EI505 Computing and Contemporary Developments

Primary Mathematics 1

19th Feb 2015

Diana Brightling

Session structure

• Revisiting EM402 and reflections on teaching maths on 1st placement

• Key features of primary mathematics in the 2014 National Curriculum

• Progression in arithmetic (NC 2014)

• Implications for EI505 Assignment

Looking back at Year 1…………

• Key learning from EM402

• Key learning from practical experience of teaching maths on placement 1

Relational and Instrumental Understanding

• Relational understanding is….”what I have always meant by understanding: knowing both what to do and why.”

• “Instrumental understanding I would have until recently not have regarded as understanding at all. It is what I have in the past described as ‘rules without reasons’ without realising that for many pupils and their teachers the possession of such a rule, and the ability to use it, was what they meant by understanding.”

Skemp, R. (1976) “Relational understanding and Instrumental understanding.” Mathematics Teaching, 77, pp 20-26.

Bruner’s modes of representational thought

enactive

iconic

symbolic

The child needs

experience at all

three levels

Text provides

experiences at

only the two

most

sophisticated

levels

Delaney, K, (2001), ‘Teaching Mathematics Resourcefully’, in Gates, P (Ed), Issues

in Mathematics Teaching, London: Routledge Falmer (available as an e-book)

Where are we now?

• The new national curriculum for Year 3, Year 4 and Year 5 came into force from September 2014.

(Year 6: KS2 SATS are unchanged for 2014/15)

• The new national curriculum for Year 6 will come into force from September 2015.

(New KS2 SATS for 2015/16 are currently in development)

N.B. Assessment and tracking pupil progress is a major challenge for schools

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

Statistics

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 explicit in the introductory aims.

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.

Catering for the needs of all pupils….

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.

Excerpt from NC 2014 mathematics programme of study (p100)

Information and communication technology (ICT)

Calculators should not be used as a substitute for good written and mental arithmetic. They should therefore only be introduced near the end of key stage 2 to support pupils’ conceptual understanding and exploration of more complex number problems, if written and mental arithmetic are secure. In both primary and secondary schools, teachers should use their judgement about when ICT tools should be used.

What does this mean?

Are we allowed to use

calculators in primary schools and if so when and what for?

What is the progression through the four operations, from mental strategies to

compact written methods?

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

‘Mathematics Education’ Area of studentcentral

(within ‘My School’ area)https://studentcentral.brighton.ac.uk/webapps/blackboard/content/listContentEditable.jsp?content_id=_1756387_1&course_id=_25291_1

• A range of resources to support teaching and learning

• E.g. Screencasts

• NS ‘Strand’ documents

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

TARGET >300

x >300

Shuffle some digit cards and make a stack. Turn over one card at a time and decide together where to put it. Will your product be more than 300? Five points if it is. How do you know? When do you know? Use grid method to calculate the answer.

Play against or with a friend

4 68 7

5 3

Division Practice

• With a partner, choose one number from the yellow cloud and one from either the green cloud or the orange cloud to create a division calculation

• Estimate the answer

• Solve the calculation using an efficient method

• Could you have used a more efficient method?

• Do you always get a remainder?

245 642 563 126246 487 623 399 280

450 266 511 188 216 160

12 14 17 23 25 29

Division practice options (to practice and refine ‘chunking’ method – using just the green cloud)

Option 1:

• What remainder do you get when you have divided your numbers?

• Put a cross or counter on the grid to match this remainder. Can you get three crosses in a row?

Option 2:

Work with a partner to solve some division calculations using the cloud numbers

What do you notice?

How can you make your chunks efficient? (use the smallest number of chunks)

What makes the answer smaller or larger?

Can you predict if you will have a remainder and how much this remainder will be?

1 4 3 2

3 1 5 6

2 3 2 1

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?

Considerations for your assignment?

Which areas of the NC are suitable for this task?

How might you include mathematical reasoning and problem solving as well as fluency?

Follow up from this session:• Revisit and update your primary maths tracker –

especially the action plan (and upload this to your e-portfolio, tagging it to TS3)

• Familiarise yourself with the resources in the Mathematics Education area of studentcentral

• Familiarise yourself with mathematics programme of study for KS2 in the 2014 National Curriculum and English specialists – consider possible content choices for your assignment.