ei505 maths 2

EI505 Computing and Contemporary Developments

Primary Mathematics 2National Curriculum 2014 Update

27th May 2014Diana Brightling

Session aims and structure

Main aim: to prepare you for teaching primary mathematics in the future:

• Reminder of key features of primary mathematics in the new national curriculum

• Teaching develop conceptual and procedural fluency in arithmetic

Secondary aim:

• For those who need it: support for the mathematics element of EI505 assignment

Looking ahead to your final year and your NQT year

2013 - 2014 2014 - 2015 2015 - 2016

Year 1 NC 1999 NC 2014 NC 2014

Year 2 NC 1999 NC 1999 NC 2014(backfill Yr 2 curriculum)

Year 3 Disapplied NC 2014(backfill Yr 2 curriculum)

NC 2014

Year 4 Disapplied NC 2014(backfill Yr 3 curriculum)

NC 2014

Year 5 NC 1999 NC 2014(backfill Yr 4 curriculum)

NC 2014

Year 6 NC 1999 NC 1999 NC 2014(backfill Yr 5 curriculum)

So what do schools need to do?

Identify changes to current

programmes of study

Decide how to track progress

Discuss implementation as

a whole school staff

The new National Curriculum: Aims The national curriculum for mathematics aims to ensure that all pupils:

• become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately

• reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

• can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Three Aims

Problem-Solving

ReasoningFluency

Reasoning – what is it and why bother?

• Integral aspect of problem-solving and fluency• Needs to be explicitly taught and developed over time• Can be used to develop, assess and extend pupils’ knowledge

and understanding across mathematics

If ...then...

It can’t be because... I already know

that… so…This is

different because...This is always

true because…

I noticed that...

Problem-Solving

ReasoningFluency

“...mathematical reasoning is fundamental to reconstituting faded knowledge when a demand for it arises.”

(Ball & Bass, 2003, p.28)

Problem-Solving

• Needs to be embedded across Programmes of Study• Apply to routine and non-routine problems• Much more than word problems:

– Logic problems and puzzles– Finding rules and describing patterns – Diagram problems and visual puzzles– Finding all possibilities– Enquiry

• A useful starting point to your content – and can extend over multiple lessons

Problem-Solving

ReasoningFluency

Fluency

• Pupils’ knowledge and understanding, including facts and procedures

• Recall, application and manipulation3 + 3 = 6 so 30 + 30 = 60 and 0.3 + 0.3 = 0.6

Conceptual as well as procedural fluency

Problem-Solving

ReasoningFluency

The ‘old’ National Curriculum

Attainment targets:• Ma1: Using and

applying mathematics• Ma 2: Number• Ma 3: Shape, space

and measures• Ma 4: Handling data

The ‘new’ National Curriculum 2014

Number – and place value– addition and subtraction– multiplication and division– fractions, decimals (Y4+) and

percentages (Y5+)– Ratio and proportion (Y6+)

Algebra (Y6+)MeasurementGeometry

- properties of shape- position and direction

StatisticsProblem-Solving

ReasoningFluency Remember to include a focus on problem-solving, reasoning and fluency throughout

Some key difference between mathematics in the old and the new NC

• More detailed – and now set out in Year groups. A ‘mastery’ curriculum. NC ‘levels’ have gone

• More ambitious expectations, especially for number.

• Greater emphasis on arithmetic – especially formal written methods

• Almost no mention of problem solving, reasoning or communicating in the Programmes of Study – although these elements are there in the introduction.

Programmes of Study: Flexibility

Change to year and phase groups

• KS1• Lower KS2• Upper KS2

Flexibility within Key Stages

• Content may be shifted between year groups within the Key Stage

• Content may also be introduced in an earlier Key Stage

Programmes of Study: Written Methods

• Earlier introduction of formal written methods:– Year 4: multiply two-digit and three-digit numbers by a

one-digit number using formal written layout

• Written approaches your school could use are outlined in the appendix for all four operations

(DfE, 2014. p.46)

Guidance for teaching calculation see Haylock and also: Student Central / My School: Education / Mathematics Education / Support for Calculation

Key principles in supporting the development of written calculation methods

• Mental calculation confidence should be established before written methods are introduced

• Mental calculation strategies need to be specifically taught• We need to carefully structure progression into written

methods to ensure each new method builds on understanding• Children need to be encouraged to make decisions about which

method to use and when• Opportunities to apply and problem solve with calculation skills

and strategies should run alongside practice of them• We need to ensure that we use resources to support

understanding of how methods represent number quantities

x 3

10 200

24

Which two numbers have been multiplied together in each grid. How do you know?

