Mathematics in Early Years Natalie Alty & Claire Green
What is early mathematics? What are the key priorities for our children in Early Years? Discuss with your colleagues.
What is early mathematics? ‘ The world is a mathematical place. For young children who are naturally curious there are shapes, numbers, moving objects and patterns to behold, things to count and investigations to be undertaken. It is a creative, challenging and wonderous way of looking at life and exploring the world. Maths is an inherent part of being human. Framing the world through maths helps us make sense of what is happening and how it affects us’. J Robertson 2017 Pictures and symbols Problem – solving Real world scripts Language and reasoning Making connections
Expectations for number by the end of the EYFS. Number ELG Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. What have been the difficulties or problems with this Early Learning Goal? Discuss with your colleagues.
Challenges include: - Numbers are learnt by rote and pupils can purely put them in order to identify one more or one less - Little understanding of how these numbers are made and the number facts within them - Little time can be given to teaching concepts in depth because there is so much knowledge to teach - Can be challenging for SEN pupils to reach this goal but can be successful in understanding numbers to 10, however this isn’t recognised in data collection. - Not enough time to model how concepts can be applied across different areas of the curriculum so that pupils can make real life connections in their learning.
This year the DfE is piloting a new Early Years Foundation Stage Profile. Mathematics Educational Programme Developing a strong grounding in number is essential for providing children with the platform to excel mathematically. Children should develop a deep conceptual understanding of the numbers to 10, the relationships between them and the patterns therein . By providing frequent and varied opportunities to build and apply this understanding, children will develop a secure base of knowledge from which mathematical mastery is built. ELG Number : Children at the expected level of development will: - Have an understanding of number to 10, linking names of numbers, numerals, their value, and their position in the counting order; - Subitise (recognise quantities without counting) up to 5; - Automatically recall number bonds for numbers 0-5 and for 10, including corresponding partitioning facts. ELG Numerical Patterns: Children at the expected level of development will: - Automatically recall double facts up to 5+5; - Compare sets of objects up to 10 in different contexts, considering size and difference; - Explore patterns of numbers within numbers up to 10, including evens and odds
What is maths mastery? Connect memory: verbal, visual and spatial • Depth Mastery • Manipulatives • Structured practice (key vocabulary) • Rich tasks • Explanation and Reasoning
• Conceptual Variation : the variety of ways into a particular concept • Procedural Variation : what the children should be able to do in relation to a particular concept
Number Sense A sense of the size of a number Rounding Estimating
Use an empty number line to assess understanding of a range of numbers
Number sense Estimation How many in the jar?
The basis of mathematics is… Pattern • Children need to be able to see patterns, predict and generalise • This includes growing patterns, making comparisons, logic, reasoning and working systematically • Understanding how they work in a non-numerical sense is an essential first step in developing comprehension of pattern. Therefore must be linked to daily routines, songs, stories, movement. Numicon 2014
Pupils need to have a good understanding of pattern. To be mathematical it must have some element of repetition or symmetry.
Growing Patterns
Important skill to have acquired is seeing the odd one out and being able to explain what is same or difference between objects ? This also supports the development of reasoning skills.
Counting - 1:1 correspondence - Stable order e.g 1,2,3,4,5,6…. - Abstraction: many items or objects can be counted • Order irrelevance • Cardinality - last number said is the number of the group Gelman & Gallistel 1978 Pupils need everyday opportunities to hear and use the language of number.
Use pictures and storybooks to discuss positional number, addition and subtraction stories as well as same, different and positional language.
Scaffolding the talk • One less than__ is ___ • I have counted ___ altogether • __ comes after/before ___ • ___ has more than ___ because___ • __ has the least because___ • __ more than ___ is ___ • I have __ and he has __ so we have ___ altogether • I had __ and took ___ away so now we have__
Numicon is… Visual Whole class teaching Sensory Weighted
Numicon – explore
Number blocks - ncetm.org
helps children to develop: • cardinal number values • part whole relationships • number facts
When learning to subitize children progress from: Linear Circular Scrambled
‘Children need concrete experience of physically manipulating groups of objects into sub-groups and combining small groups to make a larger group. After these essential experiences more static materials such as 'dot cards' become very useful.’
Let’s play! How many dots can you see? Play with dot games
Ten Frames Why do we use them? • Builds number sense • Helps children visualise numbers • Help children to be able to deconstruct numbers and recombine them in a useful way • Creates a strong understanding of ten which is vital for our number system
If I know 5+5=10… … What else do I know? Relationships True or false
8+5 = 13 + How does this then support to bridge through 10?
Pupils can then begin to record their understanding. 5 = 2 + 3 5 = 3 + 2 3 + ? = 5 2 + ? = 5 ? + 3 = 5
White Rose Representations
Making Connections • Half of 8 is equal to 4 • Double 4 is equal to 8
What is the same and what is different ? 17 and 71
Planning for mathematics. Mathematics 30-50mths Numbers Find missing Introduce the Beginning to represent numbers – use the equal sign, how do Transfer from numbers using fingers, part, part, whole you write it, where pictorial to marks on paper or method to do you see it and using numerals pictures. develop reasoning what does it mean? with the Sometimes matches skills as to how How can they pictures. numeral and quantity they find the record their own correctly. missing number. addition number 40-60mths sentences using Recognises numerals 1 to pictorial 10 representation. Counts objects to 10, and beginning to count beyond 10. Selects the correct numeral to represent 1 to 5. Finds the total number of items in two groups by counting all of them. In practical activities and discussion, beginning to use the vocabulary involved in adding. Plan for differentiation through questioning, resources, depth of mastery dependent on understanding. We do same day interventions as well as those over time for pupils with specific targets .
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