Guidelines for Teachers of students with mild General learning disabilities

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Published Date:09-07-2017
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POST-PRIMARY Mathematical Studies and Applications: Mathematics, Business Studies Guidelines for Teachers of Students with MILD General Learning DisabilitiesGuidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Introduction They are part of a suite of guidelines produced by These guidelines are designed to the National Council for Curriculum and Assessment support teachers of students with with a focus on special educational needs. Each set of mild general learning disabilities guidelines corresponds to an area of experience of the Junior Cycle curriculum and offers exemplars of good who are accessing the junior classroom practice in support of the knowledge and cycle curriculum in the area of skills associated with that area of experience. Mathematics. These guidelines are is designed to support the teacher of Mathematical Studies and Applications for students with special educational needs, within the context of a whole school plan. In addition to the guidelines presented here, similar materials have been prepared for teachers working with students accessing the Primary School Curriculum. Continuity and progression are important features of the educational experience of all students,  but they are particularly important for students with special educational needs. Therefore, all the exemplars presented here include a reference to opportunities for prior learning in the Primary School Curriculum. The exemplars have been prepared to show how students with mild general learning disabilities can access the curriculum through differentiated approaches and methodologies. It is hoped that these exemplars will enable teachers to provide further access to the other areas of the curriculum. A range of assessment strategies is identified in order to ensure that students can receive meaningful feedback and experience success in learning. Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Approaches and methodologies Individual differences in talents, In Approaches and Methodologies strengths, and needs individual differences are All students will benefit from a variety of teaching emphasised, and potential areas styles and classroom activities. Students with mild of difficulty and implications for general learning disabilities will benefit particularly learning are outlined and linked if the teacher is aware of their individual talents, strengths, and needs before embarking on a new with suggestions for approaches and activity. methodologies for classroom use. Consultation and/or involvement in the Individual Education Planning process as well as teacher observation will assist the teacher of Mathematical Studies and Applications in organising an appropriate learning programme for a student with mild general learning disabilities. Such an approach will assist the teacher in selecting suitably differentiated methods for the class. If learning activities are to be made  meaningful, relevant, and achievable for all students then it is the role of the teacher to find ways to respond to that diversity by using differentiated approaches and methodologies. This can be achieved by n ensuring that objectives are realistic for the students n setting short and varied tasks n ensuring that the learning task is compatible with prior learning n providing opportunities for interacting and working with other students in small groups n allowing students to spend more time on tasks n organising the learning task into small stages n ensuring that the language used is pitched at the students’ level of comprehension and does not hinder understanding the activity n using task analysis in outlining the steps to be learned/completed in any given task n modelling task analysis by talking through the steps of a task as it is being done n posing key questions to guide students through the stages/processes, and to assist in self-direction and correctionGuidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY n using graphic symbols as reminders to assist It is important to teach mathematical language actively students’ understanding of the sequence/steps in to the students with mild general learning disabilities any given task/problem and to reinforce it on a daily basis, since they may have general language difficulties. A mathematical n creating a congenial learning environment by using dictionary of words, symbols, and diagrams can be concrete and, where possible, everyday materials, kept by the teacher and by the students themselves and by displaying word lists, laminated charts with and can be presented as a wall chart display. pictures. Teachers need to be aware of the danger of using mathematical ‘tricks’ and ‘short cuts’. Certain phrases Mathematical Language have become common in the mathematics classroom, Mathematics should be seen as a language with its particularly in the areas of arithmetic and algebra, but own vocabulary of both words and symbols. they often serve to conceal the concept behind what is occurring. Many students confuse mathematical language with ‘ordinary’ language. They say ‘He’s bigger than me’ Language that describes transformations in terms when they mean older, or ‘My table is longer than his’ of the surface structure only should be avoided, when they mean wider. It is important to teach this because it focuses attention on the form rather than language actively to the students and to reinforce it the meaning which gives rise to the transformation. on a daily basis. Students will need to be exposed to Examples of this would be: mathematical language and have it reinforced at a receptive level in a variety of situations before they will Take it over to the other side and change the sign. develop the ability to use it themselves.  