Problem solving with the grid method

Multiplication grid ITP

https://www.ncetm.org.uk/resources/40530Also on youtube - http://www.youtube.com/playlist?list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTii

Moving pupils from the grid method to the long multiplication algorithm.

4 68 7

5 3

Division Practice

• Look at the numbers in the yellow cloud and the numbers in the blue cloud.

• Choose a number from each cloud and create a division calculation

• Solve the calculation – a) by a chunking method– b) by the ‘bus stop’ written

245 642 563 126246 487 623 399 280

450 266 511 188 216 160

Teaching the ‘bus stop’ method for Conceptual and procedural fluency

• https://www.ncetm.org.uk/resources/43589

NB It’s worth joining NCETM - free –gives you access to loads of valuable resources and constantly being updated in response to the new NC.

1618 17

15 23

Long Division Practice

• Look at the numbers in the yellow cloud and the numbers in the blue cloud.

• Choose a number from each cloud and create a division calculation

• Solve the calculation – a) by a written chunking method– b) by the long division ‘bus stop’ method

245 4642 6 563 3126246 2487 623 3992

680 450 1266 511 2164 3160

New ‘Mathematics Education’ Area of studentcentral (within ‘My School’ area)

https://studentcentral.brighton.ac.uk/webapps/portal/frameset.jsp?tab_tab_group_id=_314_1&url=%2Fwebapps%2Fblackboard%2Fexecute%2Flauncher%3Ftype%3DCourse%26id%3D_25291_1%26url%3D

• A range of resources to support teaching and learning

• E.g. Screencasts

• NS ‘Strand’ documents

A selection of Computer Games – with some comments http://www.bbc.co.uk/schools/digger/9_11entry/9_11.shtmlProblem solving in a context to motivate – a simple adventure game – doesn’t teach anything but

puts problems in contexts.

http://www.bbc.co.uk/bitesize/ks1/maths/division/play/popup.shtmlTeaches conceptual understanding as well as procedural understanding http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/fractions/index.htm Various games and activities – conceptually good, no contexts. http://pbskids.org/cyberchase/math-games/melvins-make-match/ matching potion bottles (not sure why they need to be equivalent but the scales at the bottom are a

nice touch.

http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/percentages/index.htmThis one teaches how to find percentages in context of a sale – mathematically strong but a

demonstration rather than a game. http://www.arcademicskillbuilders.com/games/ratio-martian/ratio-martian.html Spotting ratios – and eating them – no explanation

Menu You have won a prize in a competition – a free meal at your favourite pizza restaurant! You want to gain the most possible from your £20 prize but cannot spend more than this amount.Which choices would you make if you choose one each from the following:• Starter• Main course• Desert• Drink?

ReferencesBall, D. L. & Bass, H. (2003) Making Mathematics Reasonable in School. In

Kilpatrick, J., Martin, W. G. & Schifter, D. (Eds.) A Research Companion to Principals and Standards for School Mathematics. Reston, VA, National Council of Teachers of Mathematics.

DfE (2013) Mathematics programmes of study: key stages 1 and 2 National curriculum in England [online] Available from https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/239129/PRIMARY_national_curriculum_-_Mathematics.pdf [accessed 25.04.14]

Haylock, D. (2010) Mathematics explained for primary teachers (4th ed.), London: Sage.

National Centre for Excellence in the Teaching of Mathematics (NCETM) website: https://www.ncetm.org.uk

QCA/DfEE. (1999) The National Curriculum: handbook for primary teachers in England: key stages 1 and 2, London: DfEE and QCA.

QCA (1999) Teaching mental calculations London: QCA

QCA (1999) Teaching written calculations London: QCA