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Mathematics Teaching Self-evaluation Tools

You are viewing a limited version of the NCETMâ€™s self-evaluation tools. Any answers you save during this session will be removed after seven days. Log in or sign up to view, and use, the full version of the tools.

For the following questions, select the statement which most accurately matches your level of confidence (1 is not confident and 4 is very confident) or choose from the alternatives detailed in the question. You do not have to answer all questions. Your answers will be saved so you can exit and come back to your self-evaluation at any time. Click Save and Results to view the next steps for questions you have answered.

1.

How confident are you in understanding and recognising that very young children:

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a.

are aware of quantities and counting?

Very young children are often attracted to the largest group of something they like (toys, sweets) and will pull a face if someone tries to take things away or even things out.

Additional User Example

As a child counts they touch an object showing an aware of relating concrete items with abstract numbers. Three objects equals number three.

Additional User Example

When giving out treats children will often ask for a larger number than the one that they have been given in the hope of acquiring more eg child is handed one biscuit and will say 'can I have 2 biscuits'.

b.

begin to know and use number names?

As soon as they begin to talk, children will include familiar number words in their speech, such as ages and house numbers. For children with English as an additional language (EAL), bilingual support can help nurture this development.

c.

develop schemas to help them count?

A schema is a consistent pattern of behaviour which a young child develops to help make sense of the world.

For example, children often repeatedly put things next to each other and/or line them up in free play. Such actions help children to organise their counting.

2.

How confident are you that you understand:

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a.

the counting principles?

Children have to learn how to do a number of things consistently in order to count successfully. These are the counting principles.

Stable order

The stable order principle refers to the understanding that numbers must always be said in the same order, i.e. 1, 2, 3, 4, 5 and not 1, 3, 2, 5, 4.

Children count spontaneously from an early age, often saying the numbers in the wrong order. Collaborative play with an adult or older child helps them to develop stable order counting. Counting things out loud and making deliberate mistakes is very effective in helping children to learn the correct counting order.

One-to-one correspondence

One-to-one correspondence refers to the ability to match one object to one number consistently. Without this skill, children will not be able to understand how many objects are in a group (the cardinal value).

Cardinality

Understanding the cardinality principle means that a child appreciates that the last number counted indicates how many things are in the set.

Abstraction

As children become more competent at counting, they begin to understand the abstract nature of number. They can count 5 apples, 5 assorted things from their pocket and even things they cannot see such as 5 steps up to their house or 5 bangs on a drum.

Order irrelevance

Many young children think that counting from one end of a collection of items will give a different answer from counting from the other. Group counting games, along with opportunities to count many different things in different settings, helps them to appreciate that the order does not matter. This is a crucial piece of knowledge when calculating with much larger numbers.

Additional User Example

Ordering numbers

Use a washing line and ask childen to peg the numbers in order on the line.

b.

subitising?

Subitising is the ability to recognise how many objects are in a set without counting. Many young children have this ability for small numbers. Acknowledge and encourage this ability by helping children to spot regular patterns on familiar objects which do not therefore need to be counted. Spots on dice and candles on a Menorah are examples.

Additional User Example

Some children recognise that one hand has five fingers or that we have two eyes two ears without counting.

3.

How confident are you that you can support children to develop counting skills:

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a.

knowing number names and sequencing numbers in order?

Children need to know the words for each number and be able to put them in order.

Working with a group of children and counting together the number of steps each one takes to cross the playground lets them practise the words and learn the sequence.

Children with EAL should have opportunities to count in their home language as well as in English.

b.

saying numbers to match counting and touching or moving objects being counted?

Providing objects to count in a variety of situations helps adults to see whether children are able to move them about to assist the count and match a number word to an object.

For example, children might help count pieces of fruit for snack time to see whether there are enough, or count animals in a book or beads in a box.

They can be encouraged to touch and move items being counted, which will improve accuracy.

Additional User Example

Counting cakes to be shared with a group or biscuits, on special occasions.

c.

organising the count?

Collections are much easier to count if they are organised systematically. Give children experience of this through activities such as planting seeds in partitioned trays, hanging cups on hooks, etc.

d.

coordinating all their skills, saying and matching numbers to objects counted?

Many activities in an early years classroom give children valuable experience in coordinating all their counting skills.

When organising some painting, ask children to fetch the materials which they need, rather than putting them out beforehand. They can then practise one-to-one correspondence by carefully placing brushes and saying and matching a number to each one counted.

Additional User Example

Organising their table for what they need e.g. pencils, colouring pencils, rubbers and paper. Counting how many pencils and paper are needed for each person on the table.