Cross multiply. Move the decimal point over. The vocabulary of mathematics, symbols, and tools Turn it upside down and multiply. are used in particular circumstances. In general the Collect all the x’s on one side of the equation. student is unlikely to hear or read much mathematical Always do to the top what you do to the bottom. language outside the classroom. The teacher, as To multiply by ten add a nought. the mediator between the student and the world of mathematics, needs to examine the classroom use These descriptions tell someone only what to do, with of mathematical language carefully. Is it consistent, the result that there is little impetus to examine them accurate, and unambiguous? Will students experience to see why they might be helpful. the same use of language as they move from one class to another? Are students able to use appropriate Consistency of approach is vital. It is important that all mathematical language precisely? Can students relate teaching staff who are in contact with the student and some mathematical language to real-world situations? parents are aware of the terminology being used. For example, where appropriate planning has Such errors can be avoided if a range of different occurred the mathematics teacher can use the examples is used to explain a concept. For example, language of measurement (length, perimeter, area, if a student is taught that Figure 1 is a right-angled longer, shorter, etc.) while at the same time the triangle and promptly labels Figure 2 a left-angled English teacher can adopt reinforcement activities triangle the presentation of a range of triangles that incorporate the same words and the science in different orientations can help correct the and/or woodwork teacher can engage the students misconception. in practical measuring activities. Parents can also be encouraged to use the words at home. Keeping parents informed of the words being used and the importance of using them frequently will help the student to use them in real contexts. Figure 1 Figure 2 Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY The following is an example of a note that could be sent to parents: This week’s keywords in mathematics are: measure, size, length, distance, units, centimetre, metre, kilometre, longer, shorter, how long? Please use them often and encourage your child to use them in appropriate situations. Students may have difficulties with mathematical symbols. Charts in the classroom showing the symbol, the word, an example, and a diagram can help to reinforce a correct interpretation of a symbol. Where possible a real-world link to the symbol should also be included. Students can build up a dictionary of symbols as they progress through the course. Symbol Word Example Diagram Real-world A road intersection is where two roads cross each other. ∩ intersection A∩B=2,3  Train tracks go on parallel XY without ever meeting. Background to the Junior post-primary level. This challenges teachers to extend and diversify their teaching styles. Certificate Foundation Level mathematics course These students still need to learn mathematics to help These guidelines are written in the context of the area them in everyday life (social mathematics), further of experience Mathematical Studies and Applications study or training (vocational mathematics), or perhaps as outlined in the Junior Cycle Review (1999). The to enhance their thinking skills and problem solving topics referred to in the exemplar material are drawn skills. The foundation level course is designed to help from the foundation level of the Junior Certificate the student to mathematics course. Links to the relevant primary school topics and the corresponding statements in the n construct a clearer knowledge of basic Junior Certificate School Programme are mentioned. mathematics This section outlines the rationale, aims, and content of the foundation level mathematics course. n develop improved skills in basic mathematics n develop an awareness of the usefulness of The foundation level Junior Certificate mathematics mathematics course is designed for students who are not ready n feel she/he is making progress through the for, or who are unsuited to the ordinary level course. introduction of new material Students may not be ready to deal with some of the more abstract mathematical concepts; they may be n engage in a range of learning styles through, for finding the transition from primary to post-primary example, the visual, spatial, and numerical aspects school particularly difficult; or they may have learning of mathematics. styles that are not met by the traditional approach at Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY The particular target group may respond well to The assessment