Mathematics for Students with Learning disabilities

mathematics guidelines for teachers of students with mild general learning disabilities and mathematics instruction for students with learning disabilities | download free pdf
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Published Date:09-07-2017
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PRIMARY Mathematics Guidelines for Teachers of Students with MILD General Learning DisabilitiesGuidelines Mild General Learning Disabilities / Mathematics / PRIMARY Rationale and introduction Rationale Mathematics gives students the The aims and objectives of the Primary School language through which they can Curriculum, Mathematics are valid for all students. interpret, analyse, describe, make However, not all students learn mathematics in an predictions, and solve problems in even and predictable manner. The abstract and conceptual nature of mathematics poses particular everyday life. challenges to students with mild general learning disabilities. The teacher has a pivotal role in mediating It allows them to participate in the objectives of the Primary School Curriculum, a wide range of mathematical Mathematics for students with mild general learning disabilities. experiences and relationships both in school and in daily living. To meet the needs of students with mild general learning disabilities, greater emphasis is placed on the social, rather than the creative and aesthetic value of mathematics without excluding those important aspects. There will be particular emphasis on  managing money, understanding timetables and using measures in everyday life situations. The acquisition of these skills must be prioritised in order to equip the student to participate fully and independently in society. Introduction A level of proficiency in basic mathematics is needed to cope independently and effectively with everyday living including telling the time, shopping, reading timetables, cooking, measuring, and so forth. These guidelines aim to provide teachers with an understanding of the particular barriers to learning mathematics that students with mild general learning disabilities may encounter, and to provide some strategies that they can employ in planning mathematical experiences for their students, whether they are in mainstream classes or in special schools. As students with mild general learning disabilities may be learning their mathematics in many different settings it is important that the teacher initially identifies the point at which the individual students are operating. The section ‘Before you start’ offers a quick checklist for teachers to identify a starting point within the Primary School Curriculum, Mathematics for individual students, many of whom will be able to access this material. Additional advice for teaching Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY mathematics to students with mild general learning Failure may be one outcome of low intellectual ability, disabilities is provided here with the caveat that the and can lead to slow progress. Slow progress is further age and stage of development of the student provides aggravated by poor memory. Language and reading the basis for mathematics learning for these students. difficulties can confound students’ difficulties with mathematics. Poor academic progress contributes The aims of the Primary School Curriculum, to the poor self-image and lack of motivation, which Mathematics are: in turn may lead to withdrawal or maladjustment of students. Low expectations can inhibit the student’s n to develop a positive attitude towards mathematics effort and performance contributing to a cycle of and an appreciation of both its practical and its failure. Teachers of students with mild general learning aesthetic aspects disabilities must strive to break that cycle by providing opportunities for students to experience success with n to develop problem-solving abilities and a facility mathematics. for the application of mathematics to everyday life Particular issues in mathematics for students n to enable the child to use mathematical language with mild general learning disabilities effectively and accurately Many students with mild general learning disabilities require a structured approach to mathematics. n to enable the child to acquire an understanding of Opportunities to practice mathematics skills and mathematical concepts and processes to his/her concepts enable students to consolidate their appropriate level of development and ability learning. Direct teaching, using explicit strategies, is essential as some students may acquire inappropriate  n to enable the child to acquire proficiency in or incorrect strategies from incidental learning. fundamental mathematical skills and in recalling While many students learn by working things out basic number facts. for themselves or observing how others work, when knowledge or skills are being used in a new context The abstract and conceptual nature of mathematics it is important to support students by making their poses particular challenges to students with mild learning explicit, since transfer of learning does not general learning disabilities. The Primary School always take place automatically. Curriculum, Mathematics stresses the importance of active learning, thus providing opportunities for Students with a mild general learning disability are not students to manipulate, touch, and see objects as always proficient at using the skills and knowledge they develop their understanding of mathematical they have already acquired if the features of the concepts. Learning within a group in which students new task are significantly different. They may have are encouraged to talk about and explain how or why difficulty extracting the key features of a task and they did something will also support development of ignoring the less important ones. For example, they their own thinking about mathematics. An integrated may focus on the numbers in a problem but not approach to mathematics will help students to consider what they are being asked to do; hence they understand the relevance of mathematics in their often just add all the numerals without considering daily lives. the purpose. They may also focus on incidental information and fail to notice the salient feature of the It is important that the teacher is fully aware of the topic. For example, they may be able to count by rote difficulties, both personal and academic, encountered but fail to understand the use of numbers as labels by students with mild general learning disabilities. for quantities (I am 7, I live in number 7, she has Personal difficulties are very often underpinned by a 7 sweets). poor self-image brought about by a long-term sense of failure. Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY that there are many ways to solve a problem, and Features of the Primary School Curriculum, that sometimes there is more than one ‘right’ answer. Mathematics The following features of the Primary School n The introduction of ‘fun areas’ such as chance Curriculum are relevant to students with mild general and mathematical trails allows for differentiated learning disabilities. approaches, which can include all learners in exciting mathematical activities. On a trail some n Early mathematical activities are aimed at students may be looking for one digit numbers, encouraging more work in pre-mathematical while others may be seeking up to three digit activities to develop concepts before commencing numbers or adding numbers together. For further formal number work. These activities are ideas see Primary School Curriculum: Mathematics, particularly beneficial for students with Teacher Guidelines (Mathematical trails). mild general learning disabilities. Teachers n The use of a broad range of assessment tools is can frequently revisit these activities in essential in the accurate identification of students’ age-appropriate settings. strengths and needs. This is particularly true in n The introduction of number limits encourages mathematics where students may need to acquire the consolidation of number facts and the certain skills or concepts before proceeding to development of the concept of place value. This more complex learning. is reflected in the reduction in the use of complex n The emphasis on using a variety of methods calculations and in the presentation of the same of recording students’ progress encourages concept in different ways. differentiation of response, which recognises n The emphasis on accurate use of mathematical different learning styles. Some students may be language and understanding of symbols  able to give an answer verbally while others would will contribute to a greater understanding of benefit from producing a diagram or drawing. All mathematics for all students. Students with mild students should have the opportunity to present general learning disabilities will need frequent their work in a variety of ways. opportunities to consolidate their understanding of n In the measures strand answers should both symbols and mathematical language. be verifiable where possible to encourage n Calculators have been introduced at fourth class, understanding and the development of personal but it is essential that students develop good benchmarks. This can provide support to students estimation skills from the earliest stages if they with mild general learning disabilities. Hand- are to use them efficiently. This is particularly true weighing and pouring activities using a variety of students with mild general learning disabilities, of shapes of container will assist in this area. who may confuse the meaning of arithmetical If students measure and label objects such as signs or have conceptual weaknesses in some bookshelves, desks, etc in the classroom, they areas. can build up visual benchmarks. For example, a student can stand beside the bookshelf and n The increased emphasis on the use of see that he/she is taller than a metre, or that the manipulatives (concrete materials) throughout teacher is shorter than the door, which is more the school, including the senior classes, means than two metres. that students who may still need the support of materials will not be perceived as being different n Increased emphasis on integration and on linkage from their peers. in strands of the Primary School Curriculum, Mathematics means that students can come to see n The Primary School Curriculum also emphasises mathematics as relevant and connected to their real-life problem-solving, using checkable own lives. Frequent reference by the teacher to answers and activities based in the student’s mathematical elements in the course of learning is environment. Encouraging students to engage with essential, for example measuring the distance from open-ended problems such as making scarves for the classroom to the office using a trundle wheel teddy, building a house using a limited number in geography, using time words in history (before, of bricks, or working out how to spend a sum of long ago, a year), measuring jumps or distances money on food for a party will help them to realise run in PE.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY School planning Curriculum planning No school plan will be complete While students with mild general learning disabilities without taking due cognisance of are expected to partake fully in the curriculum they the needs of students with mild will not be expected to do the same tasks at the general learning disabilities. With same level as the more able students. For these students, learning will concentrate on the areas of the proper planning for differentiation curriculum that provide them with essential life skills, to meet the needs of students with for example money, time, and measurement. mild general learning disabilities, they can achieve success and Students with mild general learning disabilities will need more opportunities to use concrete materials and participate fully in the curriculum engage in concrete tasks rather than working from at their own level. a textbook where their weakness in language would further aggravate their arithmetical difficulties. As their concentration span is short, they benefit most from tasks which are short and varied.  Using the same mathematical language and methodology throughout the school benefits all students, especially students with mild general learning disabilities. This is especially true in such difficult areas as subtraction with renaming, and in the teaching of fractions and decimals. For example, in doing the algorithm 9-3, if one teacher says ‘nine take three’ and another says ‘three from nine’, this will cause considerable confusion to the weaker student when she/he moves from one teacher to another or from class teacher to resource teacher. It follows, therefore, that it is important to also keep parents informed at regular intervals about what and how students are learning and their general progress. As the student with mild general learning disabilities requires the caring help of both parent and teacher in order to make satisfactory progress, it is important that parents and teachers have opportunities to meet and discuss the student’s progress. Regular communication with the class teacher and support teacher are also important as each teacher is aware of how the student is progressing in the classroom and in learning support. Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Good teaching practice needs regular assessment. As already noted, planning will ensure that the class Assessment should be informative and enable the teacher, support teacher, and the parent are working teacher to plan for further learning, and report on as a cohesive unit in supporting the student with the student’s progress. Teacher designed tests can general learning disabilities. For example, parents support the student by allowing for a certain amount could spend time with the student using mathematical of success. When failure occurs, the student will games that enhance the learning of basic facts. Some benefit from a discussion of where she/he went wrong parents may not be familiar with an algorithm, for and reassurance that making mistakes is part of the example decomposition, and try and teach the student learning process. Students with mild general learning using ‘borrow payback’, thus creating confusion. It is disabilities should be provided with a test suited to advised that teachers communicate with parents, at their abilities and stage of development. As students the beginning of the school year as to the approaches with mild general learning disabilities may be at and methodologies used, so as to enable parents to different stages of development, different teacher- support the student’s learning in the home context. designed tests and individual learning profiles may be necessary to best support their learning. Students with mild general learning disabilities very often have poor short-term/long-term memory. Homework should be used as an opportunity for reinforcing topics covered recently and in the past and Organisational planning should be appropriate to the child’s level of progress Organisational planning involves consideration of and achievement. These students need constant resource requirements, home-school policy, and a reinforcement. policy on homework. Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Classroom planning Since the Primary School Curriculum, Mathematics Classroom planning for each school is sequential and dependent on knowledge gained, setting – special school, special they may experience great difficulty in keeping class, and mainstream class – will abreast of their fellow students, although they may be able to partake in the majority of mathematical differ according to the needs of activities in the class. If, for example, the teacher particular students at any given is teaching a new concept or new algorithm he/she time. These students progress at must be careful that the calculations are simple, thus ensuring that the lack of number facts on the part of a slower rate than mainstream a student with mild general learning disabilities does students. not interfere with his/her acquisition of the concept. For example when using addition with renaming, 23+38 is a suitable example but 89+98 is not, since in the second case the student will have great difficulty calculating 8+9 and will not be able to concentrate on the concept involved. The situation is starker when it comes to multiplication. For example, 25×3 is easily managed, whereas 49×8 is likely to bring about failure  in the case of the student with mild general learning disabilities. Classroom planning for these students will involve close co-operation between the resource teacher and the class teacher in order to ensure that there is continuity and reinforcement in each other’s work. While providing special suitable work for these students the teacher should avail of any opportunity to allow participation in whole class work. Project work may provide such an opportunity. If, for example, the students are making a model of the school, the more able students can do the complex calculations relating to scale while students with mild general learning disabilities can be gainfully employed in measurement. Mathematical knowledge can be reinforced in other areas of the curriculum and such opportunities should not be missed when dealing with the student with mild general learning disabilities. For example, number and measure can be reinforced when doing running, jumping, etc. in physical education.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Some aspects of the teaching of mathematics need equivalents, and an example can help students to particular emphasis in the case of students with mild reinforce a correct interpretation of the symbol. general learning disability. These include n mathematical language + 3 + 4 = 7 plus and n symbols add n materials Plus and equals symbols are introduced first, followed n worksheets and textbooks by the minus sign and, subsequently, the greater than and less than signs (see symbols chart in the teacher n using ICT. guidelines for mathematics in the Primary School Curriculum). Mathematical language Materials Mathematics must be seen as a language with its own vocabulary of words, symbols and tools that are used Age-appropriateness in particular circumstances. It is very important that the materials used are age-appropriate. Brightly coloured counters and Many students confuse mathematical language interlocking cubes may be appropriate for younger with ‘ordinary’ language. They say ‘He’s bigger than students, but they often come to associate these  me’ when they mean older, or ‘My table is longer with the infant classes. Using football cards or coins than his’ when they mean wider. It is important to can make a counting activity more age-appropriate teach mathematical language to the students, and for older students. Pretending to be the man on the to reinforce it on a daily basis. A list of mathematical turnstile totting up the takings after a match can words can be kept either by the teacher or by the make counting more real to an older student. ‘Jobs’ students themselves (for example, taped into a that involve counting can be incorporated into the copybook), and they can tick them off as they learn mathematics class and are usually good motivators, to use them appropriately and accurately, either for example counting out information notes for orally or in writing. As already noted, keeping parents distribution to other classes, having a class sale of informed of the words being used and the importance work for charity, costing and buying foodstuff for of practicing them frequently will help the student to cookery classes, or examining the cost of popular make use of these words in real contexts. clothes such as jeans or favourite chocolate bars. Distributing milk, books, or pencils can be very valuable activities that support the modelling of Symbols language such as ‘Are there enough pencils for Some students may have difficulty with mathematical all your group? How many cartons do you usually symbols. They will often call the plus sign ‘add’, need for your group? Is there anyone absent today? and others will use ‘and’ or ‘plus’. As already noted, How many do you need today?’ The teacher can consistency of approach is vital and this is especially manipulate this actively by not giving enough items to true if the class contains students who have come the student and asking how many more are needed. from different schools or classes where they may During break times informal discussion about lunch have developed misunderstandings in relation to items can include such questions as, ‘Who has the some of the symbols. This is particularly relevant most sandwiches?’ or ‘Whose carton of juice contains if the student is moving to a new class or being the most milk?’ integrated with another class for mathematics. It is important that parents and all staff who are in contact with the student are aware of the terminology being used. In the classroom, charts with the symbol, word Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY n Do they present material in different ways for Accessibility different purposes and learning styles, for example Another important feature of using materials in the pictorially, diagrammatically, and using minimal classroom is that they must be stored in ways that language as appropriate? make them easily accessible to students. Clearly labelled and colour-coded boxes, a routine tidy-up n Is the print size appropriate to the developmental session, and procedures to maintain clean and neat stage of the student? materials will encourage students to use the materials n Over time, do worksheets/textbooks offer an appropriately and responsibly. Having a mathematics appropriate balance between the strands? table where the materials needed for the lesson are easily accessible is important and can be a role of n Do they offer opportunities for collaborative or responsibility for different students. It can be changed group work, for example active investigation and as topics change, for example ‘Our measures table’, talk-about sections, and integration opportunities ‘Sets of four’, etc. that focus on other areas of the curriculum? n Do they reflect the interests and environment of the student? Worksheets and textbooks n Do they consider the social aspects of It is important that worksheets and textbooks are mathematics, for example shopping, measuring for used carefully with students who have a mild general a purpose, life-skills? learning disability. Some mainstream textbooks move n Are computational activities carefully graded, too quickly through the content areas and therefore offering appropriate opportunities to consolidate should be seen as a complement to other means of learning at each level? instruction rather than the only source. With these 10 students it is particularly important to maintain a balance between computational and problem-solving Making sure that worksheets and textbooks are age- tasks and between the use of concrete and symbolic appropriate is extremely important, since students are representation. usually very aware that a particular book is being used by a younger brother/sister or by a more junior class In using worksheets and textbooks, the following within the school, and this can seriously impact on questions should be considered: their self-esteem. n Is there too much text in the worksheet/textbook? (This could inhibit the ability of poor readers to Using ICT engage with the mathematical content.) Many software programmes can be used at different n Is there a lot of ‘clutter’ on the page? (Students levels within the one group or class. Valuable teacher are often distracted by ‘busy’ pages containing too time can be taken up in establishing the correct much unimportant information or illustration.) starting point for a particular student. Colour codes n Are the spaces given for the answer large enough and symbolic representations taped to the front for students who may have poor motor control or of software boxes can help, and a card with clear write their numbers very large? instructions can be given to the individual student. Once students have practiced this procedure, they will n Are worksheets that are intended for homework be able to locate and load the software themselves, clear in their instructions so that parents know and an older student can either help or supervise. It is what the student is supposed to be doing? helpful to keep symbols constant and, where possible, n Do worksheets/textbooks offer a variety of task include the students in the choice of how information types, for example practical tasks, open-ended can be presented symbolically. This activity is also investigations, puzzles, games, project-based work, part of the advice provided in the Primary School and word problems? Curriculum: Mathematics, Teachers Guidelines.