RNIB supporting blind and partially sighted peopleEffective practice guide

Teaching Maths to pupils with vision impairment

About this guide

This guide explores concepts and techniques for teaching Maths to pupils who are visually impaired.

It is part of our Teaching National Curriculum Subjects series. At the end you will find the full series listed, and details of where to find them.

Contents

1. Introduction2. Learning3. Teaching4. Resources5. Recording and assessment6. Further guides

1. Introduction

Maths has the same overall value for visually impaired pupils as it does for sighted pupils. However, visually impaired pupils will need to acquire information in lessons which others obtain incidentally in everyday life through their sight, such as the use of money or percentages, or the perception of two or three dimensional shapes.For a visually impaired pupil who cannot see the environment as a whole, the physical world is made up of a series of items of knowledge which need to be fitted together like a jigsaw. Mathematics can play a central role in helping the pupil to complete the jigsaw and prepare them well for future life.

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2. Learning

Many pupils work slowly in mathematics because of a difficulty in understanding concepts or manipulating data. A visually impaired pupil may also work slowly, whatever his or her inherent ability, because of the physical problems involved in gaining access to the material.

Sighted pupils often use visual references to make estimates. Blind and partially sighted pupils need to learn estimation techniques and may need to use body parts, size of step, time and speed, and perhaps echo as references for estimating distances.

ExampleThe little fingernail equals 1 cm; width of thumb equals 1 inch; a smartie weighs 1 gramme and has a diameter of 1 cm.

Although all pupils need to learn skills of producing and interpreting graphs and diagrams, the use of the skill is very time-consuming for a visually impaired pupil, and it may be feasible to reinforce the skill, once learned, by oral classroom discussion, using a teacher or a support assistant to describe the content of the graph or diagram.

3. Teaching

Ensuring background knowledgeIt is important to be aware of any assumptions of knowledge generally and, where possible, to use these situations as opportunities to fill in gaps in knowledge or experience. This need not impede the progress of a lesson, as it can benefit all pupils to clarify, for instance, the number of players in a team, that Vienna is in Austria, or that 52 playing cards are split into four suits of equal numbers, two suits being black and two being red.

Visual and spatial concepts in two and three-dimensional geometrySome concepts are intuitive to sighted pupils, but may need to be taught explicitly to a visually impaired pupil. For instance, sighted pupils learn to recognise many transformations intuitively to begin with and only later are they taught the properties of various transformations. A visually impaired pupil will probably need to be taught these much earlier so that they can recognise a transformation.

Most pupils will need to be taught strategies to discover the visually obvious.

ExampleBlind pupils may need to fit a set square into the angle of a tactile diagram to check whether it is a right angle. Measuring sticks may be used to compare the lengths of two lines to see if they are equal.

Geometrical shapes can be related to a pupil’s experience.

ExamplePages in a book or a swimming pool are all rectangular; plates are circular, as are CDs.

There are certain principles about three-dimensional drawings which are difficult for visually impaired pupils to understand. For instance, a near object can hide a distant object; a near object will appear larger than a similar object further away; a smaller, nearer object can appear larger than a larger object further away.

ExampleA person can appear to be taller than a house which is in the background.

It may be better to use a combination of description, a two-dimensional diagram and work with the solid shape rather than using three-dimensional diagrams. For example, when setting an

exercise relating to prisms, it may be more suitable to use a two-dimensional diagram of a cross-section, accompanied by a 3D solid shape. The idea of perspective where lines converge to a vanishing point may also be difficult to grasp.

Avoiding ambiguity in aural presentationIt is not easy to read clearly questions such as ‘one plus two over three plus four’ which could have four different answers. The teacher must therefore be sure that the meaning is clear by saying, for example, ‘One plus two, all over three, then add four’.

Written exercisesIf a pupil reads so slowly that comprehension is a problem, it can be helpful to record the text onto an MP3 player for the pupil to use with the print copy. If a pupil writes very slowly it can be more effective to provide a worksheet with answers to complete. If the questions are repetitive for the purpose of reinforcement, it may be preferable for fewer questions to be attempted.

Modifying tasksIf a pupil is really slow at drawing diagrams, it can make better educational sense to use templates or a graphics facility on a computer. Similarly, finding information from a table is a slow process for visually impaired pupils whether they read print or braille. To save time and frustration, the teacher should consider reducing the size of the table to be scanned.

