number-early

Introduction

While the central focus of the maths curriculum in school is learning to count, to understand the number system and to learn to carry out calculations with numbers, it also includes the understanding of size, shape, quantity and measurement, time and money. Children begin to learn the first steps in number and the concepts for size, shape, quantity, time, money and measurement in the preschool years and children usually start primary school with a range of appropriate knowledge and skills. Children with Down syndrome show widely varying progress, but the author sees some children with Down syndrome who have the same knowledge and skills as typically developing children of the same age, so the activities in this module cover that range. Many children with Down syndrome will not achieve all these skills and concepts until they are in school, and for all children, their rate of progress may vary but it will be influenced by the amount of teaching and number games that they have experienced.

What do children typically learn?

Number

In typical development, most three year olds know and can recite some of the count word sequence (“one, two, three, four, five…….”) and can count small sets of items. At about four years of age, they show understanding of cardinality, i.e. that the last word represents the number of items in the set. At this stage, they can answer correctly the question “How many do you have?” and they can correctly give small numbers of items, 2, 3 or 4 items, from a larger set of items. By five years of age, many children can recite the count word sequence correctly to 20 or beyond and count sets of items to 10 items. They have some idea of adding and subtracting with objects, e.g. “put 2 more pigs with the pigs, now how many do we have?” and “there’s 3 birds in the tree, 1 flies away, now how many birds are in the tree?” They have learned this number knowledge mainly from games and activities with adults at home, and then at preschool. The count words are learned by copying an adult, as they count stairs and everyday items or as they sing counting songs. TODO: references 1] TODO: references 2

See also:

In their first year in school, children will be learning to understand more about the number system and the nature of the orderly relationship between numbers - i.e. that each ‘next’ number represents one more equal unit, so that 2 + 2 and 3 + 1 both equal 4. These ideas are more difficult for children than we may realise and many teachers stress the value of using apparatus designed to help children to see the relationships and to carry out calculations, such as Cuisenaire rods and Numicon ‘shapes’. TODO: references 3 (See Figure 17)

There is pattern and order in the number system and in number calculations therefore many teachers believe that games which encourage children to see patterns and order will help them to understand the number system. The teaching activities which accompany the Numicon materials for use at home and in nursery include games to encourage children to look for order and pattern. TODO: references 4 These materials encourage the children to use the shapes and colours of the ‘shapes’ to develop mental imagery for each whole number from 1 to 10. These images can support calculating with numbers mentally at a later stage. As children with Down syndrome benefit from visual support for learning, the author believes that the Numicon approach is likely to be beneficial for them.

The maths curriculum

The maths curriculum includes:

The foundations for all these aspects of maths are laid in preschool years

Colour, size and shape

Learning colour words (red, yellow, green, blue), size words (big, little, small) and shape (square, triangle, circle) words prepares children for the early parts of the maths curriculum on ‘measures, shape and space’, as do preposition words e.g. ‘in’, ‘on’, ‘under’ for ‘position, direction and movement’. Colour, size and shape differences can be ‘seen’ by children and the language for labelling these attributes can be learned through matching games. Many pre-school children with Down syndrome can begin to learn these early concepts, and doing so will be of great benefit for them when they begin school, where their understanding can be developed further through the maths curriculum.

Time

Children are learning about time as we talk about everyday activities. For example, “Today we are going swimming”, “this afternoon Granny is coming to see us”, “tomorrow is a school day, we go to school on Mondays”, “yesterday was Sunday, we went to church”, “before we go out, you must brush your teeth”, “after tea, you can watch a video”, “next time we go to the park, you can go on the swing”, “next week is a holiday”, ” at 8 o’clock you will have your bath”, “Daddy will be home at 6 o’clock”, “at 9 o’clock, we go to nursery”, “Your birthday is in June, Jo’s birthday is in November”.

Money

Children learn about money as they see it used in shops and on buses and as they begin to use it for themselves. They will learn the names of the different coins and notes before they understand their relative values, as they do with number ‘names’. Playing ‘shops’ will help them to learn the names of the coins.

Teaching children with Down syndrome

Children with Down syndrome may need more teaching and practice in order to learn about number and maths than other children. They will also benefit from special consideration of aspects of their language and cognitive profiles, and how their learning strengths and weaknesses can influence their progress (see box).