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Teachers should use a variety of assessment tools Assessment for learning that take account of different learning styles. When Students should have opportunities to experience planning a sequence of learning outcomes for a different assessment methods from an early age, and particular student or group it is necessary to keep play an active part in their own assessment. Early in mind how progress will be assessed. Too often identification of difficulties in mathematics is essential a pen and paper test at the end of a unit of work is if the students are to achieve their full potential. used. However, it is possible to assess progress by observing, for example, how a student handles money Assessment should be seen as a positive rather than in the class shop, how accurately a student can negative experience that will help them in their future continue a pattern, or can make a shape with his/her learning, and clear, constructive feedback to students body. When assessing student progress in the various is necessary if they are to play an active part in their areas of mathematics teachers should use a variety own future learning. Good communication is essential of assessment tools, including teacher observation, between the teachers and parents, other teachers and teacher-designed tasks and tests, portfolios, projects, professionals who come into contact with students work samples, and criterion reference tests. See the regarding each student's progress, strengths and assessment section in the Introduction to the Primary future learning goals. School Curriculum for further details on assessment techniques. An important issue in assessment is the evaluation of a planned test with regard to its aims and its suitability for the students for whom it is intended. The language of the test is crucial. If the language is too difficult or wordy for students who have a reading difficulty the test 11 may not accurately reflect their mathematical ability.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Approaches and methodologies Students with mild general learning disabilities need to The Primary School Curriculum build up personal support structures which they can recognises that students learn use when faced with a new situation or problem. They within a social context and are need to learn ‘how to learn', how to verbalise what the problem is, and how they intend to go about solving it. active participants in the learning process. They naturally investigate In the classroom situation, it may be good for the more and rely on their own methods able student and the less able student alike if peer teaching is introduced. The more able student can be of working out mathematical gainfully employed in helping his/her less able peer problems and therefore need in reinforcing algorithms, learning basic facts, and to experiment and discuss in in providing reinforcement of the concepts already a supportive environment that learned. enables them to build on and develop their ideas. Difficulties with numbers Students with mild general learning disabilities find it 12 very difficult to memorise basic facts. Consequently, number is an area that presents multiple difficulties. This has a debilitating effect on their success rate as very often they may have an algorithm done correctly but the answer is wrong because of lack of knowledge of basic facts. In order to overcome this difficulty, the teacher should n choose figures that are easy to calculate when teaching a new concept or algorithm n allow students to use a calculator or a one hundred square when calculating more difficult basic facts n if part of an algorithm is correct, mark the part that is correct and discuss the error in the remainder part with the student. Concrete materials When teaching new algorithms it is important (where possible) to use concrete materials, for example, in difficult areas like decomposition or fraction or decimal concepts. Students should have opportunities to use such materials until the concept is well grounded. When mistakes occur after the concrete materials are removed, they must be reintroduced to the student during the remediation process.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Some students with mild general learning disabilities Learning basic facts will have difficulties in problem-solving due to inherent Learning basic facts is very often a long and tedious limitations in their ability to abstract and generalise. task for the student with mild general learning Their ability to work independently is constrained disabilities due to possible short-term and long-term by poor attention span and retention. Hence, the memory difficulties. However, these difficulties can be learning process needs to be broken down into alleviated by short sequential steps and work done needs to be reinforced through over-learning and repetition. n providing the student with strategies for learning basic facts The difficulties experienced by these students can n using some of the large variety of table games lead to poor self-esteem and a fear of failure. These available, for example dominoes combined can lead to a sense of helplessness n using computer games to reinforce knowledge that results in the student constantly seeking help of basic facts. or refusing to proceed with even the simplest of tasks. Students may get trapped in the ‘I can’t do It is of crucial importance to match the work given maths’ syndrome. It is important that such students with the student’s ability to do it, in order to ensure experience success as often as possible and that the student will experience success. participate in fun mathematical activities if they are to overcome this feeling. The setting of realistic learning targets by teacher and student may help in the achievement of success and the return of confidence. Potential areas of difficulty It is also important for students to realise that making The potential areas of difficulty are described in order 1 mistakes is an integral part of the learning process, to outline the possible implications for learning and and that they should not be discouraged by their suggest possible differentiated teaching strategies. mistakes. Students with mild general learning disabilities are more like their peers than unalike. They have While difficulties in numeracy and literacy often the same range of interests, the same need for overshadow the student’s learning experience, it is affirmation and success, and exhibit a wide range important to provide a wide variety of learning tasks in of learning styles. Not all students with mild general order to allow students to show their skills and develop learning disabilities will exhibit all of the potential confidence in other areas of the curriculum. The use areas of difficulty, but it may be helpful for teachers of the calculator, for example, can enable the student to understand the implications that these may have to sometimes bypass arithmetical difficulties and work for their teaching and, consequently, for the student’s successfully on other mathematical topics. learning. Students need constant encouragement. They During his/her early years a student with mild need to be involved in their own learning and have general learning disabilities