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Understanding the Essence of Mathematics Education

Explore the vital role of mathematics education, from teaching for mastery to progression in calculations, with practical tips and essential skills explained.

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Understanding the Essence of Mathematics Education

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  1. WELCOME

  2. What is maths all about? Think about your own maths experience. Did you enjoy it? How were you taught? Has your own experience of maths as a child affected the way you viewed it as an adult?

  3. Which of these words would you useto describe mathematics? easy challenging • Maths is …….. fun frightening boring uncomfortable hard important scary

  4. The Essence of Maths Teaching for Mastery • Maths teaching for mastery rejects the idea that a large proportion of people ‘just can’t do maths’. • All pupils are encouraged by the belief that by working hard at maths they can succeed. • Pupils are taught through whole-class interactive teaching, where the focus is on all pupils working together on the same lesson content at the same time, as happens in Shanghai and several other regions that teach maths successfully

  5. SATs… BUT IT’S MORE THAN THAT… • Life skills • Arithmetic paper • Reasoning 1 • Reasoning 2

  6. Progression in Calculations

  7. Understanding and Using Calculations For all calculations, children need to: understand the = sign as meaning equality. see calculations where the equals sign is in different positions and what these number sentences represent, e.g. 3 + 2 = 5 and 5 = 3 + 2 decide on the most appropriate method i.e. mental, mental with jottings OR a written method approximate before calculating and check whether their answer is reasonable.

  8. Reason or Calculate? Number sense ….. Understanding the x ÷ relationship, knowing 18 is 1 more than 17 Therefore: 326 ÷ 18 = 5,542 + 326 = 5,868

  9. Reason or calculate?

  10. Addition Children need to understand the concept of addition; that it is: Combining two or more groups to give a total or sum Increasing an amount They also need to understand and work with certain principles: Inverse of subtraction Commutative i.e. 5 + 3 = 3 + 5 Associative i.e. 5 + 3 + 7 = 5 + (3 + 7)

  11. Efficient Column Addition HT U ? 2 5 7 164 257 1 4 6 + 4 2 1 ? 1 1 164 257

  12. Subtraction CHILDREN NEED TO UNDERSTAND THE CONCEPT OF SUBTRACTION, THAT IT IS: REMOVAL OF AN AMOUNT FROM A LARGER GROUP (TAKE AWAY) COMPARISON OF TWO AMOUNTS (DIFFERENCE) THEY ALSO NEED TO UNDERSTAND AND WORK WITH CERTAIN PRINCIPLES: INVERSE OF ADDITION NOT COMMUTATIVE I.E. 5 - 3 ≠ 3 - 5 NOT ASSOCIATIVE I.E. (9 – 3) – 2 ≠ 9 – (3-2)

  13. Efficient Decomposition HT U 321 1 2 1 1 3 2 1 157 ? 1 7 5 - 6 4 1 321 157 ?

  14. Finding the Difference (Counting On) 2231-1992= Children need to understand how counting on links to subtraction, e.g. 7 – 4

  15. Multiplication Children need to understand the concept of multiplication, that it is: Repeated addition/ repeated groups 3 + 3 + 3 +3 =12

  16. Multiplication They also need to understand and work with certain principles: Inverse of division Is commutative i.e. 5 x 4 = 4 x 5 Is associative i.e. 2 x (3 x 5) = (2 x 3) x 5

  17. Division CHILDREN NEED TO UNDERSTAND THE CONCEPT OF DIVISION, THAT IT IS: REPEATED SUBTRACTION, GROUPING or SHARING THEY ALSO NEED TO UNDERSTAND AND WORK WITH CERTAIN PRINCIPLES: INVERSE OF MULTIPLICATION IS NOT COMMUTATIVE I.E. 15 ÷3 ≠ 3 ÷ 15 IS NOT ASSOCIATIVE I.E. 30 ÷ (5 ÷ 2) ≠ (30 ÷ 5) ÷ 2

  18. Short division Recall of multiplication tables helps make this method more efficient.

  19. 345 ÷ 3 = 1 1 5 1 3 3 4 5

  20. KS2 SATs Questions • Multistep problems • Calculations often in a money context • Questions presented in varied ways • Addition of fractions in a shape context • Questions requiring ‘all possibilities’ • Questions involving working backwards • Number of fractions questions on arithmetic paper

  21. Some children go camping. It costs £2.20 for each child to camp each night. They go for 6 nights. How much will each child have to pay for the 6 nights? 2 marks

  22. Draw the reflection of this shape.

  23. Key Messages Standard written methods are expected to be used for all four operations The individual steps within the progression are important in scaffolding children’s understanding and should not be rushed through. Practical equipment, models and images are crucial in supporting children’s understanding. Secure knowledge and recall of times tables is essential!

  24. Support daily lessons by ensuring pupils complete their homework • Discuss maths generally and encourage children to do maths at home • Look for examples of maths in everyday life and while you are out and about – mental arithmetic • Short, sharp bursts are ideal!

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