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Introduction

The mathematics curriculum during the primary school years focuses on giving children a basic set of skills for use in their daily lives as well as a foundation for understanding more advanced mathematics. It includes learning to tell the time, to measure and to weigh, to understand volume and shape and to understand the money system. The core activity, necessary for all these applications, is learning to understand the number system - how to count, to understand that numbers represent quantities, and how to calculate using numbers. Clearly a basic competence in understanding and using numbers to 100 will be important if a child with Down syndrome is to be able to count, measure and weigh, tell the time and use money for daily activities such as shopping, cooking and for work tasks.

This module provides examples and practical ideas to help parents and teachers to teach children with Down syndrome. There is very little research into their number development but at present, the evidence indicates that they often find understanding number more difficult than learning to read. However, as in all areas of their development, there is wide variation in individual progress, with some children showing an aptitude and interest in number and learning at a rate within the range seen for typical children of their age and other children only mastering a simple level of counting by the time they leave school as teenagers. The children who have more difficulty with understanding number may still have functional skills for telling the time and for using money, based on experience in daily use and the targeted teaching of practical strategies.

Experience suggests that number work in the classroom may become too abstract too quickly, as children are expected to be able to do sums with numbers on paper. Children with Down syndrome will be more motivated to learn if they can see the application of what they are learning in their daily lives and this seems to particularly be the case for number, time and money skills. It is therefore important for parents and teachers to work together, as parents will have the opportunity to give children practice in using the skills in real situations. For this reason, the practical ideas in this module do not assume a knowledge of teaching mathematics and include a range of ideas that can be used to teach children at home and in school. Ideally teachers and parents will be working in partnership and parents can help children practice and generalise their classroom learning in real situations at home such as those which require counting or weighing or the use of money, and by playing number games with them.

The activities and strategies for supporting children's learning are based on what is known about the learning difficulties of children with Down syndrome and what is known about how typically developing children learn number. Children with Down syndrome will come into school with significantly delayed language and therefore they may not have the basic vocabulary for number, size, colour, shape and quantity that will be used in the classroom. For this reason, a list of number vocabulary is included in the module. The children will have been making slower developmental progress and this may have resulted in less opportunity to play games which teach number concepts to them in their preschool years. The children usually experience delay in developing fine motor skills and this may lead to fewer opportunities to manipulate, sort and count small objects.

In the classroom, therefore, children with Down syndrome will need help to learn number concepts and support for the practical activities of counting. They also have specific verbal short-term memory difficulties and therefore they will be helped by the use of visual supports for their learning whenever possible - using practical apparatus and using number cards and number lines for example. None of these difficulties are unique to children with Down syndrome and many teachers will be using the same strategies to support learning for other children with speech and language delay, motor difficulties or memory difficulties, in the class.

Some children with Down syndrome will have some knowledge of counting, colours, size and shape at 5 years of age but many will be just starting to learn these ideas, therefore the first part of this module provides activities to teach basic concepts and then moves on to understanding number, calculating, time and money. It includes examples of children's work and individual rates of progress, and provides guidance to targets for children with Down syndrome.

This module is intended to be used in conjunction with Number skills for individuals with Down syndrome- an overview, which provides the reader with a summary of relevant research on number development for individuals with Down syndrome and typically developing children, and the rationale for the practical approaches recommended.

Development of number skills for children with Down syndrome: examples of achievements

What skills might children bring with them to school?

Up to the age of 5 years young children with Down syndrome have learned about number and mathematical words through play, song, nursery school activities, home teaching and other life experiences. At 5 years of age, many are saying and trying to use some of the numbers from 1 to 10 in counting tasks when they begin school. They may have heard and seen higher numbers through supported counting games, in their environment and through conversation. Early learning activities, as for all children, include learning about the sequence of numbers in our number system, counting, and understanding of quantities. Sign language (using fingers) as well as materials and cards showing patterns and numerals, can help to compensate for weaknesses in speech, so a child does not need to be able to speak to be involved in number activities.

Young children with Down syndrome should experience typical mathematical language, especially words for number, in the same way as other children. Most 3 to 5 year olds with Down syndrome are capable of learning the stable order of numbers to 10, can learn to recognise numerals, develop one-to-one correspondence from games and counting exercises and can begin to learn about number by seeing different quantities. They may be beginning to link quantities they can see with number words and numerals around the time they start school.

Supported early learning activities are likely to have taught them the meanings of same and different, how to match, compare and sort, and may have introduced them to the numerals and sequence of numbers to 10.

Many children will be noticing how quantities differ, without linking this to a system of number. Some children have age-appropriate number skills: such as counting to 10, saying numbers to 15 or 20 and linking small quantities they can see with number words and numerals.

Some children will have experienced only a little number teaching before starting school, but will progress quickly in school with appropriate teaching and practice. While most children with Down syndrome at the age of 5 understand same and different, a small number of children may not understand these words and will be learning how to match in school.

What will they learn in school and how may they progress?

During the infant years, age 4, 5, 6, and 7, children will be working on developing number skills up to 20, with some knowledge of numbers beyond 20. At age 7 years some children will be working on numbers up to 5, while some will be able to count by rote beyond 20, read numbers from a 100 square, be able to add and subtract to 10, order numbers to 20 and count-on (i.e. if asked to add 4 and 2, the child can count on from 4, i.e. ''4,5,6'', and does not need to start counting from 1 in order to carry out the task). Many will be joining in with activities in school, counting to bigger numbers, or counting in twos, fives and tens, first as a rote memory game and later as a series of mental additions. All will be continuing to learn new vocabulary. Learning about money, time and measurement will be part of the curriculum for all children in this age range, and children with Down syndrome can be included in whole-class teaching, with activities simplified and differentiated as necessary.

In the junior years (ages 8 to 11 in the UK), many children will know about numbers to 100, counting in 'tens', 'fives' and 'twos', addition to 20, subtraction, early multiplication and division. They will also have increased their mathematical vocabulary knowledge. Some children can add larger numbers using learned procedures, with visual and mental strategies.

During their junior years, more children will achieve adding and subtracting skills, counting-on, will know all the combinations of numbers that add to 10 (number bonds to 10), will be working with numbers to 20, and counting to 100. Some children will be adding and subtracting confidently, others will be carrying out learned procedures but may be easily confused by changes in style of presentation, materials or language used. Some children who enjoy maths and have progressed well will be learning how to break numbers into units and tens to add and subtract larger numbers, with the support of equipment, such as cubes, 'Dienes'^[1], 'Cuisenaire'^[2], 'Numicon'^[3] or an abacus. Many will learn through explicit routines, for example, ''for adding two numbers together, put the larger number in your head and count-on''. Strategies, routines, visual aids and mnemonics will help children to understand problems, use procedures and number facts, and read tables, graphs and grids. Some children in junior schools may not have mastered number to 10, although their skills will be gradually improving. Many children with Down syndrome enjoy maths, whatever level they are working at, and a small number of children are good at maths (e.g. functioning within the range of other children of similar age).