Mathematics Mastery & The Knowledge Quartet SCITT Mentors Tues 30th Jan 2018

How does the CPA approach help pupils? What is it that makes this approach so valuable to the study of maths and particularly to the teaching for mastery? CPA is for everyone - all abilities and ages. CPA is not about getting the answer quickly.  CPA is a way to deepen and clarify mathematical thinking. What happens in your school? What are the challenges?

Can you visualise this using Ten Frames? ‘Imagine’ 8 + 5 = 9 + 4 = 8 + 4 = 8 + 9 = 7 + 8 = 6 + 5 = 2 + 5 = Can you visualise this using Ten Frames? Can you make 10? … ‘and how many more’?

C build it, make it P draw or sketch it A visualise, write it “There are 5 cars in the car park and 3 drive away.” When working mathematically… C build it, make it P draw or sketch it A visualise, write it

C P A Year 1 Mastery Video: 5 2 3 2+3=5 5-2=3 3+2=5 5-3=2 5=2+3 5=3+2 Additive Reasoning C P A “There are 5 cars in the car park… 3 drive away” 5 2 3 Children’s responses in FULL sentences… “The 3 yellow counters represent the 3 cars driving away.” 2+3=5 3+2=5 5=2+3 5=3+2 5-2=3 5-3=2 Build this with Number Rods…

Bar Model representations: (+/- problems) Additive Reasoning Bar Model representations: (+/- problems) BUILD: There are 4 yellow flowers and 3 blue flowers – how many altogether? There are 5 lollies. Jess eats 2. How many are left? 6 + [?] = 17 altogether COMPARE: There are 5 red cars and 3 yellow cars, how many more red cars? The string is 4cm, the ribbon is 8cm. How much shorter…? QUESTION: (Create your own) “John has 7 balls. Mark has 5 more…” “Beth has 6 balls. Emily has 3 less…” Represent 2 + 6 = 8. What rich variety of language could be used when reading this number sentence…?

Bar modelling with scaling up (When a unit is ‘more than 1’) Multiplicative Reasoning Peter has 4 books. Harry has five times as many books as Peter. How many books has Harry? Peter Harry                4 × 5 = 20 Harry has 20 books Show in a variety of ways… 4 Notice how each section of the bars in the problem below has a value of 4 and not 1. This many-to-one correspondence, or unitising is important and occurs early, for example in the context of money, where one coin has a value of 2p for example. It is also a useful principle in the modelling of ratio problems. 4 4 4 4 4

Additive Reasoning in italics

Teaching mathematics Common Subject Knowledge Curriculum Knowledge Pedagogical Subject Knowledge Contingency Q: What do teachers need to know to teach mathematics successfully? Common content knowledge (as a citizen) As a teacher: Specialised Curriculum Knowledge Pedagogical Subject Knowledge [The whole SCITT Course is built upon improving individual knowledge from collective knowledge]

‘The Knowledge Quartet’ Foundation Overt subject knowledge which the trainee brings to the teaching situation Transformation How well trainees are able to transform what they know in ways that make this knowledge accessible and appropriate to children Contingency The ability to ‘think on one’s feet’. Responding to the unexpected more than the ability to make predictions when planning Connection Decisions about sequencing and connectivity relating to the context of previous lessons and pupils knowledge. This will typically follow from the ability to anticipate what is complex and what is conceptually appropriate for an individual or group of pupils Discuss some ‘real-life’ examples (from your own practice) …………….. How could this be used: when giving feedback…? when planning…? when observing ‘others’…? Remember your ‘beliefs’ will influence your pedagogical choices!

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Where to find on TES pages? All White Rose downloads https://www.tes.com/teaching- resources/teaching-for-mastery- partner