MATHS INSET12th May 2015

Rachel Cowen

Aims of the session• To give an update from the Better Mathematics

Conference 2015

• To look at addition calculation methods & decide

on a progression of stages across the school

National Key Concerns for Achievement

o Although attainment is generally rising pupils are not made to think hard

enough for themselves. Pupils of all ages do too little problem solving &

application of Mathematics.

o The % of pupils meeting expected standards falls at successive key stages.

This is often due to a focus on meeting thresholds rather than securing

essential foundations for the next stage.

o FSM pupils do worse than their peers at all key stages.

o Low attainers are not helped soon enough to catch up, particularly in the

EYFS & KS1.

o High attainers not challenged enough from EYFS onwards.

Made to Measure ReportThe report draws attention to serious inequalities in

pupils’ experiences and achievements. It includes

examples of best practice that help avoid or

overcome the inequalities and weaker practice that

exacerbates them.

Teaching Findings• The best teaching develops conceptual

understanding alongside pupils’ fluent recall of knowledge & confidence in problem solving & mathematical reasoning

• In highly effective practice, teachers get ‘inside pupils’ heads’. They find out how pupils think by observing them closely, listening carefully to what they say, & asking questions to probe & extend their understanding, then adapt teaching accordingly.

• Too much teaching concentrates on the acquisition of disparate skills that enable pupils to pass tests & exams but do not equip them for the next stage of education, work & life.

Aims of the National Curriculum 2014

• Become fluent in the fundamentals of mathematics,

so that pupils develop conceptual understanding &

the ability to recall & apply knowledge rapidly &

accurately

• Reason mathematically

• Solve problems

National Teaching Key Concerns

• Conceptual understanding & problem solving are

underemphasisedo Too often teaching approaches focus on how, without understanding

why, so that pupils have insecure foundations on which to build future

learning.

o Many pupils spend too long working on straightforward questions

• Wide in school variation in teaching quality.

• Circulating to check & probe each pupil’s

understanding throughout the lesson & adapting

teaching accordingly are not strong enough.

What does ‘Outstanding’ look like?

• Problem solving & Mathematical reasoning are embedded into all parts of the Maths curriculum & not viewed as a separate entity.

• Children are discussing Maths & methods & making connections for themselves.

• Everyone is teaching for understanding.

• Practical resources, visual images & ICT foster pupils’ deeper understanding. All children are encouraged to use practical equipment, there is evidence this has real benefits in terms of developing mental imagery.

• Teachers work & plan together to support consistency & improvement.

• There is timely intervention which overcomes gaps & builds a firm foundation for future learning.

Recommendations for Primary Schools

• Improve pupils’ progress from the Early Years

Foundation Stage through to Year 2 to increase

attainment of the most able.

• Act early to secure the essential skills & knowledge

of the least able.

Questions to consider• How can we develop consistency in our teaching in

terms of subject knowledge and language choices?

• How can we ensure our calculation policy reflects the changes in the New Curriculum and the needs of the children in our school?

• How can our policy build effectively on prior learning?

• How can we improve the accuracy of children’s addition work across the school?

• How can we support the children to effectively record their mathematical thinking?

Concepts of addition• What do we think these are?

• How would we define addition?

The concept of addition• The combining of 2 or more groups to give a total or

sum

• It is the increasing of an amount.

Key principles of addition• It is the inverse of subtraction

• It is commutative i.e. 5 + 3 = 3 + 5

• It is associative i.e. 5 + 3 + 7 = 5 + (3 + 7)

Addition StructuresAggregation Augmentation

• The key language to

be developed in the

aggregation structure

of addition includes:o how many altogether?

o How much altogether?

o The total.

• The key language to

be developed in the

augmentation structure

of addition includes:o start at and count on,

o increase by,

o go up by.

Addition Structures• Children must experience the two addition

structures in a range of relevant contexts, including money (shopping, bills, wages and salaries) and various aspects of measurement.

• Then they also have to recognise addition in situations in the contexts of measurements, such as length and distance, mass, capacity and liquid volume, and time. For example, o Can you calculate the distance for this journey? If I have already travelled

63 miles and then do a further 45 miles?

o Can you find the total time for the journey? If the first stage has taken me 85 minutes and the second stage takes 65 minutes?

• Our next step is to think about the policy from the

child’s perspective:

o How would the children show you their learning at each stage?

o What would you see in their books on paper or in photos?

o How do we ensure the progression from practical to written?

How do we teach addition now?

• With your class, what methods do you use?

• What practical equipment do you use?

• What written methods do you use?

Stage 1- Combining 2 or more amounts

• Counting all methodChildren begin to develop their

ability to add by using practical

equipment to count out the

correct amount for each number

in the calculation and then

combine them to find the total.

For example, when calculating 4 +

2, they are encouraged to count

out four counters and count out

two counters.

Counting all• To find how many altogether, touch and drag them

into a line one at a time whilst counting.

1 2 3 4 5

6

Counting all

Children should be taught that addition is the combining of two or

more amounts. They will begin by counting all of the items in the

groups, then move on to counting on from the largest amount.

They can begin to record addition number sentences such as

2 + 4 = 6 and 8 = 3 + 5 and 3 + 2 + 4 = 9

Counting on

4

Stage 2- Using Number Tracks & Base 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

11 + 5 = 16

Model of Base 10 equipment

KS1 Addition Games• https://www.tes.co.uk/teaching-resource/teachers-

tv-primary-maths--calculation-6038949

What about number lines?• https://www.ncetm.org.uk/self-

evaluation/browse/topic/883

Stage 334 + 23 = 57 34 + 23 = ?

The units/ones are added first 4 + 3 = 7The tens are added next30 + 20 = 50Both answers are put together 50 + 7 = 57

Stage 4

28 + 36 = ?The units/ones are added first8 + 6 = for 1 ten.A ring is put around the units/ones not exchanged –this is the units part of the answer. The tens are then added, including the exchanged ten, to complete the sum.

Stage 5TU HTU

67 267

+ 24 + 85

1 1 (7 + 4) 12 (7 + 5)

80 (60 + 20) 140(60+80)

91 200

352

The Base 10 equipment should be used alongside to model the transition to the vertical method but this should not be recorded by the children

65 + 27 =

Stage 6

The example top left would be ‘said’ as follows:5 + 8 = 13, put 3 down and carry the 1020 + 40 + 10 that was carried over = 70 (7 written in the tens column)600 + 0 = 600 (6 written in the hundreds column)

• Children should extend the carrying method to numbers with at least four digits.

587 3587

+ 475 + 675

1062 4262

1 1 1 1 1

3121 3.20

+ 37 +2.88

+ 148 6.08

3306 1

1 1

Important Points• Children should not be made to go onto the next

stage if:

1) they are not ready.

2) they are not confident.

• Children should be encouraged to consider if a

mental calculation would be appropriate before

using written methods.

Our next steps• Look at the calculation policy for the other

operations, ensure there is a clear progression from

practical to written methods.

• Use the policy in a fluid way, look at where the child

is and what their next steps are.

HomeworkLook at the results of the Times Tables Club in your

class. Can you track progress & do some analysis

about the overall effectiveness/ impact this is having

on learning and progress?

Please bring this to the next Maths

inset on 16th June.