objectives, also stated in the syllabus, activities that deal with mathematical knowledge, understanding, and application, and with the student’s psychomotor n improve students’ self-confidence (I can do skills and the ability to communicate what they are mathematics) learning. n improve students’ confidence in the subject The content of the Primary School Curriculum is (mathematics makes sense, mathematics is useful) taken as the prerequisite for students following the n support the acquisition and consolidation of foundation level course. As will be seen from the fundamental skills exemplars that follow, many of the primary strands have been revised and treated in greater depth. In n embed mathematics in meaningful contexts this way there is a natural continuity from the primary n create opportunities for students to experience curriculum to the post-primary curriculum. success n create opportunities for students to reflect on their own experience and performance. The specific aims of the foundation level course, as stated in the syllabus, are that the course will provide students with n an understanding of the basic mathematical  concepts and relationships n confidence and competence in basic skills n the ability to solve simple problems n the experience of following clear arguments and of citing evidence to support their own ideas n an appreciation of mathematics both as an enjoyable activity through which they experience success, and as a useful body of knowledge and skills. Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Outline of the course This table outlines the course content under each topic. For more detail refer to the Junior Certificate Mathematics syllabus and the Junior Certificate Guidelines for Teachers: Mathematics. These are accessible on www.education.ie Topic Content details 1. Listing of elements of a set. Membership of a set defined by a rule. Sets Universe, subsets. Null set (empty set). Equality of sets. 2. Venn diagrams. 3. Set operations: intersection and union (for two sets only), complement. 4. Commutative property for intersection and union. Number 1. The set N of natural numbers. Order (, , , ). Idea of place value. systems Sets of multiples. Lowest common multiple. The operations of addition, subtraction, multiplication and division in N n where the answer is in N. Meaning of a for a, n N, n = 0. Evaluation of expressions containing at most one level of brackets. Examples: 2 + 7 (4 – 1) 6 + 10 x 3  3(14 – 5) – (7 + 2) Estimation leading to approximate answers. 2. The set Z of integers. Positional order on the number line. The operation of addition in Z. + 3. The set Q of positive rational numbers. Fractions: emphasis on fractions having 2, 3, 4, 7, 8, 16, 5, 10, 100 and 1000 as denominators. Equivalent fractions. The operations of addition, + subtraction and multiplication in Q . Estimation leading to approximate answers. Fractions expressed as decimals; for computations without a calculator, computation for fractions with the above denominators excluding 3, 7 and 16. Decimals: place value. The operations of addition, subtraction, multiplication and division. Rounding off to not more than three decimal places. Estimation leading to approximate answers. Percentage: fraction to percentage. Suitable fractions and decimals expressed as percentages. Example: 32 ; 32% 100 Equivalence of fractions, decimals and percentages. Example: 42 ; 0.42; 42% 100 4. Squares and square roots. 5. Commutative property. Priority of operations.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY 1. Bills: shopping; electricity, telephone, gas, etc. Value added tax (VAT). Applied Applications to meter readings and to fixed and variable charges. arithmetic and Percentage profit: to calculate selling price when given the cost price and measure the percentage profit or loss; to calculate the percentage profit or loss when given the cost and selling prices. Percentage discount. Compound interest for not more than three years. Calculating income tax. 2 3 2. SI units of length (m), area (m ), volume (m ), mass (kg), and time (s). Multiples and submultiples. Twenty-four hour clock, transport timetables. Relationship between average speed, distance and time. 3. Calculating distance from a map. Use of scales on drawings. 4. Perimeter. Area: square, rectangle, triangle. Volume of rectangular solids (i.e. solids with uniform rectangular cross-section). Length of circumference of circle = π. Length of diameter Use of formulae for length of circumference of circle (2πr), for area of 2 disc (i.e. area of region enclosed by circle, πr ). 2 Use of formula for volume of cylinder (πr h).  Statistics and 1. Collecting and recording data. Tabulating data. Drawing and interpret- data handling ing pictograms, bar-charts, pie-charts (angles to be multiples of 30° and 45°). Drawing and interpreting trend graphs. Relationships expressed by sketching such graphs and by tables of data; interpretation of such sketches and tables. 2. Discrete array expressed as a frequency table. Mean and mode.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY 1. Formulae, idea of an unknown, idea of a variable (informal treatment). Algebra Evaluation of expressions of forms such as ax + by and a(x + y) where 2 a, b, x, y N; evaluation of quadratic expressions of the form x + ax + b where a, b, x N. Examples: Find the value of 3x + 7y and of 6(x + y) for given values of x and y. 2 Find the value of x + 5x +7 when x = 4. 