A specific developmental profile

Children with Down syndrome are helped by teaching methods which take account of research into their strengths and weaknesses:

For a full discussion of these issues, see An overview of the development of infants with Down syndrome (0-5 years)

Activities, supports and teaching targets that will influence progress are summarised below and developed further in the following sections.

Early learning about number

See also:

From 2 to 5 years, like all children, young children with Down syndrome will typically be learning about number and mathematical words and ideas through play, song and life experience. Most children will be hearing, saying and trying to use numbers from 1 to 10. They will also have had some experience of higher numbers to 20 through rote counting activities with others and by hearing them used in 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.

Expectations

Number learning targets

Young children should be experiencing typical mathematical language, especially number, as they would be if they did not have Down syndrome. Most 4 to 5 year olds with Down syndrome are capable of learning about the stable order of numbers to 5 if not 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 the quantities they can see with number words and numerals around the time they start school at about 5 years.

Motor skills

Young children’s motor skills, particularly fine motor skills, may affect their opportunities for learning about maths and number through play. Play with construction materials and manipulation of objects may be difficult, depending upon the children’s skills and the types of toys and materials they have played with. They may not play with equipment for sufficiently long periods of time because of the extra effort needed due to their poor motor skills.

! Man and tractor, for learning prepositions

Figure 1. Man and tractor, for learning prepositions

Handling and moving objects

Play with bricks can be encouraged by finding small, light bricks that the child likes to hold or touch. Children can be encouraged to develop more advanced play over time, beginning by moving bricks from hand to hand, placing them in and taking them out of containers and later building with bricks to make towers and bridges, to make enclosures for toy farm animals, to engage in sorting and counting games according to colour and shape, and when playing pretend games such as shopping or tea parties. A slight rubbery texture or other grip can be helpful, so that bricks are easier to hold and manipulate.

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Figure 2. Playing with positions

Construction play

For playing with interlocking bricks or construction toys you will need bigger bricks or parts. Building activities can be made more interesting, meaningful and less reliant on imagination, by using bricks with pictures on - such as trains, buses and cars, zoo animals, farm characters, people, pets, furniture items or park features.

Bricks of different shapes and sizes as well as colours will enable games to be expanded further and lead to more comparison, thinking and language understanding.

Moving items from place to place, like toys and bricks, will help your child to learn about place and prepositions, for example, ‘in’, ‘on’, ‘over’, ‘under’, ‘through’, ‘next to’, ‘behind’ and ‘in front’ ( [Figure 1] and [Figure 2]).

Supported play

Children may need help with play to show them how to extend their play skills with bricks and other construction toys. It is also important to let them play without interruption and to allow them their own thoughts and actions, but play with them again if they become fixed on one type of play for too long, such as banging two bricks together, building towers repeatedly or sorting toys into pairs.

Learning through play, language and environment at home

Social learning

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Figure 3. Playing together

Early experience and socially mediated learning at home are important for beginning and continuing to learn about numbers and maths.

In families, where numbers are a part of everyday life and where family members play games together, there are frequent opportunities to learn number skills ( [Figure 3]). Children with Down syndrome enjoy learning in social situations and in games, taking turns with other players.

For example, the idea of ‘more’ can be introduced from a very young age. Children as young as 18 months may use this sign to obtain more food, drink or repetition of an activity (‘again’). This can be developed and elaborated with the questions “how many more?” or “how much more?” as they get older. Children can be included in dice games, counting or moving counters before they understand numbers. It will be easier to learn from adapted dice with smaller numbers. Games can be adapted with large ‘boards’ for the floor and large dice to teach the idea of counting as well as the idea of playing a game together, winning and losing. Older children (e.g. 3 and above) can learn how to play board games designed for their age group, and will see numerals and patterns on dice, as well as counting on a board. Quantifying amounts can begin early with noticing “one nose”, “two eyes” or “feet”, “five fingers”, quantities of clothing, food, and number of animals, children or toys during play.

Songs, rote counting, supported counting

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Figure 4. Toys at home for counting

Children with Down syndrome should be introduced to number games, songs and rote counting activities as early, and in the same way, as other young children. At first, they will benefit from hearing the numbers spoken in order. Later, children learn the number sequence by imitating a parent’s counting. Then, parents can count items and omit the final number for the child to say, or pause and say the final number with greater emphasis. These games stress the significance of the final number in a count sequence, this being particularly important as it represents the whole amount (cardinality).

