#secondyearmaths

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PED2022 - Maths - Session 10

Early Years 1: Continuous Provision and Role Play

What do we need to know about Early Years?

–   Transition

–   Differentiation

–   Mixed age phases

Areas of Learning and Development

The Early Years Foundation Stage Framework specifies seven areas of learning and development

Mathematics forms one of the core areas of learning and development and the aspects are: numbers, shape, space and measures.

Key Documents

EYFS Development Matters document published in 2008.

Non-statutory guidance supporting the implementation of the EYFS framework. Underpinned by four themes:

–  A Unique Child

–  Positive Relationships

–  Enabling Environments

–  Learning and Development.

Early Years Outcomes was published in 2013.

Non-statutory guidance – useful reference tool for practitioners. Supports practitioners in making best-fit judgements about a child’s development. However, it does not mention two of the four themes in the EYFS development matters – positive relationships and enabling environments.

The positive relationships section within the EYFS Development Matters highlights the importance and the role of the adult in a child’s learning; this provides key ideas for practitioners in supporting a child.

The enabling environments column supports practitioners in providing a positive and rich learning environment for the children to extend learning opportunities and suggests next steps for development.

Another area missing from the Early Years Outcomes document is the Characteristics of Effective Learning, which are:

–  Playing and exploring

–  Active learning

–  Thinking critically

The Early Years Outcomes document is specifically mentioned in OfSTED’s guidance.

Thus both documents should be used alongside each other in order to fully support children.

What is Early Years Pedagogy?

•       The EYFS promotes mathematical learning through play.

“Play is undoubtedly enjoyable for young children owing to the freedom it facilitates, the sense of ownership it affords, and the self esteem it promotes. Through play children can repeat, rehearse and refine skills, displaying what they do know and practising what they are beginning to understand”

-          Tucker, K. (2010) Mathematics Through Play in the Early Years. London: Sage.

Mathematical Learning in the Early Years Foundation Stage

Pilot school for the Foundation Phase in 2004 at an infant school in Wales: how the nursery and Reception classes are ensuring mathematical development within the play-based curriculum.

Learning mathematics through role play

Children can:

-          Explore various mathematical concepts related to money, capacity, size, weight, one-to-one correspondence.

-          Use mathematical vocabulary e.g. how much, full, empty, need more/less, heavy, light.

-          problem solve through imaginative play e.g. how much money will I need to buy this item? How many cups will I need for the family?

-          develop concept of time – breakfast, dinner, bed-time, time in doctors surgery. Refer to clocks, watches.

-          order, sort, match in role-play area.

Planning for role play – Group Activity and Presentation

Create an activity using role play which can support children’s learning in Mathematics.

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PED2022 - Maths - Session 2

Individual Needs

Teaching children for whom English is an Additional Language (EAL)

As teachers, we need to decide whether it is the language or the mathematical concept that the child cannot understand. How might reading or language difficulties affect children? Pupils with difficulties with language are often placed in lower sets/ groups for maths. Is this fair?

Possible Difficulties

·         Writing

·         Articulating their ideas

·         Understanding grammar

What helps?

·         Step by step modelling

·         Use objects and visual images to help understanding of abstract ideas.

·         Group with children who are good role-models in terms of speaking English.

·         Over emphasis of key vocabulary through facial expressions and hand movements

·         Ensuring examples are taken through to the end result. Don’t assume children will be able to finish them off.

Summary

·         Assess children in their own language before they begin

·         Provide adult support in their own language if possible

·         Pair children with like language or similar languages

·         Model the mathematics through to the end

·         Use a range of visual resources that focus on the numbers and symbols

·         Provide key vocabulary in English and their own language (try L.As, S.E.N.C.O’s, teaching assistants or parents to support with this)

·         Learn to count in other languages!

 Dyscalculia

Low Attainers

Children with SEN are not necessarily low-attainers in maths and low-attainers are not necessarily identified as SEN children.

 The National Curriculum states that: ‘Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on’ (DfE 2013 p88).

 Considerations for Low Attainers

Language – Lexical ambiguity - Where words such as face, table and difference have different mathematical meanings to those that exist in everyday life. The word ‘difference’ can be particularly problematic.

Use of mathematical equipment - Mathematical equipment. Have children been given sufficient opportunities to work with the equipment that they have been given? Consider giving pupils choices about which equipment they wish to use.

Practical activities - With regard to practical activities, the role of the adult is very important. Practical activities offer opportunities to listen, observe and question pupils in order to glean a better understanding of the strategies that they pupils use.