Working with graphsVisually impaired pupils may be placed at a disadvantage in graph work if efforts are not made to make it fully accessible. For partially sighted pupils this may entail no more than the use of simplified graph paper and a reduced expectation of accuracy. In the case of more severely visually impaired pupils, however, it may be necessary to teach them alternative techniques involving tactile skills.

A pupil who has been blind from birth may need individual help to develop graphical skills. Basic concepts such as horizontal,

vertical, rows, columns, parallel, perpendicular, diagonal, intersecting, and steeper may have to be taught. Practice may be required to locate co-ordinates using the two index fingers and to track lines - particularly those superimposed on a grid.

4. Resources

Producing your own resourcesWhen enlarging tables and diagrams, care must be taken that the finished product is manageable. Often, reducing the amount of white space is helpful. Wherever possible use A4 paper, or a split sheet of A3. As far as possible it is desirable to use a conventional page layout where the pupil reads systematically from left to right and top to bottom. If the layout of text is unusual, arrows or highlighters may be used to assist pupils in finding their way round the text.

When considering written exercises, the teacher should remember that some mathematical symbols can be indistinct if not printed clearly.

ExampleThe sign may look like a +. Decimal points may need to be emphasised. Fractions and indices may need to be written larger than normal.

Some pupils have a limited ability to see colour and contrast, so anything ‘in bold’ needs to be emphasised so that it is noticed. For example, this affects vectors where bold notation is used and also graph paper where every fifth or tenth line is emphasised. Where pupils are unable to see a line drawn on dark graph paper, a fainter or coloured grid may be used, or thicker coloured pens or pencils, or highlighters may also prove useful – but care should be taken that only colours accessible for each pupil are used.

Paper-folding techniques can provide tactile experiences of geometry. A simple example is the folding of a rectangle in order to feel that the opposite sides are equal. Pre-cut shapes will be

needed and they can be made from discarded braille paper which produces a clear crease.

Buying resourcesIt is important to be aware of the considerable range of tactile and enlarged resources that a braillist or large print user will require to gain meaningful access to a maths lesson. In addition to the materials used by the whole class, a child with a severe sight problem will also need extra concrete apparatus to compensate for diagrams which can illustrate, for example, a spatial concept at a glance. You may need to add braille yourself to some of the resources in order to make them transferable from partially sighted to blind children, or to ensure they are useful as a whole class resource. The braille can be added using clear self-adhesive labels.

The list of resources below is by no means comprehensive, but we hope that it gives you some ideas and helps to make your maths lessons more interesting and accessible for your blind and partially sighted pupils.

Information on some of the resources available from RNIB is included. Our full range of maths products can be viewed in our Online Shop at rnib.org.uk/shop

Counting, sorting and numeracy The Primary maths kit (LC102) is designed to encourage the

development of basic maths concepts to young blind and partially sighted learners, including those with learning difficulties. The kit comprises 12 curriculum activity packs and 36 activity cards which cover topics such as matching, geometry, sequencing, and probability.

Sorting trays and counters - keep an eye out when you go to the supermarket as some of the trays for pre-prepared vegetables are ideal as they are divided into sections for Tens and Units, HTU and even ThHTU (sweetcorn, baby carrot and mangetout is ideal). Cotton reels and Lego bricks can be used as sorting counters.

Read a teacher's review of our Cranmer abacus (LC118) and Slide abacus (LC159). NES Arnold do abacus discs on a loop that flip over - very good for severely blind and partially sighted pupils.

100 squares either in enlarged print or overlaid in braille - adapt/make your own using velcro strips. Blank tiles to go with the 100 square and blu-tack or Velcro to attach.

Concrete counting resources such as Multilink and coloured base ten apparatus - available from NES Arnold.

Number lines and cards in enlarged print or overlaid in braille - if possible, obtain number lines and cards that are magnetic as these are more manageable. Again blank tiles to cover numbers.

Number fans - an individual number fan for the pupil and a large print number fan for class teacher. Matt ones are better than glossy. Flip-chart number lines for single recognition - enlarged or braille (alternative to number fan for young braille users).

Magnetic place value cards - for building up two and three digit numbers (hundreds, tens and units overlay each other - these magnetic versions are larger and easier to use than the card ones commonly used in class, and they don't slip or slide, particularly useful on sloping work surfaces!).

Our fun and easy-to-see counting panel (GI36) helps children learn to count from one to 10, using detachable fabric animal shapes.

Rulers, tape measures protractors and compasses We have a range of tactile rulers and protractors and clear print,

tactile and talking tape measures.

NES Arnold do an enlarged print ruler.