It is easy to underestimate the potential for learning during the early stages of development, even though many children with Down syndrome have little or no speech and delayed motor skills. Number language and skills can be modelled through supported ‘pretend’ play, and can also be included in speech and language therapy games.

! Pictures and finger puppets for making up a number story

Figure 5. Pictures and finger puppets for making up a number story

Maths Environment

Pictures, posters and displays (e.g. on a tray) can be arranged at home as well as at nursery school to provide practice for learning about sorting by features (such as size, shape and colour), ordering and counting ( [Figure 4]). A maths rich environment will make it easier for parents and teachers to count daily with their children, with objects or by pointing at items on a picture display. They can use language like “How many can you count today?” (emphasising the use of “how many” and “count”, as this will help children understand cardinality). They can start at different numbers so that counting does not always begin at 1 and different parts of the sequence are practised. They can find a numeral for the amount counted and place it on a number line with their children. Made-up stories with different numbers of characters, illustrated by pictures, are another way to bring maths into everyday language and learning, for example, “Three ladybirds went for a walk. They went to visit….” etc. ( [Figure 5]).

Play and teaching activities

Teaching methods

Early language skills

There are many everyday activities where number and other attributes can be introduced, practised and learned through play in the home and school environment. Structured activities that include ‘errorless learning’, matching and selecting games can help many children with Down syndrome to learn new ideas. Any materials that children enjoy can be used as part of a teaching and learning game. Structured games are games that have been designed to teach one particular part of a skill that can then be built on in later games, so that every child can learn the whole skill successfully. Children can then progress in small steps, without being overwhelmed by too much new information or too many differing task requirements. Games where too much is presented at once can leave children feeling that they have failed, and they may then not want to play that game again.

Breaking the task into small structured steps usually helps children to do things for themselves; they need less explained to them and can focus on the task, without having to listen and understand spoken information simultaneously. The easier it is for children to ‘see’ how to succeed, with activities modelled and clear uncluttered, attractive resources, the more likely they will copy and engage in the tasks with enjoyment.

Many number and maths skills can be learned through play and teaching games. Targets and activities for learning pre-school and early school skills are described and illustrated below.

! Pictures for choosing number songs

Figure 6. Pictures for choosing number songs

Language and activities for learning repetition, comparing and categorising skills

Repetition

Repeat activities with use of “more” and “again?” for activities that motivate the child, such as bubbles, songs or action games.

Choice

Choosing games requires the child to look for differences between items. Toys, pictures ( [Figure 6]), food, drink and clothes can be used in choosing activities. If children find it difficult to make a choice, offer both items and when they are looking at one push it forward and praise them, quickly followed by the activity, song or giving them the item. Tell them that they chose the named item. Progress from this stage by prompting and encouraging them to touch to choose, point to choose, sign to choose and speak to choose.

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Figure 7. Picture lotto to teach “same” and “different”

Similarities and differences

Use the words and signs for “same” and “different”, with sets of identical and different items or pictures. Baskets and other neutral containers can help children to match toys to identical toys or photographs of the toys. If children are hesitant push the correct basket closer to them and if they still do not place the identical item point or show them what they should do. These stages make the tasks increasingly ‘errorless’, show them what is meant by the “same” and what is expected of them. Early picture lottos TODO: references 5 will also teach understanding of the “same” and “different” ( [Figure 7]).

Help your child to notice the similarities and differences with sets of toys by talking with them and describing attributes like colour, size, shape and number in clear and simple sentences ( [Figure 8]).

Using “gone” and “no”

! Toys for talking about “big” and “little” during play

Figure 8. Toys for talking about “big” and “little” during play

Show the idea and the word label for absence using “gone”, as well as understanding the negative “no”. When “gone” has been understood as in “all gone”, play games that practise with two ideas and words, for example, “The rabbit’s gone”, “The car’s gone”. Put a hat or shoes on and off a doll to demonstrate “no hat”, or “no shoes”. Play sharing games in which one toy or person gets “none”. These concepts will begin to prepare children to understand zero.

Matching games

Use matching games for teaching size, colour and shape names. Many types of visual matching games are useful, where the child is helped to place the “same” with the “same” and hears what it is called, by listening to the spoken word and seeing the sign. (Children with Down syndrome are often being taught signs to support their language development.) The stages in matching games are: a matching stage, a selecting stage and a naming stage (see box below). This way of teaching is very effective as it supports the child to learn in an errorless fashion, succeeding at each step, and it can be used to teach a whole range of new concepts throughout childhood. Remember to prompt the child as necessary at each step to ensure that they succeed as they learn.