may have had restricted opportunities to discuss their difficulties. Students experiences in comparison to his/her more able have valuable insights into their own learning needs peer. Restricted mobility, poor motor control, or and this should not be ignored. Teachers should help poor understanding may have resulted in fewer students towards an awareness of what their learning opportunities to use the language of mathematics – for needs are, in the context of what they can do rather example counting stairs, judging distances or heights, than what they cannot do. Effective teaching builds and learning mathematical rhymes. Teachers should on students’ strengths rather than focusing on their be aware that they may not have learned these things weaknesses. incidentally. The tables that follow outline characteristics that may be associated with a mild general learning disability, examine their implications for the learning of mathematics, and suggest a range of strategies that may assist the student.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Sometimes it is the way in which the material is When an observational picture of the students has presented to the student that creates a barrier been created they can be grouped accordingly or to learning. Using a variety of approaches and provided with individual work. However, it is very methodologies will facilitate different learning styles in important to include large group or full class work any given class group. occasionally, so that students can learn from seeing how other students approach problems. Before you start The following lists are not comprehensive but should All students will benefit from a variety of teaching serve as a guide in assessing where a student is in styles and classroom activities. Students with relation to mathematics. It is suggested that individual mild general learning disabilities will particularly teachers or groups of teachers develop their own benefit if the teacher is aware of their strengths and profiling system that will insure that instruction is weaknesses before embarking on a new topic. The tailored to meet their students’ needs and levels of following table outlines some observations that the attainment. Teachers can use this information to ask teacher may note about the student. Such informal assessment can assist the teacher in selecting suitably n Is the student’s reading level inhibiting his/her differentiated methods for the class, and may prove ability to engage with the mathematical elements? useful in providing feedback to parents and students. n If so, can the material be presented orally, diagrammatically, pictorially? 1Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY / A generic list for informal teacher observation of students Pre-test using a simple task in an area you are introducing n What is the state of readiness of the student to do this task in terms of knowledge, skills, and attitudes? n What learning strategies are being used by the student? n Can the student describe what he/she is doing and how he/she is doing it? n Does the student understand why he/she is doing this activity? n Is the student’s reading level inhibiting his/her ability to engage with the task? n Is the student’s numeracy level inhibiting his/her ability to engage with the task? n Does the student have any misconceptions about the task? Independence n How does the student cope when left alone with a task? n Does he/she give up easily, ask for help, begin the next task, sit inactively, or become disruptive? n Does the student clearly understand what to do if he/she has a problem or is finished work earlier than others? n Is the student organised in his/her work? Does the student check if he/she has the correct equipment, for example pencil, pen, ruler, graph paper? n Does he/she have other difficulties, such as hearing loss, poor vision, poor motor control, or hyperactivity, which may need to be considered? n Can the student present work in a way that can be understood by others? Group work 1 n Does the student appear to learn better in a group, alone, or in pair-work? n Can he/she take turns and listen to other students’ responses? n Can he/she present work in a clear and coherent manner on behalf of the group? Instructions n Does the student listen to and understand instructions? n Can the student read instructions? n Can he/she follow instructions given by the teacher? n Can she/he follow more than one instruction effectively? n Can he/she make appropriate responses to the instructions? n Is the student clear about routines for setting out materials and clearing up after an activity? Choosing and using the right materials n Does he/she choose appropriate support materials, for example number line or objects for counting, addition, and subtraction? n Does he/she use materials appropriately, for example use a ruler correctly to measure, use a number strip for counting on, use blocks and push away those already counted, use a number square efficiently, use a calculator appropriately (i.e. make decisions about when its use is necessary)? Readiness for mathematics n Can the student classify, compare, and order objects and pictures? n Does he/she use labelling words efficiently when questioned? ('Can you find a teddy for me? What can you see? What is this?') n Does he/she respond to different aspects of a mathematical problem, for example functions, attributes, differences, and similarities? ('Can you find all the red objects for me, please? Can you point out the red circles?') n Can the student understand negatives? ('Simon says do not stand up. Find all the blocks which are not red.') n Does he/she reason, for example predict, project, identify cause and effect, and suggest alternatives? ('Why? What if I …?')Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Addressing potential areas of difficulty for students with mild general learning disabilities s Potential area of difficulty = Implications for learning The student may have a short-term memory Retention of number facts can be a problem. difficulty. + Possible strategies n Encourage the use of visual clues to aid memory. n Use number rhymes and songs. n Provide the student with strategies for remembering facts such as doubles, near doubles, etc. n Practise estimation skills so that a calculator can be used efficiently. n Work on making number operations automatic through fun games such as table darts. s Potential area of difficulty = Implications for learning The student may have a short attention span, lack of The student finds it difficult to stay on task. concentration, and lack of application. + Possible strategies 1 n Provide shorter tasks with clear rewards for staying on task, such as computer use or game time. n Keep periods of instruction short and to the point, and recap frequently. n Provide short work sessions with achievable goals. Encourage the student to become aware of the difficulty and to try to ‘beat their target’ in staying on task. n Use teacher observation efficiently and note achievements, strengths, and preferred learning styles for use in planning future work. n Use classroom management which focuses on contingent praise and encouragement (i.e. rewarding the task behaviour and not just the answer). This includes accepting ‘good’ answers that may not be necessarily correct, for example ‘Mary found an interesting way of doing that problem; let’s see how it works’. The use of open-ended problems that have different possible answers can help to develop a positive attitude to problem-solving. s Potential area of difficulty = Implications for learning The student may have difficulty in understanding The student finds mathematics particularly difficult mathematical concepts/abstractions. and has difficulty with counting numbers, place value, and with understanding what is happening when using the four operations. + Possible strategies n Frequent practice of the concepts to be learned should be varied by use of games, ICT, and real-life problems relevant to the student’s experience. Make the learning fun by using funny names, silly scenarios, or unlikely settings, for example: 'Tommy went to Mars for his holiday and met five aliens. They each had four arms. How many arms had the aliens altogether? Draw the aliens. What if they each had eight arms?'Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY s Potential area of difficulty = Implications for learning The student may have difficulties with spatial The student may have difficulty organising awareness; he/she may not have had opportunities materials, may display left/right confusion to play with puzzles, blocks, etc. in recording, may not recognise shapes if inverted, or constantly lose items in the room. + Possible strategies n Plenty of work with three dimensional objects will be needed, with particular attention being paid to the language of spatial awareness, for example up/down, over/under, shape words. n Using jigsaws, block puzzles, and tangrams in a fun way can help students in this area. n Work on awareness of own personal space, especially in PE, left and right, distance from, etc. n Maintain consistent organisation patterns in the classroom. n Use visual cues for location and direction on charts or table top. n Give oral cues related to the student’s own position, for example on your door side. n Allow students to remain in the same seating position for group work. s Potential area of difficulty = Implications for learning The student may have difficulty applying previously The student may find it difficult to use a skill or learned knowledge. concept in another setting such as measuring in geography or science. 1 + Possible strategies n Draw the student’s attention to what is happening: ‘This is just like the measuring we did last week. What did we use to measure our books? How did we place the ruler?’ n Consciously reinforce mathematical concepts in other areas of the curriculum, for example sorting and classifying in science, space and shape in art (printing 2-D shapes, both randomly and in sequences/ patterns). s Potential area of difficulty = Implications for learning The student may have difficulty with transfer The student does not use mathematics in real to real life. situations. For example, he/she does not use any of the four operations when buying goods in a shop, does not see the need to measure when cooking, does not recognise shapes in the environment. + Possible strategies n Use real-life objects and coins in play situations. n Discuss how pocket money is spent. n If possible, provide opportunities to handle money in a real shop or school shop. n Make sure that parents are aware of the importance of counting, handling money, etc. at home, for example setting the table, dividing up food, sharing equally, weighing for cooking, or measuring when doing DIY.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY s Potential area of difficulty = Implications for learning The student may have difficulty with visual The student can’t copy from the board or from a sequencing. book, or has difficulty with sequencing numbers, mirror writing, etc. + Possible strategies n Start with tracing exercises, using tracing paper. n Teach students how to ‘chunk’ information (for example copy only one part of the sum at a time), and how to check that it is correct. n Use number rhymes and songs to reinforce sequences. n Use visual cues, for example r start here s Potential area of difficulty = Implications for learning The student may experience confusion with signs The student does not ‘read’ symbols and asks and symbols. questions like ‘Is this an add sum?’ + Possible strategies n Use charts and discussion of everyday symbols, and relate these to mathematical symbols. n Encourage students to verbalise what they should do first, for example look for and identify the symbol, or apply the correct symbol if it is a written problem. 1 s Potential area of difficulty = Implications for learning The student may display poor vocabulary/other The student cannot follow complex sentences or language difficulties. multiple meanings, may process only part of the instruction, for example when told to put a red circle around all the big things he/she may process only ‘circle’ and ‘things’. The student finds it difficult to verbalise what he/she doing in mathematics, or to relate the vocabulary of mathematics to real-life situations. + Possible strategies n Identify and specifically target mathematical language, ensuring that it is reinforced in different settings and in other areas of the curriculum, for example location words (on, in, under, etc.) in PE, drawing games that involve following instructions containing target words (draw a square in the middle of your page, put a blue triangle beside/under/to the right of the square. n Be clear in communicating to both students and parents the language that is being covered each week, for example using a note in a copy or a wall chart to list the ‘mathematics’ words of the week’.