2. Use of associative and distributive properties to simplify expressions of forms such as: a(x ± b) + c(x ± d) x(x ± a) + b(x ± c) where a, b, c, d, x N. Examples: 3(x – 2) + 2(x + 1) x(x + 1) + 2(x + 2) 3. Solution of first degree equations in one variable where the solution is a natural number. Examples: Solve 3x + 4 = 19. Solve 4(x – 1) = 12. 10 Relations, 1. Couples. Use of arrow diagrams to illustrate relations. functions and Example: “is greater than” graphs 2. Plotting points. Joining points to form a line. 3. Drawing the graph of forms such as y = ax + b for a specified range of values of x, where a, b N. Simple interpretation of the graph. Example: Draw the graph of y = 3x + 5 from x = 1 to x = 6.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY 1. Synthetic geometry: Geometry Preliminary concepts: The plane. Line ab, line segment ab, ab as the length of the line segment ab. Angle; naming an angle with three letters. Straight angle. Angle measure; ∠abc as the measure of ∠abc. Acute, right and obtuse angles. Parallel lines; perpendicular lines. Vertically opposite angles. Triangle (scalene, isosceles, equilateral), quadrilateral (convex), parallelogram, rectangle, square. Practical, intuitive approach, for example using drawings and paper-folding. For constructions, the use of compasses, set squares, protractor, and straight-edge are allowed unless otherwise specified. Use of geometrical instruments—ruler, compasses, set squares and protractor—to measure the length of a given line segment, the size of a given angle and the perimeter of a given square or rectangle. Construction: To construct a line segment of given length (ruler allowed). Construction: To construct a triangle (ruler allowed) when given: • the lengths of three sides; • the lengths of two sides and the measure of the included angle; 11 • the length of a base and the measures of the base angles. “Fact”: A straight angle measures 180°. (For interpretation of the word “Fact” see Guidelines for Teachers.) “Fact”: Vertically opposite angles are equal in measure. “Fact”: The measure of the three angles of a triangle sum to 180°. Construction: To construct a right-angled triangle, given sufficient data (ruler allowed). “Fact” (Theorem of Pythagoras): In a right-angled triangle, the square of the length of the side opposite to the right angle is equal to the sum of the squares of the lengths of the other two sides (verification by finding the areas of the squares on the three sides or otherwise). Construction: To construct a rectangle of given measurements (ruler allowed). “Fact”: A diagonal bisects the area of a rectangle (verification by paper- cutting or otherwise). Construction: To draw a line through a point parallel to a given line. Construction: To divide a line segment into two or three equal parts. Construction: To bisect an angle without using a protractor. Meaning of distance from a point to a line.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Geometry Meaning of base and corresponding perpendicular height of a parallelogram. “Fact”: The area of a parallelogram = base x (corresponding) perpendicular height. 2. Transformation geometry: Central symmetry, axial symmetry. Use of instruments to construct the image (rectilinear figures only) under (i) axial symmetry and (ii) central symmetry. 12Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Using Calculators Encouraging estimation The use of calculators is a regular feature in the Through skillful questioning students can be daily mathematics lesson in post-primary schools. encouraged to use estimation. Interesting questions Calculators are an invaluable aid for all students and such as, ‘Are 150 hours more or less than a week?’ especially those with mild learning disabilities. Most will encourage an estimated answer followed by importantly, calculators enable students with mild calculator work. general learning difficulties to achieve success in mathematics. For some of these students memorising number bonds can be a problem. This can be offset Entering correctly by using a calculator, as long as the underlying Entering the decimal point needs careful attention, operations and concepts are understood by the especially in relation to money problems, for example students. €20 is entered differently to 20c, and in turn to 2c. The overall aim in the use of calculators in the mathematics class is to enable students to know The fraction symbol when it is appropriate to use mental methods, written b methods, and calculator methods, or a combination Using the fraction symbol on the calculator a c can of these. make fraction calculation achievable for students. 1 1 2 Once mastered, a problem like + + can be 2 4 3 A simple drill of Think first, write, use the calculator, answered easily. Equivalences can be explored and write, and then compare the results against the large fractions simplified. The teacher will need to original estimate should be practised. Rounding off show this to the class and to individual students. 