Teaching new concepts through matching, selecting and naming

  1. Start with matching
    The child is asked to match by putting the object, picture or card with the one that is the same. This is the step in which you are teaching the new concept so it is important to use the appropriate language e.g. “This is a red circle, can you put it with the other red circle”. Once the child can match correctly, move on to selecting.
  2. From matching to selecting
    The child is now asked to select each of the items by name e.g. “Can you give me (or show me) the red circle?” Once the child can demonstrate correct comprehension of the words by selecting the items correctly, move to naming.
  3. From selecting to naming (using a word or sign). The child is now asked “What colour (or shape) is this?” as you point to one of the items. Continue until the child has named each of the items in the set.

Category words

It helps children to learn the concept if you use the category word - for example “these are colours” or “red colour” as well as the colour word “red”, and similarly use category words for shape and size, e.g. “What shape is this? Is it a square or a circle?” “What size is this? Is it big or small?”.

Coloured bean bags and a large piece of paper with coloured rectangles, or circles of colour with discs to match to them, make easy matching games in the early stages of colour name learning, when identical items are needed ( [Figure 9], [Figure 10] and [Figure 11]). In the author’s experience, colour learning is often helped by giving the colour name in print. When you know that the child understands the colour name and can demonstrate their understanding through selecting games, sort objects or items that share the colour feature but differ in other features.

! Bean bags for colour matching

Figure 9. Bean bags for colour matching

! Circles for colour matching

Figure 10. Circles for colour matching

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Figure 11. Child matching colours

Making books

Colour books are valuable too, with one colour per book, for example a “red colour” book, and a “blue colour” book. Use pictures of different items in each colour book, e.g. a red car, a red ball etc. to teach a new colour.

Similarly, number books can be for one number, “a number one” book up to a “number four” book, where the child sees several examples of items for a single number, all in the same book.

! Blocks for teaching attributes

Figure 12. Blocks for teaching attributes

When children can identify the colours and the numbers from the single concept books, the pages in the books can be mixed, to provide practice with different numbers or different colours in the same book.

Shape books can be created using the same principle, relating shapes to real objects in the environment.

Written words

In books, with pictures and with objects where there will be frequent repetition, the written words for numbers and other maths concepts as well as pictures and numerals should be presented on the page or on word cards. Children can see and read single words and also two and three words together, for example “blue car”, “red car”; “big yellow hat”, “small green hat”, paired with the picture.

! Shape work on the computer

Figure 13. Shape work on the computer

Combining attributes and ordering items

Logic blocks or similar educational materials are available in different shapes, colours and sizes and can be used to teach these concepts. They are also useful for teaching combinations of attributes in a sentence, by asking the child to select on two or three attributes at once (for example, “where’s the big, red circle?”) ( [Figure 12]). Children may have difficulty remembering a request with three criteria to process, so it will be important to write out or to repeat the sentence while they do the task.

The computer is a valuable aid to learning for children with Down syndrome ( [Figure 13]), and some suitable programs are listed in the references TODO: references 6

Ordering items requires a series of ‘comparisons of two’ to be made and involves looking, remembering and comparing skills, for example, for ordering in size. The number of items to be ordered can be gradually increased from three upwards. Items can be ordered on many features as well as size and number, such as the loudness of ‘noise’ the item makes, practising the vocabulary “loud” or “quiet”, or weight, “heavy” and “light”.

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Figure 14. Dolls for ordering games

The language and ideas for comparing, called comparatives, can be introduced in ordering games, for example “taller than”, “smaller than”, “heavier than” etc. ( [Figure 14]).

Extending children’s understanding of words for qualities or attributes of items (or people, animals or activities) beyond colour names, shape names, size (“big”, “small”) and number will help them to think about the concepts. Children will hear this vocabulary when they reach school if not before, and the more experience children with Down syndrome have, the faster they will learn.

These and other words and concepts will help to give children more elaborate ways of comparing and thinking. They will also help to improve the ways in which they can categorise information and improve their memory and language skills.

