Monday 4th November 2013

To revisit the new primary curriculum for maths 2014

To have an overview of EYFS maths To map out the statutory content To explain the Concrete, Pictorial,

Abstract approach further To consider concrete resources

within school To introduce the concept of

Singapore maths

Purpose of studyMathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems.

It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment.

A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

The Aims of The New Curriculum

The National Curriculum for mathematics aims to ensure all pupils: become fluent in the fundamentals of mathematics so that they are efficient in using and selecting the appropriate written algorithms and mental methods, underpinned by mathematical conceptscan solve problems by applying their mathematics to a variety of problems with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios can reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language.

Changes to curriculum (Sept 12) for Mathematics in EYFS curriculum: Currently, two strands: Numbers and Shape, Space and Measures.

EYFS Profile: ELG: Numbers: 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.

Six Term Curriculum in Foundation Stage at St Christopher.

Practical and real-life problem solving activities, rhymes, songs, stories, use of mathematical vocabulary, number patterns and methods of recording; by drawing, tallying, using standard notation where appropriate.

Encouraging children to be creative in identifying and devising problems and solutions in all areas of learning.

Increased focus on arithmetic proficiency

Instant recall of number facts Higher expectations in Fractions,

Decimals and Percentages Less emphasis on data handling

Data Handling will now be called Statistics

Shape and Space now comes under the Geometry umbrella

Three key features of our maths teaching include:

High expectations for every child More time on fewer topics Problem-solving at the heart

We aim to embed a deep understanding of maths by employing a concrete, pictorial, abstract approach – using objects and pictures before numbers and symbols so that pupils understand what they are doing rather than just learning to repeat routines without grasping what is happening.

 

Year 1 Number and place value

Addition and Subtraction

Multiplication and Division

Fractions Measurement Geometry Properties of Shape

Geometry Position and direction

Pupils should be taught to:

identify and represent numbers using concrete objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least given a number, identify one more and one less read and write numbers from 1 to 20 in digits and words. count, read and write numbers to 100 in numerals, count in different multiples including ones, twos, fives and tens

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number.

read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs

add and subtract one-digit and two-digit numbers to 20 (9 + 9, 18 - 9), including zero

represent and use number bonds and related subtraction facts within 20

solve simple one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems. E.g. 7 = - 9

solve simple one-step problems involving multiplication and division, calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

use written and mental strategies to double and half one and two digit

numbers.

recognise, find and name half as one of two equal parts of an object, shape or quantity

recognise, find and name a quarter as one of four equal parts of an object, shape quantity.

Compare, describe and solve practical problems for: lengths and heights (e.g. long/short, longer/shorter, tall/short, double/half) mass or w eight (e.g. heavy/light, heavier than, lighter than) capacity/volume (full/empty, more than, less than, quarter) time (quicker, slow er, earlier, later) Measure and begin to record the following: lengths and heights mass/w eight capacity and volume time (hours, minutes, seconds) recognise and know the value of different denominations of coins and notes (inc luding counting coins) tell the t ime to the hour and half past the hour and draw the hands on a clock face to show these times

Sequence events in chronological order using language such as:

before and after, next, f irst, today, yesterday, tomorrow , morning, afternoon and evening recognise and use language relating to dates, including days of the w eek, w eeks, months and years.

Recognise and name common 2-D and 3-D shapes, including: 2-D shapes (e.g.

rectangles (including squares), circles and triangles)

3-D shapes (e.g.

cuboids (including cubes), pyramids and spheres).

describe position, directions and movements, including half, quarter and three-quarter turns.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage.

Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

Each class teacher will use the maths primary curriculum 2014 end of year expectations/programmes of study to inform their long term planning and to derive the learning objectives.

Each teacher will be provided with a condensed reformatted version of the maths primary curriculum.

Planning should be focused on addressing the children’s specific needs and not driven by coverage.

Planned activities should involve the CPA approach and involve a range of activities.

What we want you to consider is your current approach to maths.

How do you deliver certain topics? How would you teach this?

Tom has a bag of 64 marbles, his friend gives him 28 more. How many does he have now?

Why is maths hard?

Why do people find it easy/hard?

What does this mean for the children?