1 and writing the estimate before using the calculator Students working in pairs or threes can help can ensure that cognitive skills are being developed each other. and will avoid mechanical use of the calculator. The teacher will choose whether a scientific calculator Interpreting display correctly or a simpler model will suit the student. The latter Pair work helps greatly with this. Questions like, ‘What usually has large keys and is most effective in does 12.3 mean in a money problem?’ ‘How would performing the four basic functions. However, in 3 cents be represented on the display?’ ‘How would dealing with fractions the scientific models offer great you key in twelve euro and three cent?’ will stimulate relief from lengthy and complex algorithms. The a correct reading of the display. Students should write calculator can enable the student to keep up with their answers on paper. learning in the system of natural numbers, integers, rational numbers, and real numbers. The teacher In using the memory button a teacher can judge the will familiarise himelf/herself with the various brands readiness of a student for calculations involving more of calculators being used by the students, and assist than one stage. For example, in calculating the wall them with minor differences in operating them. The area of a room 250cm X 500cm X 300cm seems following are some approaches that teachers may impossible for the student with general learning find useful. difficulties, yet 2 X 3 X 5 when stored to memory M+ (2 X 4 X 5 M+ ) can be accessed by pressing Recall Memory. This is an algorithm that can be Pair and small group work practised and used for larger numbers. Pair work is This can be of great benefit when students are very useful in this context in developing confidence learning how to manipulate the calculator and when and in exploring methods. solving problems .Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Checking answers Teaching strategies The calculator offers the teacher ways of showing When planning for teaching and learning in the area the student how to check answers using inverse of Mathematical Studies and Applications a variety of operations, thus reinforcing the learning of basic teaching strategies needs to be considered. operations. For example, 27 - 15 = 12 can be checked by 12 + 15. These will respond to the particular challenges students with mild general learning disabilities experience in engaging fully with, for example, mathematical language, oral and written Identifying students’ communication, problem-solving, and the retention misconceptions and errors of facts and concepts. The tables that follow list By observing the student and by engaging with some of the potential areas of difficulty, and suggest him/her in calculator work the teacher can ascertain appropriate strategies for classroom use. at what stage in the problem-solving process a misunderstanding may have occurred, and can deal It is important to remember that not all students with with it rather than getting bogged down in calculation mild general learning difficulties face all of these processes. If an error occurs as a result of operating challenges. Neither is it an exhaustive list. These are the calculator incorrectly, it can be dealt with on an the most commonly found potential areas of difficulty. individual, group, or class basis. Using ICT 1 Many computer programs can be used at different levels within one group or class. Useful software is available commercially and can be invaluable in reinforcing concepts, in assisting calculator usage in computation, in providing problem solving opportunities and in making mathematics fun and enjoyable. Students working, using ICT, in groups or pairs often make significantly greater progress than those who work individually, and this should be borne in mind in classroom planning. The organisation of ICT facilities varies enormously from school to school, yet the opportunity for students with mild general learning difficulties to avail frequently of ICT in the development of their mathematical skills is highly recommended. Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Addressing potential areas of difficulty for students with mild general learning disabilities s Potential area of difficulty = Implications for learning Short-term memory Retention of facts and definitions can be a problem. + Possible strategies n Encourage the use of visual clues to aid memory, for example a verbal or written definition of an isosceles triangle could be accompanied by a diagram with two sides and two angles marked as equal. n Encourage students to invent rhymes, songs or mnemonics to help them to recall facts and practise estimation skills, so that a calculator can be used efficiently. n Work on making certain operations automatic through using fun games such as table-darts or fraction-decimal equivalence dominoes. s Potential area of difficulty = Implications for learning Short attention span and poor concentration The student finds it difficult to stay on a task, may rush the task, and be easily distracted. + Possible strategies n Provide shorter tasks with clear rewards for staying on the task and for completing it. For example, allow 1 a student to try a mathematical puzzle when the task is completed. n Use a variety of teaching methodologies; keep periods of instruction short and to the point, and recap frequently. n Use teacher observation efficiently and note achievements, strengths, and preferred learning styles in planning future work. n