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# Ei505 maths 2

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### Ei505 maths 2

1. 1. EI505 Computing and Contemporary Developments Primary Mathematics 2 National Curriculum 2014 Update 27th May 2014 Diana Brightling
2. 2. 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
3. 3. 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)
4. 4. 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
5. 5. 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.
6. 6. Three Aims Problem- Solving ReasoningFluency
7. 7. 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)
8. 8. 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
9. 9. Fluency • Pupils’ knowledge and understanding, including facts and procedures • Recall, application and manipulation 3 + 3 = 6 so 30 + 30 = 60 and 0.3 + 0.3 = 0.6 Conceptual as well as procedural fluency Problem- Solving ReasoningFluency
10. 10. 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+) Measurement Geometry - properties of shape - position and direction Statistics Problem- Solving ReasoningFluency Remember to include a focus on problem- solving, reasoning and fluency throughout
11. 11. 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.
12. 12. 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
13. 13. 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
14. 14. 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
15. 15. 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/40530 Also on youtube - http://www.youtube.com/playlist?list=PLQqF8sn28L9yj34NpXK7Yffze7ZoXTii Moving pupils from the grid method to the long multiplication algorithm.
16. 16. 4 6 8 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 245 642 563 126 246 487 623 399 280 450 266 511 188 216 160
17. 17. 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.
18. 18. 16 18 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 3126 246 2487 623 3992 680 450 1266 511 2164 3160
19. 19. 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%2Fblackboar d%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
20. 20. A selection of Computer Games – with some comments http://www.bbc.co.uk/schools/digger/9_11entry/9_11.shtml Problem 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.shtml Teaches 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.htm This 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
21. 21. 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?
22. 22. References Ball, 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