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‘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’

Developing primary teachers' maths skills

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Ruth Williams from the Lampton school presents a programme supported by the London Schools Excellence Fund.

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Page 1: Developing primary teachers' maths skills

‘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’

Page 2: Developing primary teachers' maths skills

What is number sense?

Page 3: Developing primary teachers' maths skills

What is number sense?The term "number sense" is a relativelynew 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).

Page 4: Developing primary teachers' maths skills

1. Dot arrangementConsider 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?

Page 5: Developing primary teachers' maths skills

1.5 10 24670

2 327 6

2. My Numbers

Number of miles on my odometerNumber of sisters I haveHow old my car isNumber of cats I’d like to haveMy door numberNumber of years I lived in my house

Page 6: Developing primary teachers' maths skills

Arithmetic ProficiencyArithmetic 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.

Page 7: Developing primary teachers' maths skills

Arithmetic ProficiencyArithmetic 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

Page 8: Developing primary teachers' maths skills

Developing mathematical skills

MISCONCEPTIONS

STRATEGIES

RESOURCES

INCREASED TEACHER CONFIDENCE

IMPROVED PRACTICE

IMPROVED PUPIL OUTCOMES

PROBLEM SOLVING

INCREASED MOTIVATION AND ENGAGEMENT

RESILIENCE & PERSEVERANCE

Page 9: Developing primary teachers' maths skills

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?

Page 10: Developing primary teachers' maths skills

Mathematics in action

BALANCE

Procedural Fluency

Conceptual Understanding

INTEGRATION

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?

Page 11: Developing primary teachers' maths skills

Developing mathematical skills

NUMBER SENSE AND SKILLS

FLUENCY

STRATEGIES

CONCEPTUAL UNDERSTANDING

TYPICALLY SUCCESSFUL MATHEMATICIAN

Page 12: Developing primary teachers' maths skills

Mathematics in action

672 – 364 what next?

Page 13: Developing primary teachers' maths skills

Mathematics in action

672 – 364 what next?

How would you extend the more able?

Page 14: Developing primary teachers' maths skills

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?

Page 15: Developing primary teachers' maths skills

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?

Page 16: Developing primary teachers' maths skills

Mathematics in action

What about estimation and justification?

Improving teaching and learning by deepening understanding

Page 17: Developing primary teachers' maths skills

Situations seen:

Theme of lesson: Calculate squares, cubes and roots

Extending the most able: Use the 6 laws of indices

Page 18: Developing primary teachers' maths skills
Page 19: Developing primary teachers' maths skills

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.”