Calculators An appropriate calculator should be chosen for a visually

impaired pupil. Points to consider are:

size of display contrast of display (Green displays are usually preferred but

are not common.) clarity of decimal point contrast and colours on the keypad labelling on the keypad (pupils can learn this if necessary.)

Various basic talking calculators are also available from shops as well as from specialist firms. The quality of synthetic speech varies from model to model so it is important to check that the pupil can identify the numbers using the headphones. A blind pupil should be encouraged to operate the calculator with the non-reading hand leaving the other hand free to read.

View our selection of clear print and talking calculators.

Force Ten offer the Sci plus 200 large display scientific calculator and Sci plus 300 large display talking scientific calculator.

Geometry and fractions Read a teacher's review about our Folding geometric shapes

(LC168) and take a look at our other geometry products.

Our set of Montessori shapes (LC190) give children the option of using the plastic shapes and templates for drawing or for shape recognition and matching activities.

Other products to help teach children about shapes are the Waggy garden shape sorter (GI57), Shapes feely bag (GI29), Texture and shape dominoes (GP32), Magnetic shapes (GI23)

Plastic embossing film (LC22/23) (also known as German film) can be used on a Geometry mat (LC177) and drawn on using an embossing tool or 'dead' (inkless) ballpoint pen, to create tactile images.

Food colouring, water and a range of bottles/containers for showing capacity - use everyday bottles that are clear and in different sizes.

Fractions Our set of Magnetic fraction cubes and spheres (LC192) is ideal

for teaching the concept of fractions to blind and partially sighted students. Use the interchangeable pieces to show the relationship to a whole cube or sphere. For example, take a half, add two quarters to create a whole.

Also available are the two-dimensional Fraction squares (LC185) and Fraction circles (LC186).

Fractions board (labelled up in braille if necessary) are available from NES Arnold.

Time Our Big learning clock (LC138) is lightweight and has raised

black numbers and tactile markings on a white background. The two hands move independently so that the time before and after the hour can be shown without the hour hand moving.

While the hands on the Geared learning clock (LC182) cannot be moved independently of each other and can be used to demonstrate the relationship of movement between the hour and the minute hand.

An easy-to-see clock and tactile watch can also be useful, along with large display digital timers.

Graph paper and exercise books We have a range of clear print and tactile graph paper and pie

charts.

Alternatively you can make your own using thermoform, Minolta or a computer system and photocopier. There are several websites which offer free graph paper templates.

Large squared exercise books are available from Philip and Tacey.

Other useful resources Easy-to-see tactile dice (GB91). Read a carer's review of the Beetle game (GP33). The Cubarithm (LC65) is ideal for teaching braillists arithmetic

layout. and, unlike paper, allows for easy immediate correction. Wikki Stix (LC49/50/115/116). Bumpons are useful for marking points on charts and diagrams. Talking scales . A4 whiteboards are available from Synergy Learning Products. Blu-tack. Real coins.

Using alternative equipment A peg board or pin board can be used to teach transformations.

For example, the shape can be made on the board, then the board physically rotated to its new position. Reflections, rotations, translations and enlargements can also be done with cut out shapes, Blu-tack, pins and a graph board. Plastic embossing film can also be useful as tracing paper if pinned down for pupils to feel the diagram underneath. They can then mark answers to questions on the plastic film itself and have a permanent record of answers. There are also possibilities for teaching these concepts using braille symbols and the Perkins Brailler.

Educational catalogues often contain good examples of visually clear rulers, metre sticks, tape measures and measuring wheels. RNIB sells a range of tactile implements. One common problem however, is that measuring instruments move as they are being used. Some pupils will find it helpful to use Blu-tack or non-slip pads made from Dycem, or pins to hold instruments in place. Some pupils find magnification using an electronic magnifier can help with measuring exercises.

Equipment for drawing circles and other shapes A range of special compasses which can be used by

pupils to draw circles is available from the RNIB shop. For shapes other than circles, geometrical templates enable sketch diagrams to be produced quickly.

Computer software is also available to help visually impaired pupils produce good quality drawings.

For learning about three dimensional objects, it is essential to provide visually impaired pupils with the actual solid. Commercially produced plastic models are usually available in most mathematics departments, but the faces may need to be coloured, textured or labelled according to the pupil’s needs. A pupil may find it helpful to fit the faces of solids into two-dimensional outlines which can be prepared on a tactile diagram.

For those pupils unable to use the normal 2mm graph paper, paper marked in larger squares such as centimetre squares is often appropriate. Grids printed in different colours can be obtained from RNIB.