4.

How confident are you that you understand and recognise progression in children’s counting from knowing the basic skills to understanding key concepts such as:

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a.

cardinal value?

Encouraging children to practise counting in context helps them to have a better understanding of counting principles and moves them on from having to work on each skill separately.

When children can count a collection (of pencils, name tags, aprons, etc) and respond correctly to the question ‘How many?’ they have understood that the last number gives the cardinal value of the group. Those who have not quite grasped this may well give the entire sequence (1, 2, 3, 4) rather than the final number (there are 4).

Additional User Example

Counting at snack time and asking a child on a table "how many want milk/water?" The child could answer what is required on her table e.g "Four children want milk and two want water."

b.

self-checking counting?

A child who recounts and checks a set of aprons before handing them round to her friends has also progressed to understanding key concepts of counting.

5.

How confident are you that you understand and can support:

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a.

the difference between numerals and numbers?

A numeral is a digit, which is a single symbol. There are 10 in the European counting system: 0,1,2,3,4,5,6,7,8 and 9.

The counting numbers are an infinite set. They are made by combining numerals. A 3, a 6 and a 9 can be used to make 369, 936, 963 and so on.

b.

the language of counting?

As children learn to speak, they develop their own ways of counting. Adults can build and extend this early vocabulary through joining in the conversation and rephrasing what they say.

‘I’m putting teddy and panda and giraffe in the box. One, two three!’

‘You’ve put them all together: one teddy, one panda and one giraffe. That makes three.’

Additional User Example

Counting songs e.g. 1, 2, 3 once I caught a fish alive or 5 green bottles sitting on a wall.

c.

number and counting rhymes?

Number and counting rhymes are an ideal way to extend children’s language, because they have learned many at home and can sing, chant and practise in a relaxed way. Offer a variety from different heritages and cultural traditions, in English and other languages.

Additional User Example

Singing nursery rhymes like 10 green bottles hanging on the wall and if one green bottle should accidently fall, there is 9 green bottles hanging on the wall and so on.....

d.

counting on?

Counting on is a strategy used in addition.

Children should be able to use the strategy first in play contexts. A child may throw 5 balls into a bucket and then be offered some more to try: ‘I’ve got 5 and now I’ve done 3 more. That’s 8.’ An adult might introduce the word ‘altogether’.

e.

counting back?

Counting back is a strategy used in subtraction.

“A space craft launch is a useful way to practice counting down - 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 lift off! In this way you can begin with different starting numbers as pupils become more confident.

Another way to develop the idea of forwards and backwards counting is to have a number ladder painted on the ground in the playground. Pupils can jump forward counting as they go and then jump down the ladder counting backwards. In this way you can also begin counting up and counting back in 2s. From the ladder on the ground pupils can then be given counting ladders on paper to use their pencils/crayons to make jumps forwards and backwards.

User Example I would teach the class a song such as "10 green bottles sitting on the wall, 10 green bottles sitting on the wall and if one green bottle should accidently fall there'd be 9 green bottles sitting on the wall, etc...."

f.

numbers as labels?

Not all numbers are in the context of counting. Numbers as labels are those found written on birthday cards, clocks and doors.

Additional User Example

I would also use buses, eg: Ask the children what number bus did they travel on to get to school, home or shopping etc. You could also emphasise it as a label, eg: The 72 bus goes to Roehampton etc.

g.

the use of number lines?

Both horizontal and vertical number lines are a useful reference point for young children learning about counting, calculation and numbers. They support the beginnings of understanding that numbers represent a continuous quantity as well as discrete counting numbers. This suggests the possibility that other sets of numbers may exist between the counting numbers (fractions, or rational numbers).

Eventually, children appreciate that every point on a line may be given a numerical value, which is essential to know when drawing graphs, etc.

6.

How confident are you that you understand how children learn about number through everyday experiences and can provide:

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a.

opportunities for children to learn through play?

Children need a wide variety of resources and artefacts to stimulate their mathematical development, just as an attractive book corner stimulates language development. Offer tape measures, money, scales, cups and jugs and clocks of different types to enhance role-play.

It is important to allow children to use the things in their own way and make their own meanings, even if this is not quite what the adult had in mind.

b.

a â€˜numeracy-richâ€™ environment?

A numeracy-rich environment is one where children have many opportunities to engage with numbers in purposeful activities. Encouraging children to become independent and have some say in their learning is an obvious way to do this.