A range of vocabulary for qualities and attributes

As well as colour, shape and size words, use “quick”, “slow”, “round”, “square”, “rough”, “smooth”, “prickly”, “shiny”, “sparkly”, “soft”, “hard”, “bumpy”, “spotty” (dots), “dark”, “light”, “full”, “empty”, “hot”, “cold”, “lots of”, “a little”, “a drop”, “a bit”, “a lot”, “loads of”, “narrow”, “wide”, “long”, “short”, “tall”, “fat”, “thin” and “thick”.

Learning about ‘one-to-one’ correspondence through play

There are many games to play with young children that help them to learn about ‘one-to-one’ correspondence. This is necessary for learning how to use the number system to count and to share. The foundation for these skills can begin with playing with objects, toys and pictures that can be linked ‘one-to-one’, e.g. each toy at the party needs one plate and one cup ( [Figure 15]).

! Toys for learning about ‘one-to-one’ correspondence

Figure 15. Toys for learning about ‘one-to-one’ correspondence

Games for developing ‘one-to-one’ correspondence

Early quantity and counting through play

When playing games that use numbers and counting, use the words “how many” and “all” as well as the number in spoken sentences, so that children associate these words with counting and quantity.

In real meal or snack time situations, ask if your child wants “one x”, “two x’s” or other amounts, showing the choices on offer, or point to other people’s plates with the amounts on. Use your fingers to indicate “one” or “two” (or more) of something, and use the sign and word for “lots of” or “a lot of” for numbers over 10. Similarly, when children offer you something (like crisps) quantify your answer, e.g. “Three please” and hold up three fingers.

Early games for learning about quantity and counting

Beginning to understand money early

Children begin to learn about money by seeing people pay for things by exchanging money for goods - so it is important to take them out shopping and involve them. Play games where money is exchanged, using toy paper or card money to begin with, moving on to real coins or notes when safe to do so in supervised play. Play games of exchange with goods as well as exchange of money in pretend shop games. A pretend shop can be created, with items labelled, or you can give your child a picture (and word) list and shopping bag, for them to find toys or other items at home to place in their bag or basket and then pretend to pay you for them (and the other way around where the child plays shop keeper). Shopping games can help develop memory skills too and offer mobile activity that some children will particularly enjoy . Give children their own purse or purse belt with coins in, or give them enough money for them to pay for real items they like at the shop.

Using a calendar to begin to learn about time

Home-made calendars and timetables, that include written words, pictures or symbols for regularly occurring events, help children with Down syndrome to link ideas about time to the real, meaningful events that they experience. Home-made calendars can include words for days of the week, “morning”, “afternoon” and “night” and clock faces showing the times and words for important parts of the day, including “bed-time”.

The complexity of the calendar will vary for each child, but you can begin with squares for the days of the week, labelled with the written word and a photograph for each day to separate the weekend activities (or days at home) from nursery or child care days. This may be interesting if made as a ‘lift the flap’ chart, with the days of the week written on the outer flap. The calendar can be made more complex by having symbols or pictures and words for the separate activities of the days or evenings, when children are familiar with how to use the calendar. A pointer for “today” can be moved along each day, and for older children, “yesterday” and later “tomorrow” pointers can be added. The author suggests that a thick border is used between squares to show a “night time” slot, labelled with words and a symbol or picture of a child sleeping, so night time is visual, not implied. Showing “night time” as a slot becomes particularly helpful for understanding, counting and crossing off how many days, nights or ‘sleeps’ before a special event, like a birthday or holiday.

! Picture cards for matching and ordering

Figure 16. Picture cards for matching and ordering

Understanding number: a more formal approach

The basic ideas for learning about number come from noticing visual patterns, from learning about the order of the number system (how this always stays the same) and from counting experiences. Counting teaches children about number words as labels, the order of the number system and how to use numbers to find out how many there are.

Although counting is a complex task, children begin to learn it from an early age, and they should be encouraged to do so. However, learning to count will not necessarily teach children to understand the nature of the number system and there are additional activities that can be used to help them achieve this.

! Numicon ‘plates’ and pegs

Figure 17. Numicon ‘shapes’ and pegs

Children’s visual memory and visual learning strengths can be used to support their learning of all aspects of the number system.

Quantities or amounts can be practised and memorised as a whole, as well as being units “to count” ( [Figure 16]).