5. Recording and assessment

It is important to distinguish between a learning outcome and the ability to record the result. In many instances, a visually impaired pupil will be able to engage fully in a learning activity, using apparatus or oral approaches, but may find it difficult to produce a permanent record of the activity. In some instances, it will be appropriate for a member of support staff to produce a permanent record of practical work undertaken by pupils. It is the teacher’s responsibility to judge whether the recording process is an end in itself or incidental to the learning task.

Braille codeThere is a special braille code for mathematics which you can find athttp://www.rnib.org.uk/livingwithsightloss/readingwriting/braille/braille/codes/Pages/specialist_braille.aspx

The teacher needs to be aware that new symbols should be mastered by the pupil as they become necessary for

course work. Computer transcription of the braille code is possible and some pupils may choose to record information on computer, but many will find it easier and more immediate to use a Perkins Brailler.

Layout of arithmetic in braille Due to the way in which the Perkins brailler works, and the way braille is read, the traditional vertical methods of arithmetic may be inappropriate for a blind pupil to use. A worksheet requiring answers only to be inserted saves time and is less frustrating. A Cubarithm (see RNIB shop) can be used to set sums out in a vertical layout. Pupils often prefer a linear format but a good knowledge of place value is needed especially when decimals are involved. Pupils should be encouraged to make use of whatever method suits them best and to devise a variety of strategies.

Extended tolerancesAccurate measurement is not always either possible or practical for some visually impaired pupils. This fact is recognised in guidance on access arrangements for tests and exams and appropriate allowances for individual pupils can usually be obtained. Where the degree of accuracy expected of a sighted candidate is plus or minus 0.1cm, braille users should normally be expected to achieve a degree of accuracy not greater than plus or minus 0.5 cm. The accuracy achievable by a partially sighted pupil can range from that achieved by sighted pupils to that of braille users, and the teacher will have to advise examination boards as to what is feasible for the individual pupil. Factors affecting accuracy include the visual ability to locate points accurately, to see two points in one glance, to be aware of equipment slipping off alignment, and to differentiate a gap of 1mm.

In measuring angles, where a sighted child is expected to achieve accuracy of plus or minus 2 degrees, a braille user is normally expected to achieve a level of accuracy not normally greater than plus or minus 5 degrees, whereas a partially sighted pupil will need to be assessed by the teacher. Naturally, such allowances do not apply where accuracy of measurement forms an assessment objective in its own right.

6. Further guides

The full Teaching National Curriculum Subjects series of guides includes:

Teaching Maths to pupils with vision impairment Teaching Science to pupils with vision impairment Teaching English to pupils with vision impairment

We will be producing guides on other subjects in the near future. Please contact us if you would like more details about these, as we will certainly be able to help in some way.

In addition, you may also be interested in the following series of guides, all of which are relevant to children, young people and families:

Supporting Early Years Education series Removing barriers to learning series Teaching National Curriculum Subjects series Complex needs series Further and Higher education series

We also produce a number of stand-alone factsheets, on a range of topics, which may be of interest, please contact us to find out what we have available

All these guides can be found in electronic form at www.rnib.org.uk/guidanceonteaching For print, braille, large print or audio, please contact the RNIB Children, Young people and

Families (CYPF)Team at cypf@rnib.org.uk or call on 0121 665 4235.

For further information about RNIB

Royal National Institute of Blind People (RNIB), and its associate charity Action for Blind People, provide a range of services to support children with visual impairment, their families and the professionals who work with them.

RNIB Helpline can refer you to specialists for further advice and guidance relating to your situation. RNIB Helpline can also help you by providing information and advice on a range of topics, such as eye health, the latest products, leisure opportunities, benefits advice and emotional support.

Call the Helpline team on 0303 123 9999 or email helpline@rnib.org.uk

If you would like regular information to help your work with children who have sight problems, why not subscribe to "Insight", RNIB's magazine for all who live or work with children and young people with sight problems.

Information Disclaimer

Effective Practice Guides provide general information and ideas for consideration when working with children who have a visual impairment (and complex needs). All information provided is from the personal perspective of the author of each guide and as such, RNIB will not accept liability for any loss or damage or inconvenience arising as a consequence of the use of or the inability to use any information within this guide. Readers who use this guide and rely on any information do so at their own risk. All activities should be done with the full knowledge of the medical condition of the child and with guidance from the QTVI and other professionals involved with the child. RNIB does not represent or

warrant that the information accessible via the website, including Effective Practice Guidance are accurate, complete or up to date.

Guide updated: July 2011