Effective teaching of Early Maths “Skills- based learning” Getting children to think and talk mathematically
Feb 24, 2016
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Sorting Activities – Towards the notion of a set
• Children will sort random collections and talk about them
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Sorting Activities – Towards the notion of a set
• Children will sort one-property collections in one way and talk about their arrangements
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Sorting Activities – Towards the notion of a set
• Children will sort two-property collections in two different ways and talk about their arrangements
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Sorting Activities – Towards the notion of a set
• Children will sort three-property collections in three different ways and talk about their arrangements
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Combining sets
Children will combine 2 or more sets and talk about their arrangements
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Consolidating sorting using logic blocks
• Feely bag pg 45
• Copy Cat pg 43
• Guess my secret pg 45
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Sorting Activities
• Children will sort random collections again and talk about them. Note language.
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Key message: The Learning Process
Lower Order
Higher Order Abstract
Concrete
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Using Pictorial Representation
• Children will use Tree/Venn/Carroll diagrams to sort for one property and talk about their arrangements
• Non - set
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
• http://ppds.ie/index.php?option=com_content&task=view&id=331
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Early Understanding in Number
Sorting Relationships and
Operations
Understanding Counting andnumber recognition
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Counting Activities
Look for VARIETY
In the activitiesIn the involvement of the childrenIn the learning being promoted
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Counting Activities
Involvement of the children
Physical activityChorus responseIndividual Response
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Counting Activities
Learning being promoted
Counting forwards and backwardsRecognising/ordering numbersCounting quantitiesCounting from different startsAfter/before more/less
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
• http://ppds.ie/index.php?option=com_content&task=view&id=332
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Copy a pattern
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Continue a pattern
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Devising a pattern
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
More
Same
Language of
Relationships
Less
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Comparing Sets
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Comparing Quantities within 5
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Partitioning Calculate mentally within 5
• Box numbers game
• Make Five
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
• 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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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.
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Number activities with Cuisenaire
• Make a little train p.90
• The step pattern p.92
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Addition using Cuisenairep.93
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Box Addition using Cuisenairep.94
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
• http://ppds.ie/index.php?option=com_content&task=view&id=334
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Early Understanding in Number
Sorting Relationships and
Operations
Understanding Counting andnumber recognition
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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.
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
One-to-one correspondence
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Understanding cardinal aspect of numbers within 5
Making sets using a variety of resources
Making patterns
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Between
Before
After
Last
Second
First
Understand the language of
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Ordinal Number
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Conservation of Number
Sets remain constant even if the objects are rearranged
Children need to be tested individually for conservation of number
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
• http://ppds.ie/index.php?option=com_content&task=view&id=333
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Key message: The Learning Process
Integrating and Connecting
Applying and Problem Solving
Reasoning
Communicating and ExpressingUnderstanding and Recalling
ImplementingLower Order
Higher Order Abstract
Concrete
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Early Understanding in Number
Sorting Relationships and
Operations
Understanding Counting andnumber recognition
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Suggestions for planning
Sample Jnr Infant planReady Set Go Maths.doc
Sample Snr Infant planReady Set Go Maths.doc
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
Examples of Mathematical Problems
• Word problems• Practical tasks• Open-ended investigations• Closed questions• Puzzles• Games• Projects• Mathematical trails.
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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.
Order Online: £15 + P&P (£11.30
for up to 10 manuals)
The PDST is funded by the Department of Education and Skills under the National Development Plan, 2007-2013
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