Children will be helped to ‘visualise’ or see number patterns by using a visual representation of the number, for example Numicon ‘shapes’, teaching materials and activities ( [Figure 17]). A Numicon ‘At Home’ starter kit is available and purchase details can be found on p. 18. The Numicon materials illustrate the number system by using a set of shapes designed to clearly show that each ‘next’ number is one more. In addition the shapes can be fitted together to illustrate addition and subtraction. Pegs are included for counting and pattern activities, and each shape has holes that the pegs can fit into. Matching the shapes to each other, selecting and naming them, associating numbers of items (the Numicon pegs and other items) with each shape, ordering shapes, associating numerals and number words with them, and finding the number and shape position on a number line, are all activities that will help to develop children’s understanding of number.

The importance of teaching and practice for number learning

Some young children with Down syndrome may find the pegs difficult to manage but most children will be able to achieve success with all these activities with some support.

Counting practice

The skills needed for successful counting have been defined as the one-one principle, the stable order principle, the cardinal principle, the abstraction principle and the order irrelevance principle TODO: references 7 ( [Figure 18]). These principles can be learned through structured games, including games with whole numbers, recognising patterns and other types of visual imagery.

More practice and explicit teaching may be needed to help children with Down syndrome understand each of these principles. Many children with Down syndrome in the 3 to 5 year age range have some understanding about one-to-one correspondence and stable order, although being asked to use both at the same time may be difficult, as in a task to count objects. As each skill becomes better learned, then the two can be used simultaneously to ‘count’.

  1. The one-to-one counting principle. The child must use one and only one number word for each item to be counted, and not skip any item or double count any item

! The one-to-one counting principle

  1. The stable order principle. The child has to know the number words in the correct order and always use them in the correct order when counting

! The stable order principle

  1. The cardinal principle. The child understands that the last ‘count word’ represents the number of items in the counted set. At this stage, the child can answer “How many are there?” questions correctly and can give small sets of items correctly in response to “Give me … (2, 3 or 4) …” questions.

! The cardinal principle

  1. The order-irrelevance principle. The child understands that the order in which items are counted is irrelevant

! The order-irrelevance principle

  1. The abstraction principle. The child now understands that any items can be counted (i.e. that quantity is a concept which can be applied to any type of items). Once they realise that the spatial arrangement of the items is also irrelevant they are said to understand “conservation of number” - a significant Piagetian step in cognitive development.

! The abstraction principle

Figure 18. The “how to count” principles - and steps in understanding number, based on Gelman and Galistel. TODO: references 7

Pointing at pictures

! Cards for pointing to count

Figure 19. Cards for pointing to count

Children can be helped in the early stages of counting by counting from items in pictures and pages in books. They are not then required to hold or move an object, only to point once and move on to the next one. This game can be modelled and is copied easily by most young children with Down syndrome ( [Figure 19]).

Keeping track

Children can be helped to keep track of procedures when counting objects, by placing items already counted in a separate pile or systematically counting in one direction. They can be taught that one word goes with one item and to point to each item only once. Encouraging children to slow down can often reduce counting errors, as can increasing the size of spaces between items and using items that are not too small to hold and do not roll on flat, smooth surfaces.

Counting objects laid out in a line is easier than objects scattered about. Once your child can count in a line, try practising counting objects laid out in different patterns, which require the child to keep track of counted items (e.g. in square, triangle, zig-zag or randomly arranged).

Daily counting games and routines

If your child has learned regular patterns for numbers (e.g. Numicon shapes) objects can sometimes be arranged into these patterns, so that the child can see, reinforce and use their knowledge about the relationship between pattern and number.

Learning the number words in order

It is important that children learn the number words and how to rote count. As well as counting during play, you can develop a daily routine to practise counting skills.

The following activities will support the first stages of learning to count and will be useful for supporting later understanding of “how many”.

! Matching numeral cards

Figure 20. Matching numeral cards

! Counting with a number line

Figure 21. Counting with a number line

! Matching cards to a number line

Figure 22. Matching cards to a number line

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Figure 23. Counting with a number line

Counting with a number line will help to establish the order of numbers and help children learn to say number words more clearly through practice. Young children should first use the number line to learn the sequence of numbers to 10. Some children may also begin to practise hearing, distinguishing and saying numbers to 20 with a visual support, provided this does not confuse their learning of numbers to 10 ( [Figure 23]).

Learning about quantity

Visual cues for learning

Understanding quantity and the labels applied to differing amounts requires considerable practice, and matching games or games with prompts or visual cues for quantity will help children to learn this skill. Numicon activities can help, as the shapes are a guide to the quantity represented by each number.