Allow children to choose and count out resources for their chosen activities and organise the environment so that they see numbers in use. Having a limit to children at the water tray, number of bikes used at any one time and places at each dining table make children aware of the need to count and check and match items (cups, plates, bikes) to number labels.

Planning the curriculum to enhance mathematical understanding may involve a visit to a library, or clinic, backed up by simulated settings back in school. Rubber stamps, calculators and money give children opportunities to stamp books, calculate fines for overdue items and record the transactions, while charts, thermometers, baby scales and bandages allow them to integrate mathematical thinking in a rather different context.

Adults can further enhance the environment through carefully planned interventions, which include a focus on mathematical language and counting and recording skills.

7.

How confident are you that you understand the significance of and can develop:

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a.

childrenâ€™s mark making and â€˜number writingâ€™?

Children make marks to represent mathematical ideas in much the same way as they use emergent writing. The following activities offer children opportunities for writing numerals, using numbers as labels and representing imagined and counted quantities:

making birthday cards;

numbering the chairs for the queue in the vet’s waiting room;

having writing materials available throughout the setting for children to record their own ideas about quantities and numbers and things which they are counting.

Additional User Example

Home corner of a shop where thing are priced (labels with price tags e.g. 2p) for children to buy things using toy money.

8.

How confident are you that you can provide opportunities through play involving the number sequence so that children can:

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know some number names?

Young children learn about numbers by being involved in experiences and activities that involve numbers, an environment where numbers are part of the role play, the pretend play and in the books that are read to children. You can draw children’s attention to numbers in stories by emphasising the number.

Once upon a time there were THREE (show three fingers) little pigs.

b.

know the order of the number names?

It is almost impossible to count anything successfully unless you know the number names in order. Many children learn different parts of the number sequence and fill in the gaps with random numbers before they learn to join up the sequences. Singing and using finger play and number rhymes to recite a number sequence all help children learn the order of the numbers. Make sure that some of the rhymes can be sung backwards.

Additional User Example
I would teach them a song such as "1,2,3,4,5 once i caught a fish alive, 6,7,8,910 then i let it go again".

Additional User Example

Number songs are a great way to do this and there are loads of them - one way to emphasis numbers is to use puppets or other hand props while singing these (such as "Ten little monkeys jumping on a bed"; holding up 3 bags when singing "Baa Baa Black sheep"). These props can be used by the adult leading the song, by the children or interactively (e.g. the children taking a monkey from the adult in "Ten little monkeys" each time one falls off the bed). Loads of resource and toys shops now sell props suitable and often tailor-made for such nursery rhyme sessions but they can also be easily and cheaply "homemade" or why not get the children to make them.

c.

know what number comes next?

Children learn the number sequence by counting alongside others and learning the rhythm of the count. Without that support it is much more difficult to say the number that comes after a particular number. Initially children will each time go back to ‘one’ and start counting again. Play a game of teaching the puppet to count. Encourage children to tell the puppet what number comes next when he forgets or says the wrong number.

d.

know ordinal numbers (first, second, and so on)?

Children start by knowing ‘first’ and ‘last’ words and as they become more familiar with the number sequence they are able to use more sophisticated ordinal language. Create opportunities for children to line up dolls, cars, bricks and beads. Discuss with them what they put first, what second and what last. Use dance and gym times to discuss the order to dress and undress: What will you take off first, your socks or your shoes?

9.

How confident are you that you can provide opportunities through play involving organising counting so that children can:

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synchronise number words and pointing?

Once children are at home with knowing parts of the number sequence they need to come to terms with the complex task of counting how many objects there are. This includes pointing or touching the objects one at a time, and saying one counting number for each object. Provide an area with a wide range of materials for children to organise and count. Dramatise counting songs by providing props such as frogs for children to act out the counting.

b.

count each item once and once only?

Unless you move an object when you’ve counted it, you may not be sure you’ve counted it. Show children how to move objects out of the way as they count. This is much harder when you have to count pictures, because you can’t move them. Discuss with children how to be sure which picture they have counted. Use number track games to give children opportunities to count jumps along a track or move an object. Discuss with children strategies such as lining things up or positioning objects on a number track to make sure that each item is only counted once.

Additional User Example

Using an abacus gives a good introduction into moving items as you count them.

Additional User Example

Moving a group of children from one area to another. For example start with 10 children and ask one child to move say 5 children to a circle shape on the ground, one at a time. Start again with another child and asking that child to move 3 children but one at a time to another shape placed on the ground.

10.

How confident are you that you can provide opportunities through play involving understanding counting so that children can:

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subitise (recognising a small number of objects without counting)?