Encourage students to keep portfolios of work in which they record their mathematical achievements. s Potential area of difficulty = Implications for learning Understanding mathematical concepts and The student finds mathematics difficult and has abstractions particular difficulty with certain abstract concepts necessary for algebra and geometry. + Possible strategies n Group discussion can help the student to listen to and work with others. This is very useful when introducing a theme or concept to promote a discussion with students. n In learning concepts activities should be varied through the use of games, ICT, and real-life problems relevant to the student’s experience. n Learning can be made fun by using funny names, silly scenarios. or unlikely settings. n Encourage co-operative learning activities, including pair-work and small group exercises. n Teach the topic in ‘chunks’ rather than as a single block.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY s Potential area of difficulty = Implications for learning Spatial awareness • The student may have difficulty organising materials. • She/he may display left/right confusion when recording and may not recognise shapes if inverted or rotated. • Topics such as geometry, applied arithmetic (area and volume) and graphing will be more challenging for this type of student. + Possible strategies n The student should be given plenty of work with three-dimensional objects and particular attention should be paid to the language of spatial awareness. n Encourage the student to make simple models (from cardboard or using a dynamic geometry computer package) when learning the properties of geometrical shapes. n When discussing area or volume of a shape ensure that the student has access to a model of the relevant shape. n Using puzzles, tangrams, and shape-making kits in a fun way can help the student with this area of difficulty. n Encourage students to be aware of their own personal space. n Keep the patterns of classroom organisation consistent. 1 s Potential area of difficulty = Implications for learning Applying previously learned knowledge The student may find it difficult to apply a skill or concept already acquired in a different setting, for example measuring in Geography, Science, or Home Economics. + Possible strategies n Revisit and review previously learned knowledge regularly. n Encourage students to revisit skills and knowledge learned in a previous class, for example ‘Yesterday we learned how to do a survey and make a tally chart to show the results …’. n Use a cross-curricular approach to the teaching of skills or concepts that are common to different subjects, for example measuring angles in mathematics and technical graphics or weighing in mathematics and home economics. n Draw the students’ attention to what is happening, for example ‘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 Reinforce mathematical concepts encountered in other areas of the curriculum and encourage the student to make connections, for example ‘How did you find the volume of something in science?’Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY s Potential area of difficulty = Implications for learning Transferring of learning to real-life The student may not use mathematics in real situations. For example, she/he may not use arithmetic when buying goods in a shop, may not see the need to measure when cooking, or may not recognise shapes in the environment. + Possible strategies n Use real-life objects and coins in appropriate situations. n Discuss with the students how they spend money. n If possible, provide students with opportunities to handle real-life materials in real-life contexts; for example, money in a real shop or in the school shop. n Ensure that parents are aware of the importance of counting and handling money or of measuring at home, for example sharing equally, weighing for cooking, or measuring when doing DIY. s Potential area of difficulty = Implications for learning Visual sequencing The student may not be able to copy from the board or from a book and may have difficulty with sequencing and mirror writing. + Possible strategies 1 n Teach the student how to ‘chunk’ information and how to check if it is correct; for example, copying only one part of the sum at a time. n Present board work carefully, give clear instructions as to what the student needs to copy, and use worksheets where appropriate. n Use rhymes, songs, mnemonics and mind- maps to reinforce sequences. n Use visual cues. s Potential area of difficulty = Implications for learning Confusion with signs and symbols The student may not ‘read’ symbols and may ask questions such as ‘Is this an add sum?’ + Possible strategies n Use charts to relate mathematical symbols to everyday symbols; for example, egg + chips, price, 20% off. n Encourage students to verbalise what they are doing first; for example, looking for and identifying the symbol, or applying the correct symbol if it is a written problem. n Encourage students to keep a symbol and keyword dictionary.