Schools should: tackle in-school inconsistency of teaching increase the emphasis on problem solving across the mathematics curriculum develop the expertise of staff: in choosing teaching approaches and activities that foster pupils’ deeper understanding, in checking and probing pupils’ understanding during the lesson, in understanding the progression in strands of mathematics over time, so that they know the key knowledge and skills that underpin each stage of learning ensuring policies and guidance are backed up by professional development for staff”

Findings from Ofsted 2011: Practical, hands-on experiences of using, comparing and calculating with numbers and quantities … are of crucial importance in establishing the best mathematical start …

Understanding of place value, fluency in mental methods, and good recall of number facts … are considered by the schools to be essential precursors for learning traditional vertical algorithms (methods)

Subtraction is generally introduced alongside its inverse operation, addition, and division alongside its inverse, multiplication

High-quality teaching secures pupils 'understanding of structure and relationships in number …

The math curriculum in Singapore has been recognised worldwide for its excellence in producing students highly skilled in mathematics.

Singapore maths curriculum aims to help students develop the necessary math concepts and process skills for everyday life and to provide students with the ability to formulate, apply and solve problems.

Students can under perform in mathematics because they find it boring or they can't remember all the rules.

The Singapore method of teaching mathematics develops pupils' mathematical ability and confidence without having to resort to memorising procedures to pass tests - making mathematics more engaging and interesting.

Ofsted, the National Centre for Teaching Mathematics (NCETM), the Department for Education, and the National Curriculum Review Committee have all emphasised the pedagogy and heuristics used by Singapore. This method is now being used successfully in the UK by the Ark academies, the Harris Federation, Primary Advantage as well as numerous state, free, and independent schools.

Emphasis on problem solving and comprehension, allowing students to relate what they learn and to connect knowledge

Careful scaffolding of core competencies of : visualisation, as a platform for comprehension

mental strategies, to develop decision making abilities

pattern recognition, to support the ability to make connections and generalise

Emphasis on the foundations for learning and not on the content itself so students learn to think mathematically as opposed to merely reciting formulas or procedures.

C = Concrete

P = Pictorial

A = Abstract

http://www.youtube.com/watch?v=2Ss8xAXs_ns

Using solid, hands on resources to help with the understanding of maths.

It is important to use practical resources to ensure children understand the process of calculations, such as making a number ten times bigger or increasing a number by 12 means we now have

12 more of something, rather than maths just being an abstract activity that ‘we just do’.

Using diagrams and images to represent numbers and symbols.

Here, children move away from physical, hands on objects and instead use pictures for demonstrations and also recording.

Moving onto the use of numbers and symbols in a conventional written method.

There will ALWAYS be that one child who, no matter how many times you tell them or show them the abstract method, they will just not get it!

What you actually feel like saying to them is…

We have to ensure that we are catering for the needs of every child in our class/group.

Merely repeating the same instruction ten times does not work for some children.

They need to be able to understand the process rather than just rattle off facts.

Only then will they have a real grasp of the number system and be able to apply that to a range of problem solving activities.

How could we apply the CPA method to this problem? What strategies could we use to include CPA?

Steve has 12 sweets. Clair has 5 fewer sweets than Steve. How many sweets does Clair have?

18 Girls

¾ ¼ Boys

6 6 6 6

The whole class = 2418 + 6 = 24

http://www.watchknowlearn.org/Video.aspx?VideoID=44742&CategoryID=4912

Annie was playing with some cotton reels. Lola wanted to play too, so Annie gave Lola 6 cotton reels. Annie had 5 cotton reels left. How many did she have to start with?

Can you set out the cotton reels so that you can see the whole and the parts?

Kyle has 3 fewer cotton reels than Lauren. Lauren has 8 cotton reels. How many reels does Kyle have?

This model compares 2 quantities. You are given the value of one quantity and the difference. You have to find the value of the missing quantity. How can you show a solution to this problem?

How would you teach the children to solve this problem without the bar?

Now solve it using the bar… which way is easier?

1st class

2nd class

2nd class

2nd class

2nd class

4040 ÷ 5 = 8

1 x 8 = 8 1st class stamps4 x 8 = 32 2nd class stamps

There will be a new Maths Curriculum that we must be ready to implement in 2014.

We must bear this in mind and start to prepare this year, but it will involve gradual changes.

There will be a new routes through calculations document that will be implemented from Spring term.

There must be more focus on using the CPA approach to teaching maths starting now!

Try to start incorporating the Singapore bar to problem solving activities.