Subitising is an important link in children’s understanding of number and their recall of a particular spatial arrangement. Play lots of board and collecting games that involve using a dice and dominoes. Create situations where children need to estimate with counting.

b.

say how many things there are?

Two concepts involved in understanding counting are that children need to realise that they can count objects in any order and that even if the objects are rearranged the total will be the same. They also need to understand that the final number said describes how many.

It takes a while for some children to understand that the answer to the question ‘how many?’ actually means ‘give the total’ and not ‘count them again’. You can support children by modelling both the question and the answer.

Additional User Example

When doing any activity involving counting, change your tone of voice for the last number, emphasise the last number, confirm the total.

c.

count a number of things out from a larger group?

Children soon learn to count the number of objects in a particular set but it usually takes longer for them to develop the skill of counting out objects from a larger group. This requires them to remember the order of the numbers, coordinate that with counting the objects, and remember at what number to stop counting.

Additional User Example

Set up a home corner of a shop with a child selling number of things from a larger group e.g. 5 apples from 10. Or another child buys 5 apples using 5 pennies from 10 pennies.

11.

How confident are you that you can provide opportunities through play involving having a purpose for counting so that children can:

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understand why we need to count?

As children become more experienced in counting you need to give them time, space and lots of opportunities to count a wide range of objects in many different situations so that they know what counting is used for: to find out how many there are.

12.

How confident are you that you can provide opportunities through play involving recognising numerals so that children can:

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recognise significant numbers?

Children begin by recognising numerals that are of interest to them and name them. Examples include numbers such as their age, reinforced by birthday cards with the number printed on them, and hearing family and friends saying she’s four, he’s three. Other numbers that children might recognise are numbers on their family’s front door, or the number of the bus they get to Granny’s house.

Additional User Example

Go number spotting with children and discover how many numerals you can find and ask children to look for numbers at home e.g. telephone, computers, car number plates, clocks, etc.

b.

link numerals to amounts?

When children match numerals and amounts, although they might recognise some numerals, they often use their own personal symbols instead of the conventional ones when they are writing.

Additional User Example

Set up a situation where the children are going to invite some friends to play. They are going to decide what they need when the friends come around. For example if they are going to have a teddy bear picnic they will need:

enough teddies for each person at the picnic,

enough napkins for each person at the picnic,

enough drinking cups for each person at the picnic

enough plates for each person at the picnic

enough cakes for each person at the picnic

and enough balls to play a game after the food for each person at the picnic.

If you set up the picnic hampers with the number of people at that picnic and children could then collect the right number of objects and put them in the basket. The class can then check that each picnic hamper was packed correctly by looking at the number and counting each set of objects.

Additional User Example

Packing a suitcase for a holiday. Need to consider for how many days to pack for e.g. 7 t -shirts, 3 shorts, 4 skirts, 7 pairs of socks, etc.

13.

How confident are you that you can provide opportunities through play involving recording numbers for a purpose so that children can:

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represent numbers with pictures, tallies or numerals?

If you give children opportunities to create their own systems and strategies for recording and solving maths situations, such as There are 5 aprons and 6 children. Will we have enough? Their solutions will make more sense to them.

Children’s mathematical graphics are their own form of mathematical marks. By working alongside children and observing and joining in with their activities, you can see when they use their own marks, tallies or some representation of standard symbols. For example, if children use a simple form of tally, you could encourage them to organise the marks to make counting easier. For children already using recognisable symbols, model the standard written form in a shared activity to help them progress.

14.

How confident are you that you can provide opportunities through play involving forming numerals so that children can:

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internalise the shape of numerals?

Children need to become familiar with the shape of numerals and to recognise them in different mediums. Provide numerals in range of materials for children to touch and feel and identify.

Ask them to make the shapes of the numbers actively in the air or on each other’s bodies.

Additional User Example

A paint brush and water can be used to "paint" the numbers outside on fences, walls and the ground. Alternatively a sand tray and a finger also work well.

Additional User Example

Hiding large numbers behind Humpty Dumptys wall (a large laminated wall card) - slowly reveal the number, one bit at a time, talking about the shape of the number as it emerges.

Additional User Example

Plastic numbers in a water tray for children to discover in the water or bikes with numbers on which are parked in corresponding numbered area.

b.

write the numerals?

Children can learn to write the numerals as part of a shared writing activity. Support children in learning to write numerals by introducing activities where scores need to be kept or a record made of how much of each item has been collected.

Additional User Example

Take a group of children on an Autumnal walk with clip boards counting and writing what they pick up e.g. cones, different leaves/flowers, etc.