! Matching numeral to a plate

Figure 24. Matching numeral to a shape

Games to teach number and quantity with Numicon:

Numerals

Even before numerals can be identified reliably, the use of them may help children remember amounts, therefore use number cards or labels to place on containers or on the table as a prompt ( [Figure 26]).

Matching quantities to numerals

! Ordering Numicon plates

Figure 25. Ordering shapes

Children can also be taught about quantities by using ‘errorless’ learning methods, being offered only the correct amount of items to match to the numeral (or shape). For example, a child may be asked to put two and three items into containers (labelled with the numerals 2 and 3) with 2 and 3 items placed near each container.

Children may need help to understand the abstract nature of numbers - for example that groups of the same number but different types of objects are all sets of ‘3’. Explain this to them by showing them several groups of 3 objects, counting each set and placing a numeral ‘3’ with each set. Do the same with other numbers, first 1 to 5, then 6 to 10.

! Numeral shown with set of 3 items

Figure 26. Numeral shown with set of 3 items

‘Giving’ the whole set

To build their understanding of cardinality, children can be asked to give the whole amount of items that they have (with numeral shown) for small sets of 2, 3 or 4 items. For example, using the materials pictured in Figure 26, the child is asked “Can you give me 3 eggs?”

‘Giving’ a number of items from a larger set - leaving some behind

Children also need to understand that when asked for a number of items from a group this does not mean count or give all of the objects. It means give some and leave the rest ( [Figure 27]).

Games to practise counting part of a set and leaving some uncounted will help to teach this. Children should be supported in these games at first, so that they do not make errors, and get used to leaving some items behind. It is the author’s view that children may not receive enough modelling or practice in this type of activity. Usually early counting games require the child to count “all” in a group and they then find it hard to stop counting part way, in order to “give” a smaller set from a larger one.

! ‘Giving’ 3 items from a larger set

Figure 27. ‘Giving’ 3 items from a larger set

Children should be supported by a written numeral when asked for a set amount so that they do not forget the number they have been asked for. Having the number symbol in view for children will help them to remember and stop when their count matches the number requested.

“How many” covering and remembering games

When children have practised matching the correct amounts, practise remembering “how many” there are, by telling them how many items there are, for example “1,2. There are 2 (eggs)”. Then cover the objects (or pictures of objects). Make it fun by saying “How many (eggs) am I hiding?” If they do not answer correctly, reveal the pictures or objects and say “Look, there are two (eggs)”. When your child is successful at this task, let him or her count the items before covering them up. This task can be continued, gradually adding variations, so the child is helped to understand that counting tells us “how many” of something there is.

Rearranging the same set, ‘guessing’ and counting again

Games where the objects are counted, a numeral presented and then the same objects rearranged, followed by asking the child how many there are now, will help to develop a more conceptual understanding of number (conservation of number). Repeated counting of a set of items laid in different arrangements in this way, with discussion with an adult, will allow the child to realise that no matter what arrangement they are in, four items are still four items.

Making one more, one less, adding and taking away

When children have an understanding of the number system (to 10) and how numbers relate to quantities they can practise moving up and down the number system, and learn the meaning of “one more” and “one less”. They can begin to understand about how joining quantities together and breaking them up makes different quantities, (and that these have consistent relationships, i.e. 2 + 2 = 4, 1 + 3 = 4). These more advanced skills and activities will be described in the module for children aged 5 to 11 years.

In summary

The games and activities for teaching children about numbers in their early years should be fun and encourage an interest in learning. Developing children’s language understanding is an essential part of early maths learning and methods for promoting the development of language skills should be incorporated into pre-school maths activities. Maths activities will also promote children’s more general language and cognitive development.

The children’s visual learning strengths can be used to support learning about number and maths. Learning will also be influenced by daily activities and play with the support of their families and carers.

Developing an enjoyment of maths through play, visual and language learning games will help children to join in and progress when they go to school, as well as laying the foundations for understanding the system of number.

Introducing the language, ideas and relevance of time and money in children’s early years, together with more typical number and early maths concepts, may help children with Down syndrome to master these areas of abstract measurement and problem solving that are currently challenging for the majority of young people with Down syndrome.

See also:

[these links will take you to the relevant product page at the DSE International Online Shop]

Checklists of vocabulary and number skills

Vocabulary lists

During everyday talk, play and teaching activities children are likely to be introduced to many of the words in the following vocabulary lists. They may not understand all of these words at the age of 5, but learning about some of the less common words and ideas will help to develop their language and mathematical skills. Please think about the words that you use and try to use them in ways that help children understand what you mean.

