should ot be igored. Teachers should help studets towards a awareess of what their learig eeds are, i the cotext of what they ca do rather tha what they caot do. Effective teachig builds o studets stregths rather tha focusig o their weakesses. The tables that follow outlie characteristics that may be associated with a mild geeral learig disability, examie their implicatios for the learig of mathematics, ad suggest a rage of strategies that may assist the studet. 13

14 Sometimes it is the way i which the material is preseted to the studet that creates a barrier to learig. Usig a variety of approaches ad methodologies will facilitate differet learig styles i ay give class group. Before you start The followig lists are ot comprehesive but should serve as a guide i assessig where a studet is i relatio to mathematics. It is suggested that idividual teachers or groups of teachers develop their ow profilig system that will isure that istructio is tailored to meet their studets eeds ad levels of attaimet. Teachers ca use this iformatio to ask Is the studet s readig level ihibitig his/her ability to egage with the mathematical elemets? Whe a observatioal picture of the studets has bee created they ca be grouped accordigly or provided with idividual work. However, it is very importat to iclude large group or full class work occasioally, so that studets ca lear from seeig how other studets approach problems. All studets will beefit from a variety of teachig styles ad classroom activities. Studets with mild geeral learig disabilities will particularly beefit if the teacher is aware of their stregths ad weakesses before embarkig o a ew topic. The followig table outlies some observatios that the teacher may ote about the studet. Such iformal assessmet ca assist the teacher i selectig suitably differetiated methods for the class, ad may prove useful i providig feedback to parets ad studets. If so, ca the material be preseted orally, diagrammatically, pictorially? 14

15 / A geeric list for iformal teacher observatio of studets Pre-test usig a simple task i a area you are itroducig What is the state of readiess of the studet to do this task i terms of kowledge, skills, ad attitudes? What learig strategies are beig used by the studet? Ca the studet describe what he/she is doig ad how he/she is doig it? Does the studet uderstad why he/she is doig this activity? Is the studet s readig level ihibitig his/her ability to egage with the task? Is the studet s umeracy level ihibitig his/her ability to egage with the task? Does the studet have ay miscoceptios about the task? Idepedece How does the studet cope whe left aloe with a task? Does he/she give up easily, ask for help, begi the ext task, sit iactively, or become disruptive? Does the studet clearly uderstad what to do if he/she has a problem or is fiished work earlier tha others? Is the studet orgaised i his/her work? Does the studet check if he/she has the correct equipmet, for example pecil, pe, ruler, graph paper? Does he/she have other difficulties, such as hearig loss, poor visio, poor motor cotrol, or hyperactivity, which may eed to be cosidered? Ca the studet preset work i a way that ca be uderstood by others? Group work Does the studet appear to lear better i a group, aloe, or i pair-work? Ca he/she take turs ad liste to other studets resposes? Ca he/she preset work i a clear ad coheret maer o behalf of the group? 15 Istructios Does the studet liste to ad uderstad istructios? Ca the studet read istructios? Ca he/she follow istructios give by the teacher? Ca she/he follow more tha oe istructio effectively? Ca he/she make appropriate resposes to the istructios? Is the studet clear about routies for settig out materials ad clearig up after a activity? Choosig ad usig the right materials Does he/she choose appropriate support materials, for example umber lie or objects for coutig, additio, ad subtractio? Does he/she use materials appropriately, for example use a ruler correctly to measure, use a umber strip for coutig o, use blocks ad push away those already couted, use a umber square efficietly, use a calculator appropriately (i.e. make decisios about whe its use is ecessary)? Readiess for mathematics Ca the studet classify, compare, ad order objects ad pictures? Does he/she use labellig words efficietly whe questioed? ('Ca you fid a teddy for me? What ca you see? What is this?') Does he/she respod to differet aspects of a mathematical problem, for example fuctios, attributes, differeces, ad similarities? ('Ca you fid all the red objects for me, please? Ca you poit out the red circles?') Ca the studet uderstad egatives? ('Simo says do ot stad up. Fid all the blocks which are ot red.') Does he/she reaso, for example predict, project, idetify cause ad effect, ad suggest alteratives? ('Why? What if I?')

