1. What is great teaching and how to get it
‘Developing primary teachers’ maths skills… educating not training - a sample of the Primary Maths Programmes funded by the London Schools Excellence Fund
Ruth Williams, Lampton School’
Ruth Williams SLE

2. What is number sense?

3. What is number sense?
The term "number sense" is a relatively new one in mathematics education. It is difficult to define precisely, but broadly speaking, it refers to "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996).

4. 1. Dot arrangement
Consider each of the following arrangements of dots. What mental strategies are likely to be prompted by each card? What order would you place them in according to level of difficulty?

5. 2. My Numbers
Number of miles on my odometer Number of sisters I have How old my car is Number of cats I’d like to have My door number Number of years I lived in my house

6. Arithmetic Proficiency
Arithmetic Proficiency: achieving fluency in calculating with understanding
An appreciation of number and number operations, which enables mental calculations and written procedures to be performed efficiently, fluently and accurately.

7. Arithmetic Proficiency
Arithmetic Proficiency: achieving fluency in calculating with understanding
Public perceptions of arithmetic often relate to the ability to calculate quickly and accurately – to add, subtract, multiply and divide, both mentally and using traditional written methods.
But arithmetic taught well gives children so much more than this. Understanding about number, its structures and relationships, underpins progression from counting in nursery rhymes to calculating with and reasoning about numbers of all sizes, to working with measures, and establishing the foundations for algebraic thinking.
Ofsted report – Good practice in primary mathematics

8. Developing mathematical skills
MISCONCEPTIONS
INCREASED TEACHER CONFIDENCE
STRATEGIES
RESOURCES
INCREASED MOTIVATION AND ENGAGEMENT
PROBLEM SOLVING
IMPROVED PRACTICE
RESILIENCE & PERSEVERANCE
IMPROVED PUPIL OUTCOMES

9. Mathematics in action How would you do 672 – 364?
How would you expect to see it being taught?
Would you expect to see the same strategy every time?
© columinate 2013

10. Conceptual Understanding
Mathematics in action
How would you do 672 – 364?
How would you expect to see it being taught?
Would you expect to see the same strategy every time?
BALANCE
Procedural Fluency
Conceptual Understanding
INTEGRATION
© columinate 2013

11. Developing mathematical skills
NUMBER SENSE AND SKILLS
FLUENCY
STRATEGIES
TYPICALLY SUCCESSFUL MATHEMATICIAN
CONCEPTUAL UNDERSTANDING

12. Mathematics in action
672 – 364 what next?
© columinate 2013

13. Mathematics in action 672 – 364 what next?
How would you extend the more able?
© columinate 2013

14. Mathematics in action 672 – 364 what next?
How would you extend the more able?
How can you deepen understanding rather than just increasing procedural fluency?
© columinate 2013

15. Mathematics in action 672 – 364 what next?
How would you extend the more able?
How can you deepen understanding rather than just increasing procedural fluency?
What about estimation and justification?
© columinate 2013

16. Mathematics in action What about estimation and justification?
Improving teaching and learning by deepening understanding
© columinate 2013

17. What is great teaching and how to get it
Situations seen:
Theme of lesson: Calculate squares, cubes and roots
Extending the most able: Use the 6 laws of indices
Ruth Williams SLE

18. What is great teaching and how to get it
Ruth Williams SLE

19. Final Thought:
“Asking a student to understand something means asking a teacher to assess whether the student has understood it.
But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.”