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY s Potential area of difficulty = Implications for learning Language • The student cannot follow complex sentences or multiple meanings and may process only part of the instruction. • The student finds it difficult to verbalise what she/he is doing in mathematics. • The student has difficulty in relating the vocabulary of mathematics to real-life situations. + Possible strategies n Identify specific mathematical terms and ensure that these are reinforced in different settings and in other areas of experience. n Encourage the student to use relevant mathematical terms when appropriate. n Ensure that the mathematical language used each week is communicated clearly to students and their parents. n Use a Key Word approach by displaying a wall chart of mathematical terms used each week, thus enabling the student to build up a personal mathematical dictionary. s Potential area of difficulty = Implications for learning Reading Reading difficulties can prevent the student from 1 engaging with mathematics. He/she may be capable of completing the mathematical task but may become frustrated and confused by printed words. + Possible strategies n Present problems pictorially. n Ask the students to pick out the parts of the problem they can read and to focus on relevant information. 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 (with diagrams) or verbally delivered instructions. s Potential area of difficulty = Implications for learning Following instructions The student becomes confused when faced with more than one instruction at a time. + Possible strategies n Get the student to repeat the instruction(s). n Give short, clear instructions, and use pictorial cues. n Give verbal/written hints. For example, use graph paper. What kind of problem is it? What do you need to know? What do you do next? n Present clear guidance on how and when assistance will be given by the teacher/ other students during the lesson. 00Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY s Potential area of difficulty = Implications for learning Being overwhelmed by the learning process The student becomes overwhelmed when presented with new information or skills and consequently cannot learn. + Possible strategies n Adapt the materials given to a group. For example, have some compare the measure of angles using a protractor while others use cut-out cards. n Adapt teaching styles. For example, use more discussion at both the beginning and end of the lesson to help both teacher and student to understand how they are learning. n Adapt the responses required. The same activity can often be done with a group or class but some students will answer orally, some by using symbolic representation, or some by using a pictorial response. n Adapt the requirements of the task. One group or individual may only have to do six of the questions, whereas another may have to do ten or more. Set personal targets for the students so that they do not feel others are getting less to do than they are. 1Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY Exemplars These exemplars demonstrate how These exemplars are not intended to cover the course certain strategies outlined in the or any one part of the course entirely. Teachers previous section can be used when using them are encouraged to choose the learning outcomes, supporting activities, and assessment teaching a selection of topics from strategies that best suit the needs of their students. the syllabus. Some students may only achieve the first one or two learning outcomes while others may achieve the full range of outcomes. The important factor is their inclusion in the experience. The Junior Certificate Guidelines for Teachers: Mathematics contains further exemplar material that can be adapted to suit the needs of a variety of students. The guidelines also contain useful references to mathematical resources and websites. 20 Structure of the exemplars Each of the exemplars is preceded by an outline of the relevant sections of the Primary School Curriculum, the Junior Certificate (foundation/ordinary level) and the Junior Certificate School Programme (JCSP). Some of the potential difficulties experienced by students with mild general learning disabilities that relate specifically to the area covered in the exemplar are outlined, and suitable strategies are suggested. In addition, an approximate time scale, a list of resources, suggested outcomes, supporting activities, and assessment strategies for a lesson or series of lessons are provided. The exemplars are organised in the order in which the topics occur in the foundation level mathematics syllabus.Guidelines Mild General Learning Disabilities / Mathematics / POST-PRIMARY No. Syllabus topic Exemplar Title Page 1 Mathematics—Number systems Fraction attraction 22 2 Mathematics—Applied arithmetic and Time What’s the time 34 measure 3 Mathematics—Applied arithmetic and Walking on the edge 45 measure 4 Business Studies—The Business of Living Going shopping 54 Mathematics—Applied Arithmetic and Measure 5 Business Studies—The Business of Living Sources of income and interpreting pay slips 63 6 Business Studies—The Business of Living Preparing Analysed cash books 75 7 Business Studies—Enterprise Statistics and data handling 92 8 Mathematics—Algebra Algebra activity 100 21 9 Mathematics—Relations, functions and Plotting points 119 graphs 10 Mathematics—Geometry What kind of triangle is it? 128 11 Business Studies—The Business of Living Income and expenditure 135 12 Home Economics—Food Studies and Culinary Design and make a pizza 139 skills