Down Syndrome Vocabulary Checklists

If you are using Down Syndrome Education International’s vocabulary checklists, the following words are included.

Number vocabulary table

Many other words that will be used in school, including instructional words to help children participate in activities, are presented in the [Number vocabulary] table below.

Number vocabulary | | | Number and related words | | number words
same number/s
different number/s
number line
dice
dominoes
pegs, peg board
zero, one, two, three… to twenty and beyond
none
how many…?
count, count (up) to
more, less
how many times?
pattern,
pair
‘teens’ number
the same number as, as many as
altogether
one more, take (away),
leave
the same as
| | Measures | | size, big, small
enough, not enough
long, short, tall
wide, narrow
deep, shallow
thick, thin
ruler
weigh
heavy/light
full
empty
holds
container
| | Time words | | birthday, holiday
morning, afternoon
night
bedtime, dinnertime, playtime
today, yesterday, tomorrow
before, after
first, next, last
now, soon, early, late
quick
fast
slow
old
new
hour, o’clock,
clock, watch, hands
once, twice
| | Shape words | | shape, pattern
flat
straight
round
corner
circle
triangle
square
rectangle
star
hexagon
diamond
| | Position, direction and movement | | in, on
over, under
above, below
top, bottom, side
on, in
outside, inside
around
in front, behind
front, back
before, after
beside, next to
middle, edge
left, right
up, down
forwards, backwards
through
to, from, towards, away from
movement
slide
roll
turn
stretch, bend
number
| | Money words | | money
coin
penny
buy
spend
pay
change
names of coins (1p, 2p)
| | Instructional words | | match
listen
give me
join in
your turn, my turn,
say
remember
start
look a
point to, show me
put
find
choose
make, build
tell me
read
finish, end
count
answer |

A checklist for early number skills

How to use the checklist

The checklist is divided into sections for learning about:

  1. Number
  2. [Counting]
  3. [Quantity]
  4. [Cardinality]

There is also [a list for those using Numicon].

Activities are graded in difficulty within each section but activities from each section should be undertaken simultaneously.

For example, a child may be practising activities every day from 1c, 2c, 3a, 4a and 5, these being:

Examples of the activities and teaching methods are described in the text of this module. Numicon activities and games are described in detail on activity cards purchased with each kit, and can also be bought separately from the main kits as children progress and additional activities and equipment are needed.

1. Number

The written numerals are used from the start for children with Down syndrome, as they will benefit from the visual cues to aid the learning of the spoken number names.

1a. To recognise and name numerals to 10

1b. To recognise and name numerals to 10

1c. To say numerals in order, following a number line to 10

1d. To order numerals to 10

1e. To say number sequence ‘by rote’

1f. Repeat stages 1a to 1e for numbers 10 to 20.

2. Counting

2a. Matching: one to one correspondence (early materials)

2b. Counting: one to one correspondence

2c. Counting: one to one correspondence and correct number sequence

2d. Language for counting

3. Quantity

3a. Matching quantities to 5, one to one correspondence (later materials)

3b. Ordering

3c. Matching numerals to amounts

4. Cardinality

4a. Cardinality to 3

4b. Cardinality to 10

4c. Producing the answer confidently

5. Numicon activities

References

  1. Geary, D.C. (1994). Children’s Mathematical Development. Washington : American Psychological Association.
  2. Nunes, T., and Bryant, P. (1996). Children doing mathematics. Oxford : Blackwell Publishers.
  3. Wing, T. (2001). Serendipity, and a special need. Mathematics Teaching. *Quarterly Journal of the **Association of Teachers of Mathematics*, 174, 27-30.
  4. Numicon ‘At home’ and Numicon Nursery Kit published by Numicon Ltd., available from The Down Syndrome Educational Trust.
  5. Picture lotto available from The Down Syndrome Educational Trust.
  6. Computer software, including Speaking for myself, 123-CD, Jemima, and Tizzy’s Toybox available from The Down Syndrome Educational Trust.
  7. Gelman, R., and Gallistel, C.R. (1978). The child’s understanding of number. Cambridge, MA : Harvard.

Acknowledgements

The author would like to thank Sue Buckley, Vikki Horner and Jo Nye for their helpful comments.

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