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY s Potential area of difficulty = Implications for mathematics The student may experience reading difficulties. Reading difficulties can prevent students (For writing difficulties, see the section on from engaging with mathematics. They may communication and language.) be capable of completing the mathematical task but become frustrated and confused by printed words. + Possible strategies n Provide alternative forms of problems using visual presentation of material. n Ask the student to pick out the parts of the problem that he/she can read, and to focus on what information is relevant. There is often a lot of redundant information in a written problem. n Avoid presenting the student with pages of textbook problems by giving modified worksheets or verbally delivered instructions, for example ‘Mary has six sweets and she gives her brother four; how many has she left?’ Encourage the student to use drawings to ‘write’ down the important features, for example Mary has 0 0 0 0 0 0 'Take away four by crossing them out. How many are left?' s Potential area of difficulty = Implications for mathematics The student has difficulty in following instructions. The student becomes confused when faced with more than one instruction at a time. + Possible strategies 1 n Get the student to repeat the instruction(s). n Use short, clear instructions or pictorial cues, e.g. a picture of a copybook on the blackboard or on a card. n Use cue sheets, for example: ' Take out a copy and pencil (picture). What kind of problem is it? What do I need to know? What do I do next?' n Give clear guidance on how and when assistance will be given by the teacher/other students during the lesson. s Potential area of difficulty = Implications for mathematics The student may be overwhelmed by the learning The student becomes overwhelmed when presented process. with new information or skills, and consequently cannot learn. + Possible strategies n Vary the materials given to a group—some using number strips to five while others are using them to ten, where appropriate. n Adapt the teaching style, for example use more discussion at the beginning and at the end of the lesson to help both teacher and student to understand how learning takes place. n Introduce variety in the responses required. The same activity can often be done with a group or the class, but some students can be required to answer orally, some by using symbolic representation or some by using a pictorial response, for example a+ a a = aaa n Vary the requirements of the task. One group or individual may only have to do six of the calculations whereas another may have to do ten or more. Set personal targets for the students so that they do not feel that others are getting less to do than they are.Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY Selecting content When planning for a class, group or individual it is useful to have a checklist of elements you wish to include. Some suggestions are given in the following example. In order to maximise the cross-curricular elements of mathematics two further planning grids, with suggestions, are given in examples 2 and 3. EXAMPLE 1 Does your mathematical programme contain these elements? activities that link with other areas of activities that integrate with other areas of the mathematics (for example, using curriculum money to teach tens and units) real-life problem-solving opportunities direct teaching of mathematical Language variety in the materials to be used consideration of age-appropriateness direct teaching of mathematical strategies a balance between class, group, and methods of recording progress such as individual teaching the student’s own log books, portfolios of completed work, individual progress charts direct teaching of skills such as turn-taking or with clearly set individual targets. 20 active listening, and good work habits such as having materials ready, knowing what to do when finished, etc. AIMS OBJECTIVES What do you want to do? (strand/topic) What learning outcomes do you expect for What particularr area do you want to focus on? each student or group, including both skills (language, skill, concept?) and concepts? (These should form the basis for assessment and inform decisions about what the next target should be.) Planning cross-curricular work in mathematics ORGANISATIONAL ISSUES ASSESSMENT Can you enlist the help of other teachers/parents/ How will you record the students’ progress? assistants/students? How will you use this information to plan Is the necessary equipment easily available and are your next step? the students familiar with its use? How will you reinforce the skills/concepts in Can the topic be taught to the whole class, but with other areas? differentiated elements as outlined in the section on differentiation?Guidelines Mild General Learning Disabilities / Mathematics / PRIMARY EXAMPLE 2 Planning cross-curricular work in mathematics This is not an exhaustive list and would need to be adapted to suit the ages and ability levels of the students. The focus for the teacher should be on identifying the language to be reinforced and to consciously use it across subjects. It is very important to draw the students’ attention to the fact that measuring in geography or science is just the same as in mathematics. SESE: Geography SESE: Science Measuring the desk/room for Language of capacity: pour, fill, full, mapping exercises, measuring and empty, liquid, solid; recording rainfall and temperature, I think … My guess is … examining distances from one Properties of different materials—lots of place to another in planning a polystyrene chips are lighter than a few journey. stones; weighing activities. 21 STRAND: PE Measures Language of length, weight, time during activities (She ran the fastest; choose the heaviest ball; can you run farther than that? Today we’ll use the SPHE wide bench). Cookery—amounts of foodstuffs in Measuring jumps, and distances packaging; value for money; meaning run or walked using a trundle wheel; of: 10% extra free, 25% off; amount timing races or setting time limits on of salt, sugar, etc. in processed foods; games using a stopwatch. (These interpreting packaging information. activities can be done using non- standard measures at first). Using tally sheets to keep a record of laps run or jumps taken; estimating how far a beanbag or ball can be thrown.