Effective teaching of Early Maths

Effective teaching of Early Maths

“Skills- based learning”

Getting children to think and talk mathematically

Objectives

Teachers will be enabled to • Adapt their teaching methodologies to

promote the development and acquisition of mathematical skills through the content of the number strand in the early maths curriculum.

• Incorporate the use of mathematical language as a core element of every Maths lesson.

• Select and use appropriate Maths equipment to further enhance the acquisition of mathematical skills in the classroom.

• Adapt a Problem-Solving approach as a central methodology in the teaching and acquisition of skills through content.

• Self-reflect on their existing practice and provide feedback on new approaches suggested during the workshops.

Skills• Applying and problem-solving

• Communicating and expressing

• Integrating and connecting

• Reasoning

• Implementing

• Understanding and recalling P68/69

psc

The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013

Skills• Applying and problem-solving (HO)

• Communicating and expressing (HO)

• Integrating and connecting (HO)

• Reasoning (HO)

• Implementing (LO)

• Understanding and recalling (LO)P68/69

psc

Early Understanding in Number

Sorting Relationships and

Operations

Understanding Counting andnumber recognition


SORTING – a line of development

Sorting • Sort a random collection• Sort a one-property collection in one way• Sort a two property collection in two ways• Sort a three property collection in three ways• Revisiting random collections• Partition sets into subsets• Combine sets• Sorting and logic games


Sorting Activities – Towards the notion of a set

• Children will sort random collections and talk about them



• Children will sort one-property collections in one way and talk about their arrangements




• Children will sort two-property collections in two different ways and talk about their arrangements



• Children will sort three-property collections in three different ways and talk about their arrangements


Combining sets

Children will combine 2 or more sets and talk about their arrangements


Consolidating sorting using logic blocks

• Feely bag pg 45

• Copy Cat pg 43

• Guess my secret pg 45


Sorting Activities

• Children will sort random collections again and talk about them. Note language.


Key message: The Learning ProcessI use my mathematical

ideasI explain my ideas

I understand and use

suitable language

I use materials with the teacher’s direction


Key message: The Learning Process

Lower Order

Higher Order Abstract

Concrete


Using Pictorial Representation

• Children will use Tree/Venn/Carroll diagrams to sort for one property and talk about their arrangements

• Non - set


• http://ppds.ie/index.php?option=com_content&task=view&id=331

http://ppds.ie/index.php?option=com_content&task=view&id=331





Operations



Counting and RecognitionLine of Development

• Count forwards / backwards within 5/10/20/99/199 from different starting points

• Quick recognition of quantities 5/10/20

• Sensible guess of quantities within 10/20


Counting Activities

Look for VARIETY

In the activitiesIn the involvement of the childrenIn the learning being promoted


Counting Activities

Involvement of the children

Physical activityChorus responseIndividual Response


Counting Activities

Learning being promoted

Counting forwards and backwardsRecognising/ordering numbersCounting quantitiesCounting from different startsAfter/before more/less






Relationships and Operations

• Copy a pattern• Continue a pattern• Devise a pattern• Compare equal/unequal sets • Find components within 5/10/20• Add/subtract within 5/10/20• Consolidate experiences within 5/10

using Cuisenaire


Copy a pattern


Continue a pattern


Devising a pattern


More

Same

Language of

Relationships

Less


Comparing Sets


Comparing Quantities within 5


Partitioning sets within 5

Children are ready to partition when

• They can count collections within 5• They recognise numerals up to 5• They have conservation of number up to 5


Partitioning sets within 5

• Model partitioning sets into subsets within 5• Model the language – altogether, 5 is the

same as 3 and 2• Start partitioning with 5 and then go down to

smaller numbers• Teacher’s role is to create sets so the children

can make decisions around partitioning for size/colour



Key Steps

Teacher demonstrates activity and provides language

Children dopractical activities with support from

teacher

Children record findings pictorially

Children begin to use associated language


Partitioning Calculate mentally within 5

• Box numbers game

• Make Five


Partitioning sets within 10/20

• Extension of work within 5• Children need to have conservation of number

to 10/20• Teacher introduces the written record• Children record their findings using the

written record


Operations – Addition

• Add two numbers practically within 5 and talk about their findings

• Teacher uses a base board and number cards to demonstrate the process of addition

and altogether make

2 3 5


Operations – Subtraction

• Subtract two numbers practically within 10 and talk about their findings

• Teacher uses a base board and number cards to demonstrate the process of subtraction

take awa

y

leaves

7 3 4


Addition/Subtraction within 10

There is merit in delaying the introduction of mathematical symbols until children are very

secure in all aspects of operations

Ready Set Go Maths, p.77


• Commutative aspect of addition• Subtraction as the inverse of addition• Subtract practically by taking away• Add on/Subtract mentally within 10• Add on/Subtract the second number

practically within 10


Cuisenaire

Readiness check p.87

• Conservation of number and length needs to be secure• First understanding of components of number, addition and

subtraction should be established with random materials.


Number activities with Cuisenaire

• Make a little train p.90

• The step pattern p.92


Addition using Cuisenairep.93


Box Addition using Cuisenairep.94








Operations



Understanding Number

• The ability to recite number names in order• One to one correspondence• Appreciation that the final number in the

count refers to the whole collection and not the final object counted.


Line of Development

• One to one correspondence (including touch counting)

• Make sets for numbers within 5/10/20• Order numerals and sets within 5/10• Conservation of number within 5/10/20• First/last/between/First-tenth


One-to-one correspondence


Understanding cardinal aspect of numbers within 5

Making sets using a variety of resources

Making patterns


Cardinality of NumberJunior Infants Senior Infants

Shake and Make p.127Fill the Sweetie Jar p.128Number Bears p.128Animal Hunt p.129Snail Trail p.129

Hidey Holes p.140Humpty Dumpty p.140Memory Match p.140It must be more p.142


Between

Before

After

Last

Second

First

Understand the language of


Ordinal Number


Conservation of Number

Sets remain constant even if the objects are rearranged

Children need to be tested individually for conservation of number






Key message: The Learning Process

Integrating and Connecting

Applying and Problem Solving

Reasoning

Communicating and ExpressingUnderstanding and Recalling

ImplementingLower Order

Higher Order Abstract

Concrete




Operations



Suggestions for planning

Sample Jnr Infant planReady Set Go Maths.doc

Sample Snr Infant planReady Set Go Maths.doc



Examples of Mathematical Problems

• Word problems• Practical tasks• Open-ended investigations• Closed questions• Puzzles• Games• Projects• Mathematical trails.


Council for the Curriculum, Examinations and Assessment

(CCEA) in Belfast.Tel: 0044 2890261200. Ask to be put through to Distributions and speak to Jackie or Natasha.

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Effective teaching of Early Maths