Mathematics Mastery The Knowledge Quartet SCITT Mentors Tues

Mathematics Mastery & The Knowledge Quartet SCITT Mentors Tues 30 th 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?

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

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

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

Additive Reasoning Bar Model representations: (+/- problems) BUILD: 1. There are 4 yellow flowers and 3 blue flowers – how many altogether? 2. There are 5 lollies. Jess eats 2. How many are left? 3. 6 + [? ] = 17 altogether COMPARE: 1. There are 5 red cars and 3 yellow cars, how many more red cars? 2. The string is 4 cm, the ribbon is 8 cm. 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’) Peter has 4 books. Harry has five times as many books as Peter. How many books has Harry? Peter 4 4 4 Harry 4 × 5 = 20 Harry has 20 books Multiplicative Reasoning Show in a variety of ways…

Additive Reasoning in italics

Teaching mathematics 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 Curriculum Knowledge Pedagogical Subject Knowledge [The whole SCITT Course is built upon improving individual knowledge from collective knowledge] Common Subject 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 Remember your ‘beliefs’ will influence your pedagogical choices! Discuss some ‘real-life’ examples (from your own practice) ……………. . How could this be used: • when giving feedback…? • when planning…? • when observing ‘others’…?

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Where to find on TES pages? All White Rose downloads • https: //www. tes. com/teachingresources/teaching-for-masterypartner