16 Addressig potetial areas of difficulty for studets with mild geeral learig disabilities s Potetial area of difficulty The studet may have a short-term memory difficulty. = Implicatios for learig Retetio of umber facts ca be a problem. + Possible strategies Ecourage the use of visual clues to aid memory. Use umber rhymes ad sogs. Provide the studet with strategies for rememberig facts such as doubles, ear doubles, etc. Practise estimatio skills so that a calculator ca be used efficietly. Work o makig umber operatios automatic through fu games such as table darts. s Potetial area of difficulty The studet may have a short attetio spa, lack of cocetratio, ad lack of applicatio. = Implicatios for learig The studet fids it difficult to stay o task. + Possible strategies Provide shorter tasks with clear rewards for stayig o task, such as computer use or game time. Keep periods of istructio short ad to the poit, ad recap frequetly. Provide short work sessios with achievable goals. Ecourage the studet to become aware of the difficulty ad to try to beat their target i stayig o task. Use teacher observatio efficietly ad ote achievemets, stregths, ad preferred learig styles for use i plaig future work. Use classroom maagemet which focuses o cotiget praise ad ecouragemet (i.e. rewardig the task behaviour ad ot just the aswer). This icludes acceptig good aswers that may ot be ecessarily correct, for example Mary foud a iterestig way of doig that problem; let s see how it works. The use of ope-eded problems that have differet possible aswers ca help to develop a positive attitude to problem-solvig. 16 s Potetial area of difficulty The studet may have difficulty i uderstadig mathematical cocepts/abstractios. = Implicatios for learig The studet fids mathematics particularly difficult ad has difficulty with coutig umbers, place value, ad with uderstadig what is happeig whe usig the four operatios. + Possible strategies Frequet practice of the cocepts to be leared should be varied by use of games, ICT, ad real-life problems relevat to the studet s experiece. Make the learig fu by usig fuy ames, silly scearios, or ulikely settigs, for example: 'Tommy wet to Mars for his holiday ad met five alies. They each had four arms. How may arms had the alies altogether? Draw the alies. What if they each had eight arms?'

17 s Potetial area of difficulty The studet may have difficulties with spatial awareess; he/she may ot have had opportuities to play with puzzles, blocks, etc. = Implicatios for learig The studet may have difficulty orgaisig materials, may display left/right cofusio i recordig, may ot recogise shapes if iverted, or costatly lose items i the room. + Possible strategies Plety of work with three dimesioal objects will be eeded, with particular attetio beig paid to the laguage of spatial awareess, for example up/dow, over/uder, shape words. Usig jigsaws, block puzzles, ad tagrams i a fu way ca help studets i this area. Work o awareess of ow persoal space, especially i PE, left ad right, distace from, etc. Maitai cosistet orgaisatio patters i the classroom. Use visual cues for locatio ad directio o charts or table top. Give oral cues related to the studet s ow positio, for example o your door side. Allow studets to remai i the same seatig positio for group work. s Potetial area of difficulty The studet may have difficulty applyig previously leared kowledge. + Possible strategies = Implicatios for learig The studet may fid it difficult to use a skill or cocept i aother settig such as measurig i geography or sciece. Draw the studet s attetio to what is happeig: This is just like the measurig we did last week. What did we use to measure our books? How did we place the ruler? Cosciously reiforce mathematical cocepts i other areas of the curriculum, for example sortig ad classifyig i sciece, space ad shape i art (pritig 2-D shapes, both radomly ad i sequeces/ patters). 17 s Potetial area of difficulty The studet may have difficulty with trasfer to real life. = Implicatios for learig The studet does ot use mathematics i real situatios. For example, he/she does ot use ay of the four operatios whe buyig goods i a shop, does ot see the eed to measure whe cookig, does ot recogise shapes i the eviromet. + Possible strategies Use real-life objects ad cois i play situatios. Discuss how pocket moey is spet. If possible, provide opportuities to hadle moey i a real shop or school shop. Make sure that parets are aware of the importace of coutig, hadlig moey, etc. at home, for example settig the table, dividig up food, sharig equally, weighig for cookig, or measurig whe doig DIY.

18 s Potetial area of difficulty The studet may have difficulty with visual sequecig. = Implicatios for learig The studet ca t copy from the board or from a book, or has difficulty with sequecig umbers, mirror writig, etc. + Possible strategies Start with tracig exercises, usig tracig paper. Teach studets how to chuk iformatio (for example copy oly oe part of the sum at a time), ad how to check that it is correct. Use umber rhymes ad sogs to reiforce sequeces. Use visual cues, for example r start here s Potetial area of difficulty The studet may experiece cofusio with sigs ad symbols. = Implicatios for learig The studet does ot read symbols ad asks questios like Is this a add sum? + Possible strategies Use charts ad discussio of everyday symbols, ad relate these to mathematical symbols. Ecourage studets to verbalise what they should do first, for example look for ad idetify the symbol, or apply the correct symbol if it is a writte problem. 18 s Potetial area of difficulty The studet may display poor vocabulary/other laguage difficulties. = Implicatios for learig The studet caot follow complex seteces or multiple meaigs, may process oly part of the istructio, for example whe told to put a red circle aroud all the big thigs he/she may process oly circle ad thigs. The studet fids it difficult to verbalise what he/she doig i mathematics, or to relate the vocabulary of mathematics to real-life situatios. + Possible strategies Idetify ad specifically target mathematical laguage, esurig that it is reiforced i differet settigs ad i other areas of the curriculum, for example locatio words (o, i, uder, etc.) i PE, drawig games that ivolve followig istructios cotaiig target words (draw a square i the middle of your page, put a blue triagle beside/uder/to the right of the square. Be clear i commuicatig to both studets ad parets the laguage that is beig covered each week, for example usig a ote i a copy or a wall chart to list the mathematics words of the week.