How instructions are presented - Although keeping instructions simple and perhaps verbalising them to avoid difficulties in reading might seem like a good option, this could lead to pupils not thinking for themselves and being unable to attempt tasks where the instructions are not crystal clear.  

Model tasks carefully

Ensure that tasks are presented in different contexts - Just because a child can work successfully with numbers in one context does not necessarily mean that they can do so in another.

 Autistic Spectrum Disorder – Considerations

Resources labelled and kept in the same places - Of course this could have negative implications in terms of developing a child’s independence.

 People with ASD are often highly visual in terms of their processing style - This can be a double-edged sword – things like counters, arrays and number lines could be very useful aids but a brightly coloured display could be quite distracting.

Language processing ability - This might entail literal interpretations of instructions, difficulties in processing long instructions, repeating back what has already been said.

Difficulties in transferring knowledge across contexts - Ensure pupils are given plenty of opportunities and support to apply what they have learned to different contexts.

Number of questions - Particularly relevant to maths is how many questions the child is expected to complete. Careful assessment of a pupils’ prior attainment will be helpful in determining the correct balance.  A Child with ASD might find it difficult to cope with not completing a sheet of questions or feel pressured to complete them all and thus rush their work.

 Able, Gifted and Talented Pupils

Within the document "Effective provision for gifted and talented children in primary school" (DCSF, 2008) the definitions of able, gifted and talented pupils are:

–   Able students show ability in across many subject areas;

–   Gifted students are more able academically in one subject

–   Talented students are more able artistically, in sports or in performance.

–   However, there is no such thing as a typical able, gifted and talented student and the title covers a diverse group of students with a range of attainment.

Characteristics of able children in maths

According to DfES Guidance, some of the following traits are present in more able children:

–   Knowledge applied in new contexts

–   Systematic working

–   An ability to generalise patterns and relationships

–   Ability to make connections

–   Can pose own questions

–   Ability to reverse mathematical processes

How the needs of the able can be addressed?

–   A teacher who is knowledgeable

–   Suitable material that will challenge them. Learning to deal with occasional failure is part of the learning process.

–   Sensitive guidance through problem solving rather than direction – to be allowed to think for themselves

–   Freedom to approach problems in their own way

–   More abstract material

–   Encouragement to explain their ideas to others as well as opportunities to work with children of similar abilities

–   Not be made to feel 'different'

Why is it sometimes difficult to identify very able children?

–   Some able children don’t want to be identified

–   Provision of inappropriate work

–   Belief that mathematical ability is very rare

–   Very able children who are given extension tasks that are more of the same may learn to complete tasks in the given time rather than at their own speed

–   Teachers not appreciating incorrect but creative responses from the children.

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PED2022 - Maths - Session 1

Errors and Misconceptions

Errors

Errors in mathematics may arise for a variety of reasons.

They may be due to:

- The pace of work (Hansen, 2014)

- The slip of a pen (Hansen, 2014)

- Slight lapse of attention (Hansen, 2014)

- Lack of mathematical knowledge (Ryan and Williams 2007)

Misconceptions

Errors can be caused by many different things.

The ones that are caused by a deeper, underlying lack of mathematical knowledge are known as misconceptions.

Causes of Misconceptions

Experience – children bring to school different experience. Mathematical errors may occur when teachers make assumptions about what children already know.

Expertise – when children are asked to complete tasks, there is a certain understanding of the basic ‘rules’ of the task. Misconceptions may occur when a child lacks ability to understand what is required from the task.

Mathematical knowledge and understanding – when children make errors it may be due a lack of understanding of which strategies/ procedures to apply and how those strategies work.

Past experience– Misconceptions may occur when a child uses past experience to contribute to a mathematically incorrect answer.

Attitude and confidence – the child’s self-esteem and attitude towards their ability in mathematics and their teacher may impact on their performance. This could be related to their relationship with the teacher.

 The Teacher and Mathematical Misconceptions

Attitude and confidence – As with the child, if a teacher lacks confidence or dislikes mathematics the amount of errors made within the teaching may increase.

Imagination and creativity – A less confident teacher is more likely to teach using procedural methods. This may stifle children’s ability to use alternative methods because the teacher may not recognise them or value them (Askew, 2010).

Expertise – expertise not only in subject matter but also in communicating with children and producing effective learning environments. Without this expertise, some pupils’ mathematics may suffer (Williams, 2008).

Experience – knowledge can be gained from making mistakes. Teachers may learn about children’s misconceptions by coming across them within their teaching.

Pre-empting Misconceptions

In order to do this, the teacher needs to know:

- what the misconception might be.

- why these errors may have occurred.

- how to unravel the difficulties for the child to continue learning.

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