19 s Potetial area of difficulty The studet may experiece readig difficulties. (For writig difficulties, see the sectio o commuicatio ad laguage.) = Implicatios for mathematics Readig difficulties ca prevet studets from egagig with mathematics. They may be capable of completig the mathematical task but become frustrated ad cofused by prited words. + Possible strategies Provide alterative forms of problems usig visual presetatio of material. Ask the studet to pick out the parts of the problem that he/she ca read, ad to focus o what iformatio is relevat. There is ofte a lot of redudat iformatio i a writte problem. Avoid presetig the studet with pages of textbook problems by givig modified worksheets or verbally delivered istructios, for example Mary has six sweets ad she gives her brother four; how may has she left? Ecourage the studet to use drawigs to write dow the importat features, for example Mary has 'Take away four by crossig them out. How may are left?' s Potetial area of difficulty The studet has difficulty i followig istructios. = Implicatios for mathematics The studet becomes cofused whe faced with more tha oe istructio at a time. + Possible strategies Get the studet to repeat the istructio(s). Use short, clear istructios or pictorial cues, e.g. a picture of a copybook o the blackboard or o a card. Use cue sheets, for example: ' Take out a copy ad pecil (picture). What kid of problem is it? What do I eed to kow? What do I do ext?' Give clear guidace o how ad whe assistace will be give by the teacher/other studets durig the lesso. 19 s Potetial area of difficulty The studet may be overwhelmed by the learig process. = Implicatios for mathematics The studet becomes overwhelmed whe preseted with ew iformatio or skills, ad cosequetly caot lear. + Possible strategies Vary the materials give to a group some usig umber strips to five while others are usig them to te, where appropriate. Adapt the teachig style, for example use more discussio at the begiig ad at the ed of the lesso to help both teacher ad studet to uderstad how learig takes place. Itroduce variety i the resposes required. The same activity ca ofte be doe with a group or the class, but some studets ca be required to aswer orally, some by usig symbolic represetatio or some by usig a pictorial respose, for example a+ a a = aaa Vary the requiremets of the task. Oe group or idividual may oly have to do six of the calculatios whereas aother may have to do te or more. Set persoal targets for the studets so that they do ot feel that others are gettig less to do tha they are.

20 Selectig cotet Whe plaig for a class, group or idividual it is useful to have a checklist of elemets you wish to iclude. Some suggestios are give i the followig example. I order to maximise the cross-curricular elemets of mathematics two further plaig grids, with suggestios, are give i examples 2 ad 3. EXAMPLE 1 Does your mathematical programme cotai these elemets? activities that lik with other areas of mathematics (for example, usig moey to teach tes ad uits) direct teachig of mathematical Laguage activities that itegrate with other areas of the curriculum real-life problem-solvig opportuities variety i the materials to be used cosideratio of age-appropriateess direct teachig of mathematical strategies a balace betwee class, group, ad idividual teachig direct teachig of skills such as tur-takig or active listeig, ad good work habits such as havig materials ready, kowig what to do whe fiished, etc. methods of recordig progress such as the studet s ow log books, portfolios of completed work, idividual progress charts with clearly set idividual targets. 20 AIMS What do you wat to do? (strad/topic) What particularr area do you wat to focus o? (laguage, skill, cocept?) OBJECTIVES What learig outcomes do you expect for each studet or group, icludig both skills ad cocepts? (These should form the basis for assessmet ad iform decisios about what the ext target should be.) Plaig cross-curricular work i mathematics ORGANISATIONAL ISSUES Ca you elist the help of other teachers/parets/ assistats/studets? Is the ecessary equipmet easily available ad are the studets familiar with its use? Ca the topic be taught to the whole class, but with differetiated elemets as outlied i the sectio o differetiatio? ASSESSMENT How will you record the studets progress? How will you use this iformatio to pla your ext step? How will you reiforce the skills/cocepts i other areas?

21 EXAMPLE 2 Plaig cross-curricular work i mathematics This is ot a exhaustive list ad would eed to be adapted to suit the ages ad ability levels of the studets. The focus for the teacher should be o idetifyig the laguage to be reiforced ad to cosciously use it across subjects. It is very importat to draw the studets attetio to the fact that measurig i geography or sciece is just the same as i mathematics. SESE: Sciece Laguage of capacity: pour, fill, full, empty, liquid, solid; I thik My guess is Properties of differet materials lots of polystyree chips are lighter tha a few stoes; weighig activities. SESE: Geography Measurig the desk/room for mappig exercises, measurig ad recordig raifall ad temperature, examiig distaces from oe place to aother i plaig a jourey. 21 SPHE Cookery amouts of foodstuffs i packagig; value for moey; meaig of: 10% extra free, 25% off; amout of salt, sugar, etc. i processed foods; iterpretig packagig iformatio. STRAND: Measures PE Laguage of legth, weight, time durig activities (She ra the fastest; choose the heaviest ball; ca you ru farther tha that? Today we ll use the wide bech). Measurig jumps, ad distaces ru or walked usig a trudle wheel; timig races or settig time limits o games usig a stopwatch. (These activities ca be doe usig ostadard measures at first). Usig tally sheets to keep a record of laps ru or jumps take; estimatig how far a beabag or ball ca be throw.

22 EXAMPLE 3 Plaig topic work i mathematics Below is a example of how a area of mathematics (measures) ca be explored through topic work. The age-appropriateess of the activities must be cosidered at all times. Computer software packages ad books which support the vocabulary are easily available. Gloves ad scarves Comparig sizes of hads ad gloves; Usig appropriate laguage small, smaller tha, smallest, too big/small, just right, etc.; comparig legths of scarves; makig felt scarves for teddies ad sortig by legth, colour, etc. 22 Shoes Big ad small sizes of shoes; sizes of feet; relatioship betwee foot size ad height; data collectio o popular types of shoe.. TOPIC: Clothes STRAND: Measures Trousers Leg legths, waist sizes. Early mathematical activities Puttig clothes o i order logical sequecig. Coats ad jackets Heavy ad light; log ad short; sizes.

23 Strategies for teachig studets with mild geeral learig disabilities Geeral strategies The strategies outlied i this sectio use readily available cocrete materials, allow studets to experimet while learig ew cocepts, ad ecourage studets to discuss their ideas o workig out mathematical problems. I usig the strategies that follow, the followig approach should be take: (i) The teacher demostrates the algorithm o the board while usig the cocrete materials, iteractig with the studets ad posig questios as outlied i the idividual strategies. (ii) The studets apply the algorithm usig cocrete materials util the steps are iteralised ad the cocept is well grouded. (iii) The studets practice usig the algorithm without cocrete materials. (iv) A studet is guided to retur to the use of cocrete materials whe problems occur. The followig list of geeral strategies may prove helpful i the teachig ad learig of ew facts, cocepts, algorithms, ad skills. Draw out importat facts through classroom discussio. Try to pla for the cosistet use of laguage ad methodology throughout the school ad, if possible, i the home. Ecourage the studet to work at a slow pace ad i a very structured way. Avoid great leaps, takig very small, carefully thought out steps oe at a time. Provide opportuities for the studet to talk about a problem ad to say how he/she ca go about solvig it. Ecourage studets to practice ad apply the skill of estimatio as ofte as possible. Provide the studet with strategies for learig basic facts, ad use a variety of table games ad computer games to reiforce this kowledge. Use wall charts ad display boards to show the facts ad cocepts that are relevat to the curret classroom work. Provide regular opportuities for the studet to use cocrete materials util a ew cocept is well grouded. If a studet has difficulties with a ew cocept ad eeds remediatio, ecourage him/her to retur to usig cocrete materials. Choose figures that are easy to calculate whe teachig a ew cocept or algorithm. Use materials that ca be decostructed where appropriate, for example usig a budle of te lollipop sticks allows the studets to see the te sigle uits, ulike a te euro ote. Iitial use of lollipop sticks or Uifix cubes followed by the use of moey meas that the studet is movig from a cocrete to a more abstract use of materials. Use maageable materials where appropriate, for example moey is far more maageable tha lollipop sticks for larger umbers (hudreds), ad cheques may be appropriate for eve larger umbers (thousads). The studets should oly record the algorithm i the correct mathematical format whe they are very familiar with the algorithm ad eve